ECareers BB EL Manual XL PDF

8/20/2019 ECareers BB EL Manual XL PDF

http://slidepdf.com/reader/full/ecareers-bb-el-manual-xl-pdf 1/683

Third Edition

Lean Six SigmaBlack Belt

e–Careers Limited



© 2013 e-Careers Limited. All rights are reserved. Individual Copy. Noportion of these materials may be reproduced, transmitted, stored in a

retrieval system or translated into any language in any form or by any means.

Lean Six Sigma Black Belt

An e-Careers Limited Publication

10 Riverside Business ParkStony Common RoadStansted Mountfitchet

Essex. CM24 8PL. United KingdomEmail: [email protected] (UK 0044) (0) 1279 799 444

Third Edition ManualBased on Version 11.0XL Training MaterialsUtilizing SigmaXL Statistical Software


http://slidepdf.com/reader/full/ecareers-bb-el-manual-xl-pdf 3/683LSS Black Belt Manual XL v11 © 2013 e-Careers Limited

Table of Contents

Define Phase

Understanding Six Sigma…………………………..………………………………..….…….… 1

Six Sigma Fundamentals………..………..………………………..………………..……..…. 22

Selecting Projects………………………….……………………………………..……..……… 42

Elements of Waste……………………..…………………………...……………………………64Wrap Up and Action Items……………...………………………………………………….……77

Measure Phase

Welcome to Measure……………………………………………………………….……..….....83

Process Discovery………………………..………………………………………………………86

Six Sigma Statistics…………………..………………….………………………………….….135

Measurement System Analysis…………….………………………………………………....168

Process Capability ………………………...………………………………………… ……….202

Wrap Up and Action Items …………………………………………………………………….223

Analyze PhaseWelcome to Analyze……………………………………………………………………… .…..229

“X” Sifting………………………………….…...………..………………………….……….….232

Inferential Statistics………………………………….………………………..………….…….259

Introduction to Hypothesis Testing……………………………..……….…………………….274

Hypothesis Testing Normal Data Part 1……………………….……………..………………290

Hypothesis Testing Normal Data Part 2 ………………….…………………………….……333

Hypothesis Testing Non-Normal Data Part 1………………………………………….……362

Hypothesis Testing Non-Normal Data Part 2……………………………………………….389

Wrap Up and Action Items ………………………………………..…………………....……..409

Improve Phase

Welcome to Improve…………………………….…………………….…………………...…..415

Process Modeling Regression…………………………………………………..…………….418

Advanced Process Modeling…………………….…………………………………………….436

Designing Experiments………………………….……………………………..………………464

Experimental Methods………………………….………………………………………………479

Full Factorial Experiments………………………..…………………………..……………..…494

Fractional Factorial Experiments………………...…………………….……………….……..524

Wrap Up and Action Items………………………………………………………..……………544

Control Phase

Welcome to Control……………………………………………………………………………550

Advanced Experiments…………………………………………………………………….…..553 Advanced Capability……………………………..……………………………………………..563

Lean Controls……………………………………………………………………………………580

Defect Controls……………………………………………………………………….…………595

Statistical Process Control………………….………………………………………………….607

Six Sigma Control Plans…………………..….…………………………………..……………648

Wrap Up and Action Items………………..….……………………………..……………….…668

Glossary

Page



1

LSS Black Belt Manual XL v11 © 2013 e-Careers Limited

Lean Six Sigma

Black Belt Training

Welcome to the Black Belt Training Course.

This course has been designed to build your knowledge and capability to improve theperformance of processes and subsequently the performance of the business of which you are apart. The focus of the course is process centric. Your role in process performance improvementis to be through the use of the methodologies of Six Sigma, Lean and Process Management.

By taking this course you will have a well rounded and firm grasp of many of the tools of thesemethodologies. We firmly believe this is one of the most effective classes you will ever take and itis our commitment to assure that this is the case.

We begin in the Define Phase with “Understanding Six Sigma”.

Define PhaseUnderstanding Six Sigma



2


Understanding Six Sigma

Overview

Six Sigma Vocabulary

In order to dosomethingdifferently, wemust first learnthe vocabularyand understandthe meaning ofthe variousterms. Pleaseread and be

familiar withthese terms.

DefinitionsHistory

Strategy

Problem Solving

Six Sigma Fundamentals

Selecting Projects

Elements of Waste

Wrap Up & Action Items


The core fundamentalsof this phase areDefinitions, History,Strategy, Problem

Solving and Roles andResponsibilities.

We will examine themeaning of each ofthese and show youhow to apply them.

Roles & Responsibilities



3


Definition of Six Sigma

Six Sigma represents a great deal to a business enterprise. At the basic level it is a processimprovement tool set yet when linked to corporate strategy it becomes an operating philosophy ofgreat assistance to the accomplishment of corporate objectives.

company it creates a standardized way for co-workers to communicate thereby improvingunderstanding. Also, with its commitment to data and specific operating metrics a system isestablished whereby process performance can be tracked in a succinct manner. Should any process

begin yielding out-of-spec performance it is known immediately.


What is Six Sigma…as a Methodology?

As a methodology to befollowed bypractitioners Six Sigmais a standardizedapproach to problemsolving or opportunitygrasping. Following theDMAIC approachthrough a Six Sigmaproject creates aframework wherebyone has the greatestprobability of arriving ata true solution withassociated means ofretaining the gains.

Additionally, with SixSigma broadly basedthroughout the



4


addition to improving profitability, customer and employee satisfaction are also improved.

This pictorial depicts the percentage of data which falls between Standard Deviations within aNormal Distribution. In this specific example, 99.73% of the data points fall within +/- 3 StandardDeviations of the Mean; this is Six Sigma performance.

Those data points at the outer edge of the bell curve represent the greatest variation in our process.They are the ones causing customer dissatisfaction and we want to eliminate them.


What is Six Sigma…as a Philosophy?

As a philosophy ofOperational Excellence, SixSigma has a targetedquality performance level ofno more than 3.4 defectsper million opportunities.

When an output of aprocess operates at thisquality performance, it issaid to be a “Six Sigmaperforming process.” Ittakes a great deal of effortand time to move throughall the processes of acompany. However, thateffort is positively correlatedto the operatingperformance of thecompany.

What is Six Sigma…as a Business Strategy?

Six Sigma is also abusiness strategythat provides newknowledge and

capability toemployees so theycan better organizethe process activityof the business,solve businessproblems and makebetter decisions.Using Six Sigma isnow a common wayto solve business

problems andremove wasteresulting insignificantprofitabilityimprovements. In



5


What is Six Sigma…as a Process Measurement?

Additionally, Six Sigma isa process measurementand managementsystem that enables

employees andcompanies to take aprocess oriented view ofthe entire business.Using the variousconcepts embedded inSix Sigma, keyprocesses are identified,the outputs of theseprocesses are prioritized,the capability is

determined,improvements are made,if necessary, and amanagement structure is

As you can see from this graphic, as the sigma performance level is improved the operatingefficiency improves yielding lower costs for the same output and more customer satisfying productsand services.


What is Six Sigma…as a Benchmark?

put in place to assure the ongoing success of the business.

With key metrics identified for processes a commonality of measurement is established for allprocesses.



6


What is Six Sigma…as a Tool?


Six Sigma has not creatednew tools. It is theappropriate application of thetools that makes all thedifference. This courseteaches the use of thesetools, equips a belt with theknowledge of which shouldbe utilized when and whatthe desired results of theirapplication is expected to be. Additionally, the use of thetools is additive; that is,information garnered fromone leads to the use of

another until such time asthe sought after answers areobtained.

What is Six Sigma…as a Tool?

This is a high level view of the approach used when conducting what is called a “Six SigmaProject”. A Six Sigma project is a specific effort to fix a defined problem. We will be studying thisapproach throughout most of this course.



7


What is Six Sigma…as a Goal?

To give you a better example the concept of the sigma level can be related to hanging fruit. The higherthe fruit, the more challenging it is to obtain. And, the more sophisticated the tools necessary to obtainthem.

History of Six Sigma


Sweet Fruit Design for Six Sigma

Bulk of Fruit Process

Characterizationand Optimization

Low Hanging Fruit Basic Tools of

Problem Solving

Ground Fruit Simplify and

Standardize

1 - 2 Sigma

3 Sigma

3 - 5 Sigma

5+ Sigma

Goal highest level of process performance possible.

• 1984 Bob Galvin of Motorola articulated the first objectives of aProcess Improvement Program

– 10x levels of improvement in service and quality by 1989

–

100x improvement by 1991 –

Six Sigma capability by 1992

– Bill Smith, an engineer from Motorola, is the person credited as the father

of Six Sigma

• 1984 Texas Instruments and ABB Work closely with Motorola to

further develop Six Sigma

And so it begins!..

It continues!..



8


Six Sigma created a realistic and quantifiable goal in terms of its target of 3.4 defects per million

operations. It was also accompanied by a methodology to attain that goal. That methodologywas a problem solving strategy made up of four steps: measure, analyze, improve and control.When GE launched Six Sigma they improved the methodology to include the Define Phase.

History of Six Sigma (cont.)

And, as you may well know, Six Sigma has been embraced worldwide as a powerful and effectiveprocess improvement methodology. Its history continues to be written…


The Phase Approach of Six Sigma

Today the Define Phase is an important aspect to the methodology. Motorola was a mature culturefrom a process perspective and didn’t necessarily have a need for the Define Phase.

Most organizations today DEFINITELY need it to properly approach improvement projects.

As you will learn, properly defining a problem or an opportunity is key to putting you on the righttrack to solve it or take advantage of it.

• 1994 Application experts leave Motorola

• 1995 AlliedSignal begins Six Sigma initiative as directed by Larry

Bossidy

– Captured the interest of Wall Street

•

1995 General Electric, led by Jack Welch, began the most widespread

undertaking of Six Sigma even attempted

• 1997 to Present: Six Sigma spans industries worldwide

Keeps getting better



9


DMAIC Phases Roadmap

This roadmap provides an overview of the DMAIC approach.

Define Phase Deployment


!"#$%&'( *+,-.#/ 0+#1

! " # $ % & ' (

)

* + ' , - . .

0 1 ( - +

2 - 3 & ( -

4 - # . 5 + -

6 ( # 7 8 9 -

: $ % + ' ; -

! ' ( < + ' 7

022#22 3%1-&.&%(4 51 61- &.&%(4 1$" 7#128+#/#$% 3(2%#/2

!"#$%&'( 1$" *+&,+&%&9# 0.. :;2

*+,<#=>&26+,<# !/61?% :;2 @1<# A $ *+,-.#/

!"#$%&'(4 *+&,+&%&9#4 3#.#?% 3,.8%&,$2 5,$%+,. ,+ B.&/&$1%# :;2 51 82&$C *+,-.#/2

!/6.#/#$% 3,.8%&,$2 %, 5 ,$%+,. ,+ B.&/&$1%# :;2 5 182&$C *+,-.#/2

!/6.#/#$% 5 ,$%+,. *.1$ %, B$28+# *+,-.#/ >,#2 D ,% E#%8+$

F#+&'( G&$1$?&1. !/61?%

>#%#+/&$# 066+,6+&1%# *+,H#?% G,?82

B2%&/1%# 5A *I

5 J1+%#+ *+,H#?%

!"#$%&'( *+,-.#/ 0+#1

! " # $ % & ' (

)

* + ' , - . .

0 1 ( - +

2 - 3 & ( -

4 - # . 5 + -

6 ( # 7 8 9 -

: $ % + ' ; -

! ' ( < + ' 7

022#22 3%1-&.&%(4 51 61- &.&%(4 1$" 7#128+#/#$% 3(2%#/2

!"#$%&'( 1$" *+&,+&%&9# 0.. :;2

*+,<#=>&26+,<# !/61?% :;2 @1<# A $ *+,-.#/

!"#$%&'(4 *+&,+&%&9#4 3#.#?% 3,.8%&,$2 5,$%+,. ,+ B.&/&$1%# :;2 51 82&$C *+,-.#/2

!/6.#/#$% 3,.8%&,$2 %, 5 ,$%+,. ,+ B.&/&$1%# :;2 5 182&$C *+,-.#/2

!/6.#/#$% 5 ,$%+,. *.1$ %, B$28+# *+,-.#/ >,#2 D ,% E#%8+$

F#+&'( G&$1$?&1. !/61?%

>#%#+/&$# 066+,6+&1%# *+,H#?% G,?82

B2%&/1%# 5A *I

5 J1+%#+ *+,H#?%

!"#$%&## ( )#&

*&+&,-&.

/ 0-$12 !&+-# )%. * -)3&40+.&5#

( 5&)-& 6$7489&:&+ ;50,&## <)=

>&-&5?$%& @ ==50=5$)-& ;50A&,- B0,"#

C;)5&-0D ;50A&,- >&#$5)E$+$-2F

>&1$%& G ( 4)5-&5 ;50A&,-

C;50E+&? *-)-&?&%-D H EA&,-$:&D ;5$?)52 <&-5$,D *&,0%.)52 <&-5$,F

I#-$?)-& ( H ;J

K&,0??&%. ;50A&,- B0,"#

( 5&)-& L&)?

( 4)5-&5 L&)?

K&).2 105 <&)#"5&

@==50:&.

;50A&,-

B0,"#

/

M

!"#$%&## ( )#&

*&+&,-&.

/ 0-$12 !&+-# )%. * -)3&40+.&5#

( 5&)-& 6$7489&:&+ ;50,&## <)=

>&-&5?$%& @ ==50=5$)-& ;50A&,- B0,"#

C;)5&-0D ;50A&,- >&#$5)E$+$-2F

>&1$%& G ( 4)5-&5 ;50A&,-

C;50E+&? *-)-&?&%-D H EA&,-$:&D ;5$?)52 <&-5$,D *&,0%.)52 <&-5$,F

I#-$?)-& ( H ;J

K&,0??&%. ;50A&,- B0,"#

( 5&)-& L&)?

( 4)5-&5 L&)?

K&).2 105 <&)#"5&

@==50:&.

;50A&,-

B0,"#

//

MM

Here is a more granularlook of the DefinePhase.

This is what you willlater learn to be a Level2 Process Map.



10


Define Phase Deliverables


The Define Phase deliverables listed above are discussed throughout the Define course. By theend of this course, you should understand what would be necessary to provide thesedeliverables in a presentation.

Six Sigma Strategy

Six Sigma places the emphasis on the Process

–

Using a structured, data driven approach centered on the customer Six Sigma can resolvebusiness problems where they are rooted, for example:

!

Month end reports!

Capital expenditure approval!

New hire recruiting

Six Sigma is a Breakthrough Strategy

–

Widened the scope of the definition of quality

!

includes the value and the utility ofthe product/service to both thecompany and the customer.

Success of Six Sigma depends on the extent of

transformation achieved in each of these levels.

Six Sigma as a breakthrough strategy to process improvement. Many people mistakenlyassume that Six Sigma only works in manufacturing type operations. That is categoricallyuntrue. It applies to all aspects of either a product or service based business.

Wherever there are processes, Six Sigma can improve their performance.

Deliverables:

– Charter Benefits Analysis

– Team Members (Team Meeting Attendance)

– Process Map – high level

– Primary Metric

– Secondary Metric(s)

– Lean Opportunities

–

Stakeholder Analysis

– Project Plan

– Issues and Barriers



11


Conventional Strategy


Conventional definitions of quality focused on conformance to standards.

Requirement

or

LSL

Requirement

or

USL

Bad Bad

Target

Good

Requirement

or

LSL

Requirement

or

USL

Bad Bad

Target

Good

Conventional strategy was to create a product or service that met certain specifications.

! Assumed that if products and services were of good quality then theirperformance standards were correct.!

Rework was required to ensure final quality.!

Efforts were overlooked and unquantified (time, money, equipmentusage, etc).

Problem Solving Strategy

!"# %&' ()#* + '), -./ 0#1"'2 ')'/ 3 4'567#7 '.8

! "#$%&'()#$*#+ (-% &%.)(*/#'-*0 1%(2%%# *#$%0%#$%#( 3)&*) 1.%')#$ (-% $%0%#$)#( 3)&*)1.%4

! 5$%#(*67*#+ (-% 3*() . 6%2 *#$%0%#$%#( 3)&*)1.%' (-)( %66%8( (-%$%0%#$)#( 3)&*)1.%4

! 9 0(*:*;*#+ (-% *#$%0%#$%#( 3)&*) 1.%' '/ )' (/ 8/#(&/. /<&$%0%#$)#( 3)&*)1.%='>4

! ?/#*(/&*#+ (-% /0(*:*;%$ *#$%0%#$%#( 3)&*) 1.%='>4

!"# & # 9& # * 9 .3 # : 9 * ; )# 7 1' 2# 75 & -(# 2 # ;# .29 .1 9 .2-.2#;#. 2#. 1 &# )9 1-'.7" -;7<

! @ % $%'8&*1% (-*' 8/#8%0 ( *# (%&:' /6 (-% %A<)(*/#B

! C-*' %A<)(*/# *' ).'/ 8/::/#.7 &%6%&&%$ (/ )' ) (&)#'6%& 6<#8(*/#

Y=f (Xi) Y=f (Xi)!"-7 7 -* ;)3 719 1#7 1"9 1 = -7 9 46.51-'. '4 1"#

> ?7 < @. '1"#& A '&2 7 = -7 2-519 1#2 ( 3 1"# > ?7 <

!"# %&' ()#* + '), -./ 0#1"'2 ')'/ 3 4'567#7 '.8

! "#$%&'()#$*#+ (-% &%.)(*/#'-*0 1%(2%%# *#$%0%#$%#( 3)&*) 1.%')#$ (-% $%0%#$)#( 3)&*)1.%4

! 5$%#(*67*#+ (-% 3*() . 6%2 *#$%0%#$%#( 3)&*)1.%' (-)( %66%8( (-%$%0%#$)#( 3)&*)1.%4

! 9 0(*:*;*#+ (-% *#$%0%#$%#( 3)&*) 1.%' '/ )' (/ 8/#(&/. /<&$%0%#$)#( 3)&*)1.%='>4

! ?/#*(/&*#+ (-% /0(*:*;%$ *#$%0%#$%#( 3)&*) 1.%='>4

!"# & # 9& # * 9 .3 # : 9 * ; )# 7 1' 2# 75 & -(# 2 # ;# .29 .1 9 .2-.2#;#. 2#. 1 &# )9 1-'.7" -;7<

! @ % $%'8&*1% (-*' 8/#8%0 ( *# (%&:' /6 (-% %A<)(*/#B

! C-*' %A<)(*/# *' ).'/ 8/::/#.7 &%6%&&%$ (/ )' ) (&)#'6%& 6<#8(*/#

Y=f (Xi) Y=f (Xi)!"-7 7 -* ;)3 719 1#7 1"9 1 = -7 9 46.51-'. '4 1"#

> ?7 < @. '1"#& A '&2 7 = -7 2-519 1#2 ( 3 1"# > ?7 <

The conventional strategy was to create a product or service that met certain specifications. It wasassumed that if products and services were of good quality, then their performance standards werecorrect irrespective of how they were met.

Using this strategy often required rework to ensure final quality or the rejection and trashing of someproducts and the efforts to accomplish this “inspect in quality” were largely overlooked and un-quantified.

You will see more about this issues when we investigate the Hidden Factory.



12


Problem Solving Strategy (contd)

Y=f(x) is a transfer function tool to determine what input variables (X’s) affect the outputresponses (Y’s). The observed output is a function of the inputs. The difficulty lies in determiningwhich X’s are critical to describe the behavior of the Y’s.

The X’s determine how the Y performs.

In the Measure Phase we will introduce a tool to manage the long list of input variable and theirrelationship to the output responses. It is the X-Y Matrix or Input-Output Matrix.


Y = f(x) is a key concept that you must fully understand and remember. It is a fundamental principleto the Six Sigma methodology. In its simplest form it is called “cause and effect”. In its more robustmathematical form it is called “Y is equal to a function of X”. In the mathematical sense it is datadriven and precise, as you would expect in a Six Sigma approach. Six Sigma will always refer to anoutput or the result as a Y and will always refer to an input that is associated with or creates theoutput as an X.

Another way of saying this is that the output is dependent on the inputs that create it through theblending that occurs from the activities in the process. Since the output is dependent on the inputswe cannot directly control it, we can only monitor it.

Example

! "#$" & '($)** + , '#, -.)* /$, 0*)* 1 ", + ) $'#2#$, . #3& , $2 (4

2") (02&02 /)55)$216

Y=f (Xi) Y=f (Xi)

Crusher Yield

Time to Close

=f ( )

= f ( )Xn

Trial

Balance

Correct

Accounts

Applied

Sub

Accounts

Credit

MemosEntry

Mistakes, , , , ,

Feed

Material

Type

Tool

Wear Lubricant, , , ,Speed

! "#$" & '($)** + , '#, -.)* /$, 0*)* 1 ", + ) $'#2#$, . #3& , $2 (4

2") (02&02 /)55)$216

Y=f (Xi) Y=f (Xi)

Crusher Yield

Time to Close

=f ( )

= f ( )Xn

Trial

Balance

Correct

Accounts

Applied

Sub

Accounts

Credit

MemosEntry

Mistakes, , , , ,

Feed

Material

Type

Tool

Wear Lubricant, , , ,Speed=f ( )

= f ( )Xn

Trial

Balance

Correct

Accounts

Applied

Sub

Accounts

Credit

MemosEntry

Mistakes, , , , ,Trial

Balance

Correct

Accounts

Applied

Sub

Accounts

Credit

MemosEntry

Mistakes, , , , ,

Feed

Material

Type

Tool

Wear Lubricant, , , ,Speed

If we are so good at the X s why are weconstantly testing and inspecting the Y?



13


Y=f(X) Exercise


Exercise:

Consider establishing a Y = f (x) equation for asimple everyday activity such as producing a

cup of espresso. In this case our output or Y isespresso.

Espresso = f ( )X1 , , , ,X2 X3 X4 Xn

Notes



14


Six Sigma Strategy

As you go through the application of DMAIC you will have a goal to find the root causes to theproblem you are solving. Remember that a vital component of problem solving is cause and effectthinking or Y=f(X). To aid you in doing so, you should create a visual model of this goal as a funnel -a funnel that takes in a large number of the “trivial many contributors,” and narrows them to the“vital few contributors” by the time they leave the bottom.

At the top of the funnel you are faced with all possible causes - the “vital few” mixed in with the“trivial many.” When you work an improvement effort or project, you must start with this type ofthinking. You will use various tools and techniques to brainstorm possible causes of performanceproblems and operational issues based on data from the process. In summary, you will be applyingan appropriate set of “analytical methods” and the “Y is a function of X” thinking, to transform datainto the useful knowledge needed to find the solution to the problem. It is a mathematical fact that

80 percent of a problem is related to six or fewer causes, the X’s. In most cases it is between oneand three.

The goal is to find the one to three Critical X’s from the many potential causes when we start animprovement project. In a nutshell, this is how the Six Sigma methodology works.


(X1)

(X7)

(X6)

(X5)(X3)

(X2)

(X4)

(X8)

(X10)

(X9)

We use a variety of Six Sigmatools to help separate the vital

few variables effecting our Y fromthe trivial many.

Some processes contain many,many variables. However, our Y is

not effected equally by all of them.

By focusing on the vital few weinstantly gain leverage.

Archimedes said: Give me a lever big enough andfulcrum on which to place it and I shall move the world.

Archimedes not

shown actual size!



15


Breakthrough Strategy

Six Sigma puts a strong emphasis on the customer because they are the ones assessing our performanceand they respond by either continuing to purchase our products and services or….by NOT!

So, while the customer is the primary concern we must keep in mind the Voice of the Business – how do wemeet the business’s needs so we stay in business? And we must keep in mind the Voice of the Employee -how do we meet employees needs such that they remain employed by our firm and remain inspired andproductive?


! "# % &'( #' )#

* +, %&'(# ')# - + ) . / ) 0 ' ( 1 +

! " #

$ %% #

230+

& ' ( ) * + "

! , - " . /0 , % 1 * 0

& ' ( ) * + "

! , - " . /0 , % 1 * 0 !" #!" #

#"##"#

!" #!" #

#"##"#

!"#$%&' ( "$)*+, .$ %/0 112 0, !1'345 !"#$%

! "# % &'( #' )#

* +, %&'(# ')# - + ) . / ) 0 ' ( 1 +

! " #

$ %% #

230+

& ' ( ) * + "

! , - " . /0 , % 1 * 0

& ' ( ) * + "

! , - " . /0 , % 1 * 0 !" #!" #

#"##"#

!" #!" #

#"##"#

!"#$%&' ( "$)*+, .$ %/0 112 0, !1'345 !"#$%

By utilizing the DMAIC problem solving methodology to identify and optimize the vital few variables wewill realize sustainable breakthrough performance as opposed to incremental improvements or, evenworse, temporary and non-sustainable improvement.

The image above shows how after applying the Six Sigma tools, variation stays within the specificationlimits.

VOC, VOB, VOE

Thefoundation ofSix SigmarequiresFocus on thevoices of theCustomer, theBusiness, andthe Employeewhichprovides:

!

Awareness of the needs that are critical to the quality (CTQ) of our products andservices

!

Identification of the gaps between “what is” and “what should be” !

Identification of the process defects that contribute to the “gap” !

Knowledge of which processes are “most broken” ! Enlightenment as to the unacceptable Costs of Poor Quality (COPQ)

VOC is Customer Driven

VOB is Profit Driven

VOE is Process Driven



16


Six Sigma Roles and Responsibilities

Executive Leadership


There are many roles and responsibilities for successful implementation of Six Sigma.

Yel low e l t s

Green e l t s

lack el t s

M

Yel low e l t s

Green e l t s

lack el t s

M

!

Executive Leadership!

Champion/Process Owner! Master Black Belt!

Black Belt!

Green Belt!

Yellow Belt

Just like a winning sports team, various people who have specific positions or roles have definedresponsibilities. Six Sigma is similar - each person is trained to be able to understand and perform theresponsibilities of their role. The end result is a knowledgeable and well coordinated winning businessteam.

The division of training and skill will be delivered across the organization in such a way as to provide aspecialist: it is based on an assistant structure much as you would find in the medical field between aDoctor, 1st year Intern, Nurse, etc. The following slides discuss these roles in more detail.

In addition to the roles described herein, all other employees are expected to have essential Six Sigmaskills for process improvement and to provide assistance and support for the goals of Six Sigma and thecompany.

Six Sigma has been designed to provide a structure with various skill levels and knowledge for allmembers of the organization. Each group has well defined roles and responsibilities and communicationlinks. When all individuals are actively applying Six Sigma principles, the company operates and performsat a higher level. This leads to increased profitability, and greater employee and customer satisfaction.

Not all Six Sigma deployments are driven from the top by executive leadership. The data is clear,however, that those deployments that are driven by executive management are much more successfulthan those that are not.

!

Makes decision to implement the Six Sigma initiative and develop accountabilitymethod

!

Sets meaningful goals and objectives for the corporation

!

Sets performance expectations for the corporation

!

Ensures continuous improvement in the process

!

Eliminates barriers

The executive leadership owns the vision for the business, they provide sponsorship and setexpectations for the results from Six Sigma. They enable the organization to apply Six Sigma and thenmonitor the progress against expectations.



17


Champion/Process Owner


Champions identify and select the most meaningful projects to work on, they provide guidance tothe Six Sigma Belt and open the doors for the belts to apply the process improvement technologies.

! Own project selection, execution control, implementation and realization

of gains!

Own Project selection

!

Obtain needed project resources and eliminates roadblocks

!

Participate in all project reviews

! Ask good questions…

!

One to three hours per week commitment

Champions are responsible for functional business activities and to provide business deliverables toeither internal or external customers. They are in a position to be able to recognize problem areas ofthe business, define improvement projects, assign projects to appropriate individuals, review projects

and support their completion. They are also responsible for a business roadmap and employeetraining plan to achieve the goals and objectives of Six Sigma within their area of accountability.

Master Black Belt

MBB should be well versed with all aspects of Six Sigma, from technical applications to ProjectManagement. MBBs need to have the ability to influence change and motivate others.

!

Provide advice and counsel to Executive Staff

!

Provide training and support

- In class training- On site mentoring

!

Develop sustainability for the business

!

Facilitate cultural change

A Master Black Belt is a technical expert, a “go to” person for the Six Sigma methodology. MasterBlack Belts mentor Black Belts and Green Belts through their projects and support Champions. Inaddition to applying Six Sigma, Master Black Belts are capable of teaching others in the practicesand tools.

Being a Master Black Belt is a full time position.



18


Black Belt


Black Belts are application experts and work projects within the business. They should be wellversed with The Six Sigma Technologies and have the ability to drive results.

!

Project team leader

! Facilitates DMAIC teams in applying Six Sigmamethods to solve problems

!

Works cross-functionally

! Contributes to the accomplishment of organizationalgoals

! Provides technical support to improvement efforts

lack elts

Green Belt

A Black Belt is a project team leader, working full time to solve problems under the direction of a

Champion, and with technical support from the Master Black Belt. Black Belts work on projectsthat are relatively complex and require significant focus to resolve. Most Black Belts conduct anaverage of 4 to 6 projects a year -- projects that usually have a high financial return for thecompany.

Green Belts are practitioners of Six Sigma Methodology and typically work within their

functional areas or support larger Black Belt Projects.

•

Well versed in the definition & measurement of critical processes

- Creating Process Control Systems

! Typically works project in existing functional area

!

Involved in identifying improvement opportunities

! Involved in continuous improvement efforts

- Applying basic tools and PDCA

! Team members on DMAIC teams

- Supporting projects with process knowledge & datacollection

Green elts

Green Belts are capable of solving problems within their local span of control. Green Belts remain intheir current positions, but apply the concepts and principles of Six Sigma to their job environment.Green Belts usually address less complex problems than Black Belts and perform at least two projectsper year. They may also be a part of a Black Belt’s team, helping to complete the Black Belt project.



19



Yellow Belt

!

Provide support to Black Belts and Green Belts asneeded

!

May be team members on DMAIC teams

- Supporting projects with processknowledge and data collection

Yellow elts

Yellow Belts participate in process management activities. They fully understand the principles of SixSigma and are capable of characterizing processes, solving problems associated with their workresponsibilities and implementing and maintaining the gains from improvements. They apply SixSigma concepts to their work assignments. They may also participate on Green and Black Beltprojects.

The Life of a Six Sigma Belt

Training as a Six Sigma Belt can be one of the most rewarding undertakings of your career andone of the most difficult.

You can expect to experience:

!

Hard work (becoming a Six Sigma Belt is not easy)

! Long hours of training

! Be a change agent for your organization

! Work effectively as a team leader

!

Prepare and present reports on progress

!

Receive mentoring from your Master Black Belt

!

Perform mentoring for your team members!

ACHIEVE RESULTS!

You

re going places



20


Black & Green Belt Certification


To achieve certification, Belts typically must::

! Complete all course work:- Be familiar with tools and their application

- Practice using tools in theoretical situations- Discuss how tools will apply to actual projects

! Demonstrate application of learning to training project:- Use the tools to effect a financially measurableand significant business impact through theirprojects- Show ability to use tools beyond the trainingenvironment

!

Must complete two projects within one year from beginning of training

!

Achieve results and make a difference

!

Submit a final report which documents tool understanding andapplication as well as process changes and financial impact for eachproject

Organizational Behaviors

All players in the Six Sigma process must be willing to step up and act according to the Six Sigmaset of behaviors.

!

Leadership by example: “walk the talk”

!

Encourage and reward individual initiative

! Align incentive systems to support desired behaviors

!

Eliminate functional barriers

! Embrace “systems” thinking

!

Balance standardization with flexibility

Six Sigma is a system of improvement. It develops people skills and capability for the participants. It

consists of proven set of analytical tools, project-management techniques, reporting methods andmanagement methods combined to form a powerful problem-solving and business-improvementmethodology. It solves problems, resulting in increased revenue and profit, and business growth.

The strategy of Six Sigma is a data-driven, structured approach to managing processes, quantifyingproblems, and removing waste by reducing variation and eliminating defects.

The tactics of Six Sigma are the use of process exploration and analysis tools to solve the equationof Y = f(X) and to translate this into a controllable practical solution.

As a performance goal, a Six Sigma process produces less than 3.4 defects per millionopportunities. As a business goal, Six Sigma can achieve 40% or more improvement in the

profitability of a company. It is a philosophy that every process can be improved, at breakthroughlevels.

We ll be

watching



21



At this point, you should be able to:

! Describe the objectives of Six Sigma

!

Describe the relationship between variation and sigma

! Recognize some Six Sigma concepts

!

Recognize the Six Sigma implementation model

! Describe the general roles and responsibilities in Six

Sigma

You have now completed Define Phase – Understanding Six Sigma.

Notes



22


Lean Six Sigma

Black Belt Training

Now we will continue in the Define Phase with the “Six Sigma Fundamentals”.

The output of the Define Phase is a well developed and articulated project. It has been correctly

stated that 50% of the success of a project is dependent on how well the effort has been defined.

There’s that Y=f (X) thinking again.

Define PhaseSix Sigma Fundamentals



23



Overview

What is a Process?

What is a Process? Many people do or conduct a process everyday but do you really think of it as aprocess? Our definition of a process is a repetitive and systematic series of steps or activities whereinputs are modified to achieve a value-added output.

Usually a successful process needs to be well defined and developed.

The core fundamentalsof this phase areProcess Maps, Voice ofthe Customer, Cost of

Poor Quality andProcess Metrics.

We will examine the

meaning of each ofthese and show youhow to apply them.

!"#$% "' ()% *+,("-%.!"#$% "' ()% *+,("-%.

*" ,( "' / "" . 0 +1 2#(3*" ,( "' /" ". 0 +1 2#(3

/ . " $% , , 4 1 5 ,/ . " $% , , 4 1 5 ,

/."$%,, 4%(.#$,/."$%,, 4%(.#$,

6 #7 6 #8 - 1 9 + : ; 1 - % : (1 2,

6%2%$(#:8 /."<%$(,

=2%-%: (, "' > 1 ,(%

?:; %.,(1 :;#:8 6 #7 6 #8 - 1

> .1 5 ?5 @ A $(#": B (%- ,

!"#$% "' ()% *+,("-%.!"#$% "' ()% *+,("-%.

*" ,( "' / "" . 0 +1 2#(3*" ,( "' /" ". 0 +1 2#(3

/ . " $% , , 4 1 5 ,/ . " $% , , 4 1 5 ,

/."$%,, 4%(.#$,/."$%,, 4%(.#$,

6 #7 6 #8 - 1 9 + : ; 1 - % : (1 2,

6%2%$(#:8 /."<%$(,6%2%$(#:8 /."<%$(,

=2%-%: (, "' > 1 ,(%

?:; %.,(1 :;#:8 6 #7 6 #8 - 1

> .1 5 ?5 @ A $(#": B (%- ,> .1 5 ?5 @ A $(#": B (%- ,

! " # " % &' % ( ) * +', , -* +. , /

! "# %& '() *)+&,-.()+ /#% ()+ %/0 %#,1 2&.- +#)&

! 3# '/( ,('.&,45& '*-.#6&, 7 -*8894&, ,&9(.4#)-/48-

! 3# 6()(2 & :#, 6(;46*6 '*-.#6&, -(.4-:('.4#) %/49& *.4945 4)2

64)46*6 ,&-#*,'&-

! 3# -&& ./& 8,#'&-- :,#6 -.(,. .# :4)4-/ (- 4. 4- !"##$%&'( <&4)2

8&,:#,6&+

! =9( 6& ./& 8,#'&--> %)& ./& 8&#89&

8,#'?&-- @8,#-! &-A !" ! B )'('010 1&' %23 ,#,0'4%01+ -&,4&-

#: ,0'(, *) % +01&101', %/&,& 12(.0, (,& 6#+4:4&+ .# ('/4&C&

( C(9*&D(++&+ *.0(.0

8,#'?&-- @8,#-! &-A !" ! B )'('010 1&' %23 ,#,0'4%01+ -&,4&-

#: ,0'( , * ) % +01&101', %/&,& 12(.0, (,& 6#+4:4&+ .# ('/4&C&

( C(9*&D(++&+ *.0(.0

! " # " % &' % ( ) * +', , -* +. , /

! "# %& '() *)+&,-.()+ /#% ()+ %/0 %#,1 2&.- +#)&

! 3# '/( ,('.&,45& '*-.#6&, 7 -*8894&, ,&9(.4#)-/48-

! 3# 6()(2 & :#, 6(;46*6 '*-.#6&, -(.4-:('.4#) %/49& *.4945 4)2

64)46*6 ,&-#*,'&-

! 3# -&& ./& 8,#'&-- :,#6 -.(,. .# :4)4-/ (- 4. 4- !"##$%&'( <&4)2

8&,:#,6&+

! =9( 6& ./& 8,#'&--> %)& ./& 8&#89&

8,#'?&-- @8,#-! &-A !" ! B )'('010 1&' %23 ,#,0'4%01+ -&,4&-

#: ,0'(, *) % +01&101', %/&,& 12(.0, (,& 6#+4:4&+ .# ('/4&C&

( C(9*&D(++&+ *.0(.0

8,#'?&-- @8,#-! &-A !" ! B )'('010 1&' %23 ,#,0'4%01+ -&,4&-

#: ,0'( , * ) % +01&101', %/&,& 12(.0, (,& 6#+4:4&+ .# ('/4&C&

( C(9*&D(++&+ *.0(.0



24


Examples of Processes

Process Maps

until you have adequately mapped the process.

There are many reasons for creating a Process Map:- It helps all process members understand their part in the process and how their process fits into thebigger picture.

- It describes how activities are performed and how the work effort flows, it is a visual way of standingabove the process and watching how work is done. In fact, Process Maps can be easily uploaded intomodel and simulation software allowing you to simulate the process and visually see how it works.- It can be used as an aid in training new people.- It will show you where you can take measurements that will help you to run the process better.- It will help you understand where problems occur and what some of the causes may be.- It leverages other analytical tools by providing a source of data and inputs into these tools.- It identifies many important characteristics you will need as you strive to make improvements.

The individual processes are linked together to see the total effort and flow for meeting business andcustomer needs. In order to improve or to correctly manage a process, you must be able to describe itin a way that can be easily understood. Process Mapping is the most important and powerful tool you

will use to improve the effectiveness and efficiency of a process.


We go thru processes everyday. Below are some examples of processes. Can you think

of other processes within your daily environment?

!

Injection molding

! Decanting solutions

! Filling vial/bottles

!

Crushing ore

!

Refining oil

! Turning screws

!

Building custom homes

!

Paving roads

!

Changing a tire

!

Recruiting staff

!

Processing invoices

! Conducting research

! Opening accounts

!

Reconciling accounts

!

Filling out a timesheet

!

Distributing mail

!

Backing up files

!

Issuing purchase orders

Process Mapping, also calledflowcharting, is a technique tovisualize the tasks, activities andsteps necessary to produce a productor a service. The preferred method fordescribing a process is to identify itwith a generic name, show theworkflow with a Process Map anddescribe its purpose with anoperational description.

Remember that a process is a

blending of inputs to produce somedesired output. The intent of eachtask, activity and step is to add value,as perceived by the customer, to theproduct or service we are producing.You cannot discover if this is the case

Step AStart

I n s p e c t

FinishStep B Step C Step D

Process Map

Purpose: – Identify the complexity of the process

– Communicate the focus of problem solving

Living documents: – They represent what is currently happening, not what you think is

happening.

– They should be created by the people who are closest to the process



25


Standard symbols for Process Mapping:(available in Microsoft Office™, Visio™, iGrafx™ , SigmaFlow™ and other products)

A RECTANGLE indicates an

activity. Statements withinthe rectangle should begin

with a verb

A DIAMOND signifies a decision point. Only two paths emerge

from a decision point: No and Yes

An ELLIPSE shows the startand end of the process

A PARALLELAGRAM shows

that there are data

An ARROW shows theconnection and direction

of flow

1 A CIRCLE WITH A LETTER OR

NUMBER INSIDE symbolizesthe continuation of aflowchart to another page

Process Map Symbols

At a minimum a highlevel Process Mapmust include; startand stop points, allprocess steps, alldecision points anddirectional flow.

Also be sure toinclude Value

Categories such asValue Added(Customer Focus) andValue Enabling(External Stakeholderfocus).

High Level Process Map

There may be several interpretations of some of the process mapping symbols; however, justabout everyone uses these primary symbols to document processes. As you become morepracticed you will find additional symbols useful, i.e. reports, data storage etc. For now we willstart with just these symbols.




27


Process Map Exercise


Notes



29


What is a Customer?

Value Chain

Every process has adeliverable. Theperson or entity whoreceives this

deliverable is acustomer.

There are twodifferent types ofcustomers; Externaland Internal. Peoplegenerally forget aboutthe Internal customerand they are just asimportant as the

customers who arebuying your product.

The disconnect from Design and Production in some organizations is a good example. IfProduction is not fed the proper information from Design how can Production properly build aproduct?

Every activity (process) must be linked to move from raw materials to a finished product on a storeshelf.


!"#$# &$# '())#$#*+ +,-#. /) 01.+/2#$. 3"(0" '(0+&+#. "/3 3# (*+#$&0+

3(+" +"#2 (* +"# -$/0#..4 (* /$'#$ +/ ('#*+(), 01.+/2#$ &*' .1--5(#$

$#61($#2#*+. 3# 21.+ )($.+ '#)(*# 3"/ +"# 01.+/2#$. &$#7

! " #$ % & ' (

8 9($#0+7 +"/.# 3"/ $#0#(:# +"# /1+-1+ /) ,/1$ .#$:(0#.4 +"#, ;#*#$&55, &$#

+"# ./1$0# /) ,/1$ $#:#*1#

8 <*'($#0+7 +"/.# 3"/ '/ */+ $#0#(:# /$ -& , )/$ +"# /1+-1+ /) ,/1$ .#$:(0#.

=1+ "&:# & :#.+#' (*+#$#.+ (* 3"&+ ,/1 '/ >;/:#$*2#*+ &;#*0(#.?

) & # $ % & ' (

@ +"/.# 3(+"(* ,/1$ /$;&*(A&+(/*

3"/ $#0#(:# +"# /1+-1+ /) ,/1$

3/$B

!"#$# &$# '())#$#*+ +,-#. /) 01.+/2#$. 3"(0" '(0+&+#. "/3 3# (*+#$&0+

3(+" +"#2 (* +"# -$/0#..4 (* /$'#$ +/ ('#*+(), 01.+/2#$ &*' .1--5(#$

$#61($#2#*+. 3# 21.+ )($.+ '#)(*# 3"/ +"# 01.+/2#$. &$#7

! " #$ % & ' (

8 9($#0+7 +"/.# 3"/ $#0#(:# +"# /1+-1+ /) ,/1$ .#$:(0#.4 +"#, ;#*#$&55, &$#

+"# ./1$0# /) ,/1$ $#:#*1#

8 <*'($#0+7 +"/.# 3"/ '/ */+ $#0#(:# /$ -& , )/$ +"# /1+-1+ /) ,/1$ .#$:(0#.

=1+ "&:# & :#.+#' (*+#$#.+ (* 3"&+ ,/1 '/ >;/:#$*2#*+ &;#*0(#.?

) & # $ % & ' (

@ +"/.# 3(+"(* ,/1$ /$;&*(A&+(/*

3"/ $#0#(:# +"# /1+-1+ /) ,/1$

3/$B

The relationship from one process to the next in an organization creates a

Value Chain of suppliers and receivers of process outputs.

Each process has a contribution and accountability to the next to satisfy the

external customer.

External customers needs and requirements are best met when all process

owners work cooperatively in the Value Chain.

Careful –

each move

has many

impacts



30


Step 3Capture VOC

• Review existing performance

• Determine gaps in what you need to know

• Select tools that provide data on gaps

• Collect data on the gaps

Step 2Validate CTQ s

• Translate VOC to CTQs

• Prioritize the CTQs

• Set Specified Requirements

• Confirm CTQs with customer

Step 1Identify Customers

• Listing

• Segmentation

• Prioritization

What is a CTQ?

Example: Making anOnline Purchase

Reliability – Correctamount of money istaken from account

Responsiveness –How long to you waitfor product after theMerchant receivestheir money

Security – is your

sensitive bankinginformation stored insecure place

Developing CTQ s

The steps in developingCTQ’s are identifyingthe customer, capturingthe Voice of theCustomer and finallyvalidating the CTQ’s.




31


Cost of Poor Quality (COPQ)

The Essence of COPQ

You will use the concept of COPQ to quantify the benefits of an improvement effort and also todetermine where you might want to investigate improvement opportunities.


Another important tool fromthis phase is COPQ, Cost ofPoor Quality. COPQ

represents the financialopportunity of your team’simprovement efforts. Thoseopportunities are tied toeither hard or soft savings.

COPQ, is a symptommeasured in loss of profit(financial quantification) thatresults from errors (defects)and other inefficiencies in our processes. This is what weare seeking to eliminate!

! " # $% '()*+ ,+ ,-.(/+01-. 0'( 23-1-431 ) 35*1 40 62 */67)(5+ 4/(10(.

78 .(2(40+9

! " # $% 3+ 1 !" # $ %&# ' -60 1 )* +*,%

: $/6;(40+ 23< .(2(40+ =30' 0'( 3-0(-0 62 35*/6>3-? +85*065+9

! @'( 46-4(*0+ 62 0/1.3036-1) % ,1)308 " 6+0 1/( 0'( 26,-.1036- 26/

" # $% 9

: A<0(/-1)B C-0(/-1)B $/(>(-036-B D**/13+1 )

! D +3?-32341 -0 *6/036- 62 " # $% 2/65 1-8 .(2(40 465(+ 2/65 (22(40+

0'10 1/( .32234,)0 06 E,1-0328 1-. 5,+0 7( (+03510(.9

There are fourelements that make upCOPQ; External Costs,Internal Costs,

Prevention Costs and Appraisal Costs.Internal Costs areopportunities of errorfound in a process thatis within yourorganization. Whereas,External Costs arecosts associated to thefinish productassociated with the

internal and externalcustomer.

Prevention Costs are typically cost associated to product quality, this is viewed as an investment thatcompanies make to ensure product quality. The final element is Appraisal costs, these are tied toproduct inspection and auditing.

This idea was of COPQ was defined by Joseph Juran and is a great point of reference to gain afurther understanding.

Over time and with Six Sigma, COPQ has migrated towards the reduction of waste. Waste is a betterterm, because it includes poor quality and all other costs that are not integral to the product or

service your company provides. Waste does not add value in the eyes of customers, employees orinvestors.

• COPQ stands for Cost of Poor Quality

• As a Six Sigma Belt, one of your tasks will be to estimate COPQ for

your process

•

Through your process exploration and project definition work you will

develop a refined estimate of the COPQ in your project

•

This project COPQ represents the financial opportunity of yourteams improvement effort (VOB)

• Calculating COPQ is iterative and will change as you learn more

about the process

No, not that kind

of cop queue



32


COPQ - Iceberg

COPQ - Categories


!"# $%&

'()*"+,-$(. /%%/ (,0

!"1"+,)

2$), )/4")

2/," 5"4 -6"%0

7(8- (""% - (8 +9/(8" $%5"%)

2$(8 +0+ 4 " ,- :")

7; *"5 -,-(8 +$),)

7; +")) -(6 "(,$%0

< - 5 5 " ( = $ ) ,)

>-) -?4" =$),)

2$), = @),$:"% 2$0 /4 ,0

A$%" B ", C@*)

D- :" 6/4 @" $E :$("0

. $%& -(8 =/* -,/4

/4 4$+/,-$()

7; +"))-6" A/,"%-/4

F %5"%)GH4 /((- (8

!"+$5"

I 4")) $?6-$@)J

!"# $%&

'()*"+,-$(. /%%/ (,0

!"1"+,)

2$), )/4")

2/," 5"4 -6"%0

7(8- (""% - (8 +9/(8" $%5"%)

2$(8 +0+ 4 " ,- :")

7; *"5 -,-(8 +$),)

7; +")) -(6 "(,$%0

< - 5 5 " ( = $ ) ,)

>-) -?4" =$),)

2$), = @),$:"% 2$0 /4 ,0

A$%" B ", C@*)

D- :" 6/4 @" $E :$("0

. $%& -(8 =/* -,/4

/4 4$+/,-$()

7; +"))-6" A/,"%-/4

F %5"%)GH4 /((- (8

!"+$5"

I 4")) $?6-$@)J

Generally speakingCOPQ can beclassified as tangible

(easy to see) andintangible (hard tosee). Visually youcan think of COPQas an iceberg. Mostof the iceberg isbelow the waterwhere you cannotsee it.

Similarly the tangiblequality costs arecosts theorganization israther conscious of,may be measuring already or could easily be measured. The COPQ metric is reported as a percent ofsales revenue. For example tangible costs like inspection, rework, warranty, etc can cost anorganization in the range of 4 percent to 10 percent of every sales dollar it receives. If a companymakes a billion dollars in revenue, this means there are tangible wastes between 40 and 100 milliondollars.

Even worse are the intangible Costs of Poor Quality. These are typically 20 to 35% of sales. If youaverage the intangible and tangible costs together, it is not uncommon for a company to be spending

25% of their revenue on COPQ or waste.

External COPQ

• Warranty

•

Customer Complaint RelatedTravel

•

Customer Charge Back Costs

•

Etc!

Prevention

•

Error Proofing Devices

•

Supplier Certification

•

Design for Six Sigma

• Etc!

Detection

•

Supplier Audits

•

Sorting Incoming Parts

•

Repaired Material

•

Etc!

Internal COPQ

•

Quality Control

Department•

Inspection

•

Quarantined Inventory

•

Etc!



33


COPQ and Lean


!"#$ &$'"() (*+"

," -" $ &."/ "$'+ 01 2 #+ '" !

u " #$$%&'(#)

u *$#&%++(),

u " #)-%./)&%

u 0#'(#)

u 1 /('(),

u 2 -%$3$#45&'(#)

u 6)-%)'#$.

2 #+ '" 3 0"+ $0 ' #3 34 +56 '(#7' 0( 0'8"(9 *+" / 03 *1: '8"

'8(0 5; 8) 5' *$ # 9 #: '8# ' *+ ) "(7"*-" 3 6: '8" 75+ '0/ "( '0

# 3 3 - # . 5 "<

7 6) +#9% &/+%+: ;/+'% !"# <%)%&%++/$.: <5' +=#5>4 <%$%&#,)(?%4 /)4 %@3>#$%4A

B 6)+3%&'(#): " #$$%&'(#): 1 /('(),() +5+3%)+%

B C%&(+(#) 4(/9#)4+: <.4%D()('(#): /$% )#)E-/>5% /44%4

7 2 D'%): ;/+'% &/) 3$#-(4%

#33#$'5)('(%+ D#$ /44('(#)/> 4%D%&'+'# #&&5$F

7 1 % ;(>> 4(+&5++ G%/) () 9#$%4%'/(> >/'%$ '=(+ ;%%HF

!"#$ &$'"() (*+"

," -" $ &."/ "$'+ 01 2 #+ '" !

u " #$$%&'(#)

u *$#&%++(),

u " #)-%./)&%

u 0#'(#)

u 1 /('(),

u 2 -%$3$#45&'(#)

u 6)-%)'#$.

2 #+ '" 3 0"+ $0 ' #3 34 +56 '(#7' 0( 0'8"(9 *+" / 03 *1: '8"

'8(0 5; 8) 5' *$ # 9 #: '8# ' *+ ) "(7"*-" 3 6: '8" 75+ '0/ "( '0

# 3 3 - # . 5 "<

7 6) +#9% &/+%+: ;/+'% !"# <%)%&%++/$.: <5' +=#5>4 <%$%&#,)(?%4 /)4 %@3>#$%4A

B 6)+3%&'(#): " #$$%&'(#): 1 /('(),() +5+3%)+%

B C%&(+(#) 4(/9#)4+: <.4%D()('(#): /$% )#)E-/>5% /44%4

7 2 D'%): ;/+'% &/) 3$#-(4%

#33#$'5)('(%+ D#$ /44('(#)/> 4%D%&'+'# #&&5$F

7 1 % ;(>> 4(+&5++ G%/) () 9#$%4%'/(> >/'%$ '=(+ ;%%HF

Implementing Lean fundamentals can also help identify areas of COPQ. Lean will be discussed later.

COPQ and Lean

•

Labor Savings•

Cycle Time Improvements

•

Scrap Reductions

•

Hidden Factory Costs

•

Inventory Carrying Cost

COPQ – Soft Savings

•

Gaining Lost Sales

•

Missed Opportunities

•

Customer Loyalty

•

Strategic Savings

•

Preventing Regulatory Fines

COPQ – Hard Savings

While hard savings are always more desirable because

they are easier to quantify, it is also necessary to think

about soft savings.



34


COPQ Exercise


!" #$%&'# )* +#%,&-# . !"#$%&'( *+,,#$% - . /0

1221,%+$&%&#3 &$ (1+, "&,#*% 4,#45

6 5 7,4&$3%1,8 4 9&3% 1' - . /0 1221,%+$&%&#35

: 5 - 4%#;1,&<# %=# %12 > 31+,*#3 1' - . /0 '1, %=#

'1+, *9433&'&*4%&1$3?

@ !$%#,$49

@ AB%#,$49

@ /,#C#$%&1$

@ D#%#*%&1$

!" #$%&'# )* +#%,&- # . !"#$%&'( *+,,#$% - . /0

1221,%+$&%&#3 &$ (1+, "&,#*% 4,#45

6 5 7,4&$3%1,8 4 9&3% 1' - . /0 1221,%+$&%&#35

: 5 - 4%#;1,&<# %=# %12 > 31+,*#3 1' - . /0 '1, %=#

'1+, *9433&'&*4%&1$3?

@ !$%#,$49

@ AB%#,$49

@ /,#C#$%&1$

@ D#%#*%&1$

Notes

Use Excel file“

Define Templates.xls”

, COPQ Brainstorm



35


The Basic Six Sigma Metrics

The previous slides have been discussing process management and the concepts behind a processperspective. Now we begin to discuss process improvement and the metrics used.

Some of these metrics are:

DPU: defects per unit produced.DPMO: defects per million opportunities, assuming there is more than oneopportunity to fail in a given unit of output.RTY: rolled throughput yield, the probability that any unit will go through a processdefect-free.


Cycle Time Defined

!"#$% '( )* +,- !#.- #$ /-0. 1 '( *' 20 30' 42 +/ '0 /05 $15 +/#'$

#$ /"- -*-1 '( /"- +21/'.-0 '( /"- 30'+-116

! "# %& #'( #%)( *(+,%*(- ./* #'( 0*/-,1# /* #*23&21#%/3 #/ 4/ #'*/,4' #'(

(3#%*( 0*/1(&&5 .*/) 6(4%33%34 #/ (3-

! "# %& 3/# &%)078 #'( 9#/,1' #%)(: /. #'( ;2 7,(<2--(- 0/*#%/3 /. #'( 0*/1(&&

7 "5 / #1 /"- +* + ,- /#.- ' ( /"- 3 0'+-11 * '2 . 5 33 -48

91 /"-0- 5 $* :5 0#5/#'$ #$ /"- +* + ,- /#.-8 7 "* 8

!"#$% '( )* +,- !#.- #$ /-0. 1 '( *' 20 30' 42 +/ '0 /05 $15 +/#'$

#$ /"- -*-1 '( /"- +21/'.-0 '( /"- 30'+-116

! "# %& #'( #%)( *(+,%*(- ./* #'( 0*/-,1# /* #*23&21#%/3 #/ 4/ #'*/,4' #'(

(3#%*( 0*/1(&&5 .*/) 6(4%33%34 #/ (3-

! "# %& 3/# &%)078 #'( 9#/,1' #%)(: /. #'( ;2 7,(<2--(- 0/*#%/3 /. #'( 0*/1(&&

7 "5 / #1 /"- +* + ,- /#.- ' ( /"- 3 0'+-11 * '2 . 5 33 -48

91 /"-0- 5 $* :5 0#5/#'$ #$ /"- +* + ,- /#.-8 7 "* 8

Cycle time includes any wait or queue time for either people or products.



36


!"# !"%&' &()*+,- ./'0)"12 "0,"3",/'4 ,(1(5)- '0, 0+) 6/-) ,(1(5)"3(-

7 8(1(5)- ' 55+/0) 1+9 ' 44 (99+9- +0 ' /0")

: ; /0") &'2 *' 3( &/4)"<4( ,(1(5)-

: ;0 "05+99(5) "03+"5( &'2 *'3( )*( =9+0% ' &+/0) ,/( !"# )*( =9+0%,/( ,')(

7 8(1(5)"3(- -"&<42 54' --"1"(- )*( /0") >' ,

: 8+(-0?) &'))(9 *+= &'02 ,(1(5)- )*(9( '9(

: @*( "03+"5( "- =9+0%A 5'/-(- '9( /0B0+=0

7 ; /0")C

: D- )*( &('-/9( +1 3+4/&( +1 +/)</) 19+& 2+/9 '9(' E

: D- +>-(93' >4( '0, 5+/0)'>4(E D) *'- ' , "-59()( -)'9) '0, -)+< <+"0)E

: D) "- '0 "0,"3",/' 4 &('-/9(&(0) '0, 0+) '0 ' 3(9'% ( +1

&('-/9(&(0)-E

!" # % & '& ()* + , & % & '& ()- . &

!"# !"%&' &()*+,- ./'0)"12 "0,"3",/'4 ,(1(5)- '0, 0+) 6/-) ,(1(5)"3(-

7 8(1(5)- ' 55+/0) 1+9 ' 44 (99+9- +0 ' /0")

: ; /0") &'2 *' 3( &/4)"<4( ,(1(5)-

: ;0 "05+99(5) "03+"5( &'2 *'3( )*( =9+0% ' &+/0) ,/( !"# )*( =9+0%,/( ,')(

7 8(1(5)"3(- -"&<42 54' --"1"(- )*( /0") >' ,

: 8+(-0?) &'))(9 *+= &'02 ,(1(5)- )*(9( '9(

: @*( "03+"5( "- =9+0%A 5'/-(- '9( /0B0+=0

7 ; /0")C

: D- )*( &('-/9( +1 3+4/&( +1 +/)</) 19+& 2+/9 '9(' E

: D- +>-(93' >4( '0, 5+/0)'>4(E D) *'- ' , "-59()( -)'9) '0, -)+< <+"0)E

: D) "- '0 "0,"3",/' 4 &('-/9(&(0) '0, 0+) '0 ' 3(9'% ( +1

&('-/9(&(0)-E

!" # % & '& ()* + , & % & '& ()- . &!" # % & '& ()* + , & % & '& ()- . &

Defects Per Unit (DPU)

DPU or Defects per Unitquantifies individual defectson a unit and not justdefective units. A returnedunit or transaction can bedefective and have morethan one defect.

Defect : A physical count ofall errors on a unit,regardless of the dispositionof the unit.

EXAMPLES: An error in a

Online transaction has

(typed wrong card number,internet failed). In this caseone online transaction had 2defects (DPU=2).

First Time Yield

Traditional metricswhen chosenpoorly can lead theteam in a directionthat is notconsistent with thefocus of thebusiness. Some

of the metrics wemust beconcerned aboutwould be FTY -FIRST TIMEYIELD. It is verypossible to have100% FTY andspend tremendousamounts in excessrepairs and

rework.


A Mobile Computer that has 1 broken video screen, 2 broken keyboard keys and 1 dead battery,

has a total of 4 defects. (DPU=4)

Is a process that produces 1 DPU better or worse than a process that generates 4 DPU? If youassume equal weight on the defects, obviously a process that generates 1 DPU is better; however,cost and severity should be considered. However, the only way you can model or predict a processis to count all the defects.



37


Rolled Throughput Yield

RTY Estimate

Instead of relying on FTY - First Time Yield, a more efficient metric to use is RTY-Rolled ThroughputYield. RTY has a direct correlation (relationship) to Cost of Poor Quality.

In the few organizations where data is readily available, the RTY can be calculated using actual defectdata. The data provided by this calculation would be a binomial distribution since the lowest yieldpossible would be zero.

As depicted here, RTY is the multiplied yield of each subsequent operation throughout a process (X1 *X2 * X3…)

a defect, there are several things that must be held for consideration. While this would seem to be aconstraint, it is appropriate to note that if a process has in excess of 10% defects, there is little need toconcern yourself with the RTY.

In such extreme cases, it would be much more prudent to correct the problem at hand before worryingabout how to calculate yield.


! "# %&#' ()*&#+, &-+(#. -/0 1(#* -0)% 2& -& )034+)02 -(

5&1541&-0 678 +. #(- &9&+1&:10; <0 5&# /(<090) 0.-+%&-0

678 4.+#* & =#(<# >?@ &. 1(#* &. 50)-&+# 5(#2+-+(#. &)0

%0-A

! 7/0 ?(+..(# 2+.-)+:4-+(# * 0#0)&11' /(12. -)40 B() -/0

)&#2(% 2+.-)+:4-+(# (B 20B05-. +# & 4#+- (B C)(245- &#2 +.

-/0 :&.+. B() -/0 0.-+%&-+(#A

D 7/0 :0.- 0.-+%&-0 (B -/0 C)(C()-+(# (B 4#+-. 5(#-&+#+#*

#( 20B05-.; () 678 +.E

678 F 0G2C4678 F 0G2C4

The mathematical constant e is the base of the natural logarithm.

e ! 2.71828 18284 59045 23536 02874 7135

! "# %&#' ()*&#+, &-+(#. -/0 1(#* -0)% 2& -& )034+)02 -(

5&1541&-0 678 +. #(- &9&+1&:10; <0 5&# /(<090) 0.-+%&-0

678 4.+#* & =#(<# >?@ &. 1(#* &. 50)-&+# 5(#2+-+(#. &)0

%0-A

! 7/0 ?(+..(# 2+.-)+:4-+(# * 0#0)&11' /(12. -)40 B() -/0

)&#2(% 2+.-)+:4-+(# (B 20B05-. +# & 4#+- (B C)(245- &#2 +.

-/0 :&.+. B() -/0 0.-+%&-+(#A

D 7/0 :0.- 0.-+%&-0 (B -/0 C)(C()-+(# (B 4#+-. 5(#-&+#+#*

#( 20B05-.; () 678 +.E

678 F 0G2C4678 F 0G2C4

The mathematical constant e is the base of the natural logarithm.

e ! 2.71828 18284 59045 23536 02874 7135

Sadly, in most companies there isnot enough data to calculate RTYin the long term. Installing datacollection practices required toprovide such data would not becost effective. In those instances,it is necessary to utilize aprediction of RTY in the form of e-dpu (e to the negative dpu).

When using the e-dpu equation tocalculate the probability of aproduct or service moving throughthe entire process without



38


Deriving RTY from DPU

Our goal is to predict yield. For process improvement, the “yield” of interest is the ability of aprocess to produce zero defects (r=0). Question: What happens to the Poisson equation when r=0?

Deriving RTY from DPU - Modeling

Probability that an opportunity is a defect = 0.1

Probability that an opportunity is not a defect = 1 - 0.1 = 0.9

Probability that all 10 opportunities are defect-free = 0.910 = 0.34867844


!"# %&'()&*+ ,&-./&01.&(' &- ."# ./1# )(,#+ 2(/ ,#2#3. ,*.*4 01. ."# 5(&--(' &- ."#3('6#'&#'. )(,#+ 2(/ ,#2#3. ,* .*7 !"# 5(&--(' ,(#- * 8 ((, 9(0 ( 2 :/#,&3.&'8;"#' ."# ,#2#3. /*.#- */# +(;7

' < '1)0#/ (2 1'&.-

/ < '1)0#/ (2 :/#,&3.#, ,#2#3.-: < :/(0*0&+&.= (2 * ,#2#3. (331//#'3#

> < ? @ :

Poisson VS Binomial (r=0,n=1)

0%

20%

40%

60%

80%

100%

120%

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Probability of a defect

Y i e l d ( R T Y )

Yield (Binomial)

Yield (Poisson)


0%

20%

40%

60%

80%

100%

120%

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0


Y i e l d ( R T Y )

Yield (Binomial)

Yield (Poisson)

A(/ +(; ,#2#3. /*.#- B: C D7?E4 ."# 5(&--(' *::/(F&)*.#- ."# %&'()&*+ 2*&/+= ;#++7

!"#$%"& '

($"))$#

Probability

of a defect

Yield

(Binomial)

Yield

(Poisson)

% Over

Estimated

0.0 100% 100% 0%

0.1 90% 90% 0%

0.2 80% 82% 2%

0.3 70% 74% 4%

0.4 60% 67% 7%

0.5 50% 61% 11%

0.6 40% 55% 15%

0.7 30% 50% 20%

0.8 20% 45% 25%

0.9 10% 41% 31%

1.0 0% 37% 37%

Probability

of a defect

Yield

(Binomial)

Yield

(Poisson)

% Over

Estimated 0.0 100% 100% 0%

0.1 90% 90% 0%

0.2 80% 82% 2%

0.3 70% 74% 4%

0.4 60% 67% 7%

0.5 50% 61% 11%

0.6 40% 55% 15%

0.7 30% 50% 20%

0.8 20% 45% 25%

0.9 10% 41% 31%

1.0 0% 37% 37%

!"# %&'()&*+ ,&-./&01.&(' &- ."# ./1# )(,#+ 2(/ ,#2#3. ,*.*4 01. ."# 5(&--(' &- ."#3('6#'&#'. )(,#+ 2(/ ,#2#3. ,* .*7 !"# 5(&--(' ,(#- * 8 ((, 9(0 ( 2 :/#,&3.&'8;"#' ."# ,#2#3. /*.#- */# +(;7

' < '1)0#/ (2 1'&.-

/ < '1)0#/ (2 :/#,&3.#, ,#2#3.-: < :/(0*0&+&.= (2 * ,#2#3. (331//#'3#

> < ? @ :


0%

20%

40%

60%

80%

100%

120%

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0


Y i e l d ( R T Y )

Yield (Binomial)

Yield (Poisson)


0%

20%

40%

60%

80%

100%

120%

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0


Y i e l d ( R T Y )

Yield (Binomial)

Yield (Poisson)

A(/ +(; ,#2#3. /*.#- B: C D7?E4 ."# 5(&--(' *::/(F&)*.#- ."# %&'()&*+ 2*&/+= ;#++7

!"#$%"& '

($"))$#

Probability

of a defect

Yield

(Binomial)

Yield

(Poisson)

% Over

Estimated

0.0 100% 100% 0%

0.1 90% 90% 0%

0.2 80% 82% 2%

0.3 70% 74% 4%

0.4 60% 67% 7%

0.5 50% 61% 11%

0.6 40% 55% 15%

0.7 30% 50% 20%

0.8 20% 45% 25%

0.9 10% 41% 31%

1.0 0% 37% 37%

Probability

of a defect

Yield

(Binomial)

Yield

(Poisson)

% Over

Estimated 0.0 100% 100% 0%

0.1 90% 90% 0%

0.2 80% 82% 2%

0.3 70% 74% 4%

0.4 60% 67% 7%

0.5 50% 61% 11%

0.6 40% 55% 15%

0.7 30% 50% 20%

0.8 20% 45% 25%

0.9 10% 41% 31%

1.0 0% 37% 37%

! "#$ &'( )*+& ,'#-* ./#0( &'( 1#22#-+*3

4.&. -., 3.&'($(45

6 78 4(1(9&, #/ ,($0(4

6 78 )*+&, : $#9(,,(4

! ; '.& +, &'( <=>?

! ; '.& +, :$#/./+2+&@ &'.& .*@ 3+0(*

#::#$&)*+&@ -+22 /( . 4(1(9&?

! ; '.& +, &'( :$#/./+2+&@ &'.& .*@ 3+0(*

#::#$&)*+&@ -+22 A B C /( . 4(1(9& +,5

! C'( :$#/./+2+&@ &'.& .22 D8 #::#$&)*+&+(,

#* ,+*32( )*+& -+22 /( 4(1(9&E1$(( +,5

RTY for DPU = 1

0.348

0.352

0.356

0.36

0.364

0.368

10 100 1000 10000 100000 1000000

Chances Per Unit

Y i e l d

RTY for DPU = 1

0.348

0.352

0.356

0.36

0.364

0.368

10 100 1000 10000 100000 1 000000

Chances Per Unit

Y i e l d

!" #$% ' ()#*$+,- ! "#$ &' $"( )&*()&"++, +- ./+,01 &23 # 02&$ 4&$" 5 (/+ ,(-(1$'6

.,$*

/ 00+1 *(,$*2

Opportunities P(defect) P(no defect) RTY (Prob defect free unit)

10 0.1 0.9 0.34867844

100 0.01 0.99 0.366032341

1000 0.001 0.999 0.367695425

10000 0.0001 0.9999 0.367861046

100000 0.00001 0.99999 0.367877602

1000000 0.000001 0.999999 0.367879257

7- 4( (8$(2, $"( 1+21(.$ $+ #2 &2-&2&$( 209:(/+- +..+/$02&$&('; #)) #$ # <=> +- ?@A; 4( 4&))

#../+#1" $"( B#)0( +- A@CDE@

! "#$ &'( )*+& ,'#-* ./#0( &'( 1#22#-+*3

4.&. -., 3.&'($(45

6 78 4(1(9&, #/ ,($0(4

6 78 )*+&, : $#9(,,(4

! ; '.& +, &'( <=>?

! ; '.& +, :$#/./+2+&@ &'.& .*@ 3+0(*

#::#$&)*+&@ -+22 /( . 4(1(9&?

! ; '.& +, &'( :$#/./+2+&@ &'.& .*@ 3+0(*

#::#$&)*+&@ -+22 A B C /( . 4(1(9& +,5

! C'( :$#/./+2+&@ &'.& .22 D8 #::#$&)*+&+(,

#* ,+*32( )*+& -+22 /( 4(1(9&E1$(( +,5

RTY for DPU = 1

0.348

0.352

0.356

0.36

0.364

0.368

10 100 1000 10000 100000 1000000

Chances Per Unit

Y i e l d

RTY for DPU = 1

0.348

0.352

0.356

0.36

0.364

0.368

10 100 1000 10000 100000 1 000000

Chances Per Unit

Y i e l d

!" #$% ' ()#*$+,- ! "#$ &' $"( )&*()&"++, +- ./+,01 &23 # 02&$ 4&$" 5 (/+ ,(-(1$'6

.,$*

/ 00+1 *(,$*2

Opportunities P(defect) P(no defect) RTY (Prob defect free unit)

10 0.1 0.9 0.34867844

100 0.01 0.99 0.366032341

1000 0.001 0.999 0.367695425

10000 0.0001 0.9999 0.367861046

100000 0.00001 0.99999 0.367877602

1000000 0.000001 0.999999 0.367879257

7- 4( (8$(2, $"( 1+21(.$ $+ #2 &2-&2&$( 209:(/+- +..+/$02&$&('; #)) #$ # <=> +- ?@A; 4( 4&))

#../+#1" $"( B#)0( +- A@CDE@

Given aprobability thatany opportunity isa defect = #defects / (# unitsx # opps per unit):

To what value isthe P(0)converging?

Note: Ultimately,this means that

you need theability to track allthe individualdefects whichoccur per unit viayour datacollection system.



39


RTY Prediction — Poisson Model

Six Sigma Metrics – Calculating DPU

The point of this slide is to demonstrate the mathematical model used to predict the probability of anoutcome of interest. It has little practical purpose other than to acquaint the Six Sigma Belt with the mathbehind the tool they are learning and let them understand that there is a logical basis for the equation.

When the number of steps in a process continually increase, we then continue to multiply the yieldfrom each step to find the overall process yield. For the sake of simplicity let’s say we are calculatingthe RTY for a process with 8 steps. Each step in our process has a yield of .98. Again, there will be adirect correlation between the RTY and the dollars spent to correct errors in our process.


! "#$ &'$ ()*+,)-. &+ $#&),-&$ &'$ /0+(-().)&1 +2 - 3)#40$&$ $5$*&67++38 (-39 :'$* #-,/.)*7 20+, - 0$.-&)5$.1 .-07$ /+/;.-&)+*<* = >?< @ / A BC>C

! D '$* 0EB < :$ 4+,/;&$ &'$ /0+(- ().)&1 +2 2)*3)*7 F$0+ 3$2$4&# /$0;*)& 64-..$3 G0+..$3 &'0+;7'/;& 1)$.3H9C

! I'$ &-(.$ &+ &'$ 0)7'& #'+:# &'$ /0+/+0&)+* +2 /0+3;4& :')4' :). .'-5$

J B 3$2$4&# 60E B9

J > 3$2$4& 60E>9 ! "# $ & ' ()*

J K 3$2$4&# 60E K9< $&4L

! D '$*< +* -5$0-7$< :$ '-5$ - /0+4$##< :)&' > 3$2$4& /$0 ;*)&<&'$* :$ #-1 &'$0$ )# - M?CNOP 4'-*4$ +2 2)*3)*7 - ;*)& :)&' F$0+3$2$4&#C I'$0$ )# +*.1 - >CQMP 4'-*4$ +2 2)*3)*7 - ;*)& :)&' R3$2$4&#C

! D '$* 0E> < &')# $S;-&)+* #),/.)2)$# &+T

! I+ /0$3)4& &'$ P +2 ;*)&# :)&' F $0+ 3$2$4& 6)C$C< UIV9T

J 4+;*& &'$ *;,($0 +2 3$2$4&# 2+;*3

J 4+;*& &'$ *;,($0 +2 ;*)&# /0+3 ;4$3

J 4+,/;&$ &'$ 3/; - *3 $*&$0 ) & )* &'$ 3/; $S;- &)+*T

B B CM ? NO

> B CM ? NO

K B C> W MO

M B CB ? >M

R B CB > QMQ B CB B M>

? B CB B BQ

N B CB B B>

W B CB B BB

+ , -+./ )

01, 23 + # 4 1 , 2

+5

! "#$ &'$ ()*+,)-. &+ $#&),-&$ &'$ /0+(-().)&1 +2 - 3)#40$&$ $5$*&67++38 (-39 :'$* #-,/.)*7 20+, - 0$.-&)5$.1 .-07$ /+/;.-&)+*<* = >?< @ / A BC>C

! D '$* 0EB < :$ 4+,/;&$ &'$ /0+(- ().)&1 +2 2)*3)*7 F$0+ 3$2$4&# /$0;*)& 64-..$3 G0+..$3 &'0+;7'/;& 1)$.3H9C

! I'$ &-(.$ &+ &'$ 0)7'& #'+:# &'$ /0+/+0&)+* +2 /0+3;4& :')4' :). .'-5$

J B 3$2$4&# 60E B9

J > 3$2$4& 60E>9 ! "# $ & ' ()*

J K 3$2$4&# 60E K9< $&4L

! D '$*< +* -5$0-7$< :$ '-5$ - /0+4$##< :)&' > 3$2$4& /$0 ;*)&<&'$* :$ #-1 &'$0$ )# - M?CNOP 4'-*4$ +2 2)*3)*7 - ;*)& :)&' F$0+3$2$4&#C I'$0$ )# +*.1 - >CQMP 4'-*4$ +2 2)*3)*7 - ;*)& :)&' R3$2$4&#C

! D '$* 0E> < &')# $S;-&)+* #),/.)2)$# &+T

! I+ /0$3)4& &'$ P +2 ;*)&# :)&' F $0+ 3$2$4& 6)C$C< UIV9T

J 4+;*& &'$ *;,($0 +2 3$2$4&# 2+;*3

J 4+;*& &'$ *;,($0 +2 ;*)&# /0+3 ;4$3

J 4+,/;&$ &'$ 3/; - *3 $*&$0 ) & )* &'$ 3/; $S;- &)+*T

B B CM ? NO

> B CM ? NO

K B C> W MO

M B CB ? >M

R B CB > QMQ B CB B M>

? B CB B BQ

N B CB B B>

W B CB B BB

+ , -+./ )

01, 23 + # 4 1 , 2

+5/ )

01, 23 + # 4 1 , 2

+5

!"# %&' ()* + ,-.#/ )0#*+1-)/ 2+/ 3# 2+4254+1#6 37 6-.-6-/, 1"# /583#* )(

6#(#219 ()5/6 -/ 1"# )0#*+1-)/ 37 1"# /583#* )( 5/-19 #/1#*-/, 1"# )0#*+1-)/+4

91#0:

;( 1"# 0*)2#99 "+6 )/47 < 0*)2#99 91#09 =-1" 1"# 9+8# 7-#46 1"# 0*)2#99

>!? =)546 3#@ A:BC D A :BC D A:B C D A:BC D A:BC E A:BA FBG H )* BA :FBI: J-/2# )5*

8#1*-2 )( 0*-8+*7 2)/2#*/ -9 1"# K L &M )( 1"-9 0*)2#99N =# 2+ / 9+ 7 1"+1 -/ 4#99 1"+/ B I )(

1"# 1-8# =# =-44 3# 90#/6-/, 6)44+*9 -/ #O2#99 )( 1"# 0*#P6#1#*8-/#6 91+/6+*6 )* .+45#

+66#6 +8)5/1 1) ="-2" 1"-9 0*)2#99 -9 #/1-14#6:

!"#$% & ' ( )

* + , % ' & .

! "#.% & ' ( )

* + , % ' & .

! "#/% & ' ( )

* + , % ' & .

! "#0% & ' ( )

* + , % ' & .

! "#1

% & ' ( )

* + , % ' & .

! "# "2 "% & ' ( &

0

* + ,"2 "

% '$

! "# "2 "% & ' ( &

0

* + , "2 " % '$

$ & & + 3 4 56 7 , 8 9 5

. *:;:<56 8*:=58 ;8:* 3 =* <>44:<5:*

* + , % & ' & .

? > ! "# ;> 4 5@ 86 6 5: + A > , 9 * 7 : : B ' & . C '( ) & $ ( ( D > 4 ( ) ' & . E '

! "#$% '() * + ,- +# .$ ,- /#01/ 0$2 345"++ 3 15"4$++ 6

7 8 9 * + 35 $ 322 $ 2 34 5 " + + 3 15 " 4 $ + + :

!"# %&' ()* + ,-.#/ )0#*+1-)/ 2+/ 3# 2+4254+1#6 37 6-.-6-/, 1"# /583#* )(

6#(#219 ()5/6 -/ 1"# )0#*+1-)/ 37 1"# /583#* )( 5/-19 #/1#*-/, 1"# )0#*+1-)/+4

91#0:

;( 1"# 0*)2#99 "+6 )/47 < 0*)2#99 91#09 =-1" 1"# 9+8# 7-#46 1"# 0*)2#99

>!? =)546 3#@ A:BC D A :BC D A:B C D A:BC D A:BC E A:BA FBG H )* BA :FBI: J-/2# )5*

8#1*-2 )( 0*-8+*7 2)/2#*/ -9 1"# K L &M )( 1"-9 0*)2#99N =# 2+ / 9+ 7 1"+1 -/ 4#99 1"+/ B I )(

1"# 1-8# =# =-44 3# 90#/6-/, 6)44+*9 -/ #O2#99 )( 1"# 0*#P6#1#*8-/#6 91+/6+*6 )* .+45#

+66#6 +8)5/1 1) ="-2" 1"-9 0*)2#99 -9 #/1-14#6:

!"#$% & ' ( )

* + , % ' & .

! "#.% & ' ( )

* + , % ' & .

! "#/% & ' ( )

* + , % ' & .

! "#0% & ' ( )

* + , % ' & .

! "#1

% & ' ( )

* + , % ' & .

! "# "2 "% & ' ( &

0

* + ,"2 "

% '$

! "# "2 "% & ' ( &

0

* + , "2 " % '$

$ & & + 3 4 56 7 , 8 9 5

. *:;:<56 8*:=58 ;8:* 3 =* <>44:<5:*

* + , % & ' & .

? > ! "# ;> 4 5@ 86 6 5: + A > , 9 * 7 : : B ' & . C '( ) & $ ( ( D > 4 ( ) ' & . E '

! "#$% '() * + ,- +# .$ ,- /#01/ 0$2 345"++ 3 15"4$++ 6

7 8 9 * + 35 $ 322 $ 2 34 5 " + + 3 15 " 4 $ + + :

When r = 1,thisequationsimplifiesto:(dpu)*e-dpu



40


Focusing our Effort – FTY vs. RTY

If we chose only to examine the FTY in our decision making process, it would be difficult to determinethe process and product on which our resources should be focused.

As you have seen, there are many factors behind the final number for FTY. That’s where we need to

look for process improvements.

Focusing our Effort – FTY vs. RTY

Answer Slidequestions.

Now we have a betteridea of:

“What does a defectcost?”

“What product shouldget the focus?”


Assume we are creating two products in ourorganization that use similar processes.

FTY = 80%

FTY = 80%

How do you know what to work on?

Product A

Product B

*None of the data used herein is associated with th e products shown herein. Pictures are no more than illustration to make a point to teach the concep t.

Let

s look at the DPU of each product assuming equal

opportunities and margin!

Product A

Product B

dpu 200 / 100 = 2 dpudpu 100 / 100 = 1 dpu

Now, can you tell which to work on?

The product with the highest DPU? !think again!

More questions to answer -How much more time and/or raw material are required?

How much extra floor space do we need?How much extra staff or hours are required to perform the rework?

How many extra shipments are we paying for from our suppliers?

How much testing have we built in to capture our defects?*None of the data used herein is associated with the products shown herein. Pictures are no more than illustration to make a point to teach the concept.



41



You have now completed Define Phase – Six Sigma Fundamentals.


! Describe what is meant by “Process Focus”

!

Generate a Process Map

!

Describe the importance of VOC, VOB and VOE, and CTQ’s

! Explain COPQ

! Describe the Basic Six Sigma metrics

! Explain the difference between FTY and RTY

! Explain how to calculate “Defects per Unit” (DPU)

Notes



42


Lean Six Sigma

Black Belt Training

Now we will continue in the Define Phase with the“Selecting Projects

”.

Define PhaseSelecting Projects



43


Selecting Projects

Overview

Approaches to Project Selection

organization. Furthermore in an organization that does not have an intelligent problem-solvingmethodology in-place, such as Six Sigma, Lean or even TQM, what follows the project selection processbrainstorm is ANOTHER brainstorming session focused on coming up with ideas on how to SOLVE theseproblems.

Although brainstorming itself can be very structured it falls far short of being a systematic means ofidentifying projects that will reduce cost of poor quality throughout the organization. Why…for severalreasons. One, it does not ensure that we are dealing with the most important high-impact problems, butrather what happens to be the recent fire fight initiatives. Two, usually brainstorming does not utilize adata based approach, it relies on tribal knowledge, experience and what people THINK is happening. Aswe know what people THINK is happening and what is ACTUALLY happening can be two very different

things.

In this module we are going to learn about establishing a structured approach for Project Selection.

The core fundamentals of thisphase are Selecting Projects,Refining and Defining andFinancial Evaluation.

The output of the Define Phaseis a well developed andarticulated project. It has beencorrectly stated that 50% of thesuccess of a project isdependent on how well theeffort has been defined.

!"#"$%&'( *+,-"$%.!"#"$%&'( *+,-"$%.

/"0&'&'( 1 2"0&'&'(/"0&'&'( 1 2"0&'&'(

3&'4'$&4 # 564 #74%&,'3&'4'$&4 # 564#74%&,'

!"# ! "% & ' ()*+' & ,*-' ./

!,.,0-"*% 1234,0-/

5.,& ,*-/ 3 6 7 ' /-,

8*+ ,2/-' *+ "*% !"# !"% & '

7 2' 9 89 : ; 0-"3* <-,& /

!"#"$%&'( *+,-"$%.!"#"$%&'( *+,-"$%.

/"0&'&'( 1 2"0&'&'(/"0&'&'( 1 2"0&'&'(

3&'4'$&4 # 564 #74%&,'3&'4'$&4 # 564#74%&,'

!"# ! "% & ' ()*+' & ,*-' ./

!,.,0-"*% 1234,0-/!,.,0-"*% 1234,0-/

5.,& ,*-/ 3 6 7 ' /-,

8*+ ,2/-' *+ "*% !"# !"% & '

7 2' 9 89 : ; 0-"3* <-,& /

Here are three approachesfor identifying projects. Doyou know what the bestapproach is?

The most popular process

for generating and selectingprojects is by holding“brainstorming” sessions. Inbrainstorming sessions agroup of people get together,sometimes after pollingprocess owners for what“blatantly obvious” problemsare occurring, and as a teamtry to identify and refine a listof problems that MAY be

causing issues in the



44


Project Selection – Core Components

Project Selection - Governance

Selecting Projects

With every project there must be a minimum of 3 deliverables:

Business CaseProject CharterBenefits Analysis

! "#$%"# '

()*)+),)-

- ./01%$" 234$5677

! 8"649 :

;%< ;%#0/ =6>?

=6"6@%?7 - /1?A46

*/"/#64 $4

B"%? C%"/"5%/> D61

!"#"$%&'

( # ) * + ' % '

! "#$%"#

- ./01%$" 234$5677

! 8"649 :

*/7?64 =>/5E =6>?

;%< ;%# 0/ =6>?,-./"0&

1 2) -& "-

F ' +=A7%"677 B"%?

*60G647

- ./01%$"

234$5677 ! 8"649

!3' %#"''

1 ) ' "

4-"53"#0+

.$ 789) &":"'.3-0"'

:"'8.#' %; *"

,)-&+

! "#$%"# '

()*)+),)-

- ./01%$" 234$5677

! 8"649 :

;%< ;%#0/ =6>?

=6"6@%?7 - /1?A46

*/"/#64 $4

B"%? C%"/"5%/> D61

!"#"$%&'

( # ) * + ' % '

! "#$%"#

- ./01%$" 234$5677

! 8"649 :

*/7?64 =>/5E =6>?

;%< ;%# 0/ =6>?,-./"0&

1 2) -& "-

F ' +=A7%"677 B"%?

*60G647

- ./01%$"

234$5677 ! 8"649

!3' %#"''

1 ) ' "

4-"53"#0+

.$ 789) &":"'.3-0"'

:"'8.#' %; *"

,)-&+



45


Level 1

Level 2

Level 2

Level 2

Level 2

!

EBIT

!

Cycle time

!

Defects

!

Cost

!

Revenue

!

Complaints

!

Compliance

!

Safety

The Starting Point is defined by the Champion or Process Owner with the

Business Case is the output.

– The tree diagram is used to facilitate the process of breaking down the

metric of interest.

A Structured Approach – A Starting Point

Once a metric pointhas been determinedanother importantquestion needs to beasked - What is mymetric a function of?In other words whatare all of the thingsthat affect this metric?

We utilize the TreeDiagram to facilitatethe process ofbreaking down themetric of interest.

A Structured Approach - Snapshot

and yield issues eroding market share? Is the fastest growing division of the business therefurbishing department?

It depends because the motivation for organizations vary so much and all projects should be directlyaligned with the organizations objectives. Answer the question: What metrics are my department notmeeting? What is causing us pain?

Selecting Projects

These are someexamples ofBusiness Metrics orKey Performance

Indicators.

What metric shouldyou focus on…itdepends? What isthe project focus?What are yourorganizationsstrategic goals?

Are Cost of Salespreventing growth?

Are customercomplaintsresulting in lostearnings? Areexcess cycle times

!"# % &'() *##+ ,- . /-0 #* +- 1 * 2*,- 3 4,2-*3 .5# 5#6 #5)7

89) 2*# )) :# 3)9/# )

% #; &#/<-/= 3 *4# '*+ 243 ,-/) >% &')?@4, 2-*3.5# A#6#5

A#6#5 B

A#6#5 C

A#6#5 C

A#6#5 D

A#6#5 E

@ 4 ,2 62,2# ) & /- 4# )) #)

@ 4 ,2 62,2# ) & /- 4# )) #)

!"# % &'() *##+ ,- . /-0 #* +- 1 * 2*,- 3 4,2-*3 .5# 5#6 #5)7

89) 2*# )) :# 3)9/# )

% #; &#/<-/= 3 *4# '*+ 243 ,-/) >% &')?@4, 2-*3.5# A#6#5

A#6#5 B

A#6#5 C

A#6#5 C

A#6#5 D

A#6#5 E

@ 4 ,2 62,2# ) & /- 4# )) #)

@ 4 ,2 62,2# ) & /- 4# )) #)

A#6#5 B

A#6#5 C

A#6#5 C

A#6#5 D

A#6#5 E

@ 4 ,2 62,2# ) & /- 4# )) #)

@ 4 ,2 62,2# ) & /- 4# )) #)

When creating the tree diagram you will eventually run into activities which are made up ofprocesses. This is where projects will be focused because this is where defects, errors andwaste occur.



46


Primary Business

Measure

BusinessMeasure

BusinessMeasure

BusinessMeasure

BusinessMeasure

Activities Processes

Activities Processes

Unless you can measure it….

You can t do much about it

! " #$ % "& ( ) * #+ , * * - , % * ) ", . " / , & ! , " 0. "$ % + 1,2+3#1% 4." 5/ !26

! "#$%& #( #() *+,-.+/ 0%&,()&& -).&%+) #+ 1234

! 2+,-.+/ 0%&,()&& -).&%+) &5#%67 0). + . 7,+)$8 6,() #9 &,8) :,85 85)#+;. (,<.8,#(& &8+.8); ,$ #0=)$8,>)4

! ?& 85) @ 5.-*,#( (.++#:& ,( #( 85) ;+).8)&8 #**#+8%(,8/ 9#+,-*+#>)-)(8A 85,& *+#>,7)& . $6).+ 9#$%& 9#+ 5#: 85) &%$$)&& :,66 0)-).&%+)74

7,8,9 :

7,8,9 ;

7,8,9 ;

7,8,9 <

7,8,9 =

> 14#8 #4#, * ! ". 1, ** ,*

> 14#8 #4#, * ! ". 1, ** ,*

! " #$ % "& ( ) * #+ , * * - , % * ) ", . " / , & ! , " 0. "$ % + 1,2+3#1% 4." 5/ !26

! "#$%& #( #() *+,-.+/ 0%&,()&& -).&%+) #+ 1234

! 2+,-.+/ 0%&,()&& -).&%+) &5#%67 0). + . 7,+)$8 6,() #9 &,8) :,85 85)#+;. (,<.8,#(& &8+.8); ,$ #0=)$8,>)4

! ?& 85) @ 5.-*,#( (.++#:& ,( #( 85) ;+).8)&8 #**#+8%(,8/ 9#+,-*+#>)-)(8A 85,& *+#>,7)& . $6).+ 9#$%& 9#+ 5#: 85) &%$$)&& :,66 0)-).&%+)74

7,8,9 :

7,8,9 ;

7,8,9 ;

7,8,9 <

7,8,9 =

> 14#8 #4#, * ! ". 1, ** ,*

> 14#8 #4#, * ! ". 1, ** ,*

7,8,9 :

7,8,9 ;

7,8,9 ;

7,8,9 <

7,8,9 =

> 14#8 #4#, * ! ". 1, ** ,*

> 14#8 #4#, * ! ". 1, ** ,*

Business Case Components – Level 1

Be sure to start with higher level metrics, whether they are measured at the Corporate Level,Division Level or Department Level, projects should track to the Metrics of interest within a givenarea. Primary Business Measures or Key Performance Indicators (KPI’s) serve as indicators of thesuccess of a critical objective.

Business Case Components – Business Measures

Post business measures (product/service) of the primary business measure are lower levelmetrics and must focus on the end product to avoid internal optimization at expense of totaloptimization.

Selecting Projects



47


Business Case Components - Activities

Business measures are a function of activities. These activities are usually created or enforced bydirect supervision of functional managers. Activities are usually made up of a series of processes orspecific processes.

Business Case Components - Processes

The processes represent the final stage of the matrix where multiple steps result in the deliveryof some output for the customer. These deliverables are set by the business and customer andare captured within the Voice of the Customer, Voice of the Business or Voice of the Employee.What makes up these process are the X’s that determine the performance of the Y which iswhere the actual breakthrough projects should be focused.

Selecting Projects

! # ! $% & ' % ( ' % ) * % + ,

! "# $ %&& ()"*&+#,*- . ! /$ %&&"0 1 2)3%#*3"0 ()"*&+#,*-"4 5- 6

7&%89 7*5 :)"#,-; . ! /<2)8,=,8%#,*-"0 <,>+&%#,*-0 ?-;,-))3,-; 4 % +,

-. /0 1. 2 34 5 /+65 5

7615 4 . 6

345/+655

7615 4 . 6

345/+655

7615 4 . 6

345/+655

7615 4 . 6

345/+655

7615 4 . 6

8 9:/; /:/6 5 - .< 96 55 65

8 9:/; /:/6 5 - .< 96 55 65

! # ! $% & ' % ( ' % ) * % + ,

! "# $ %&& ()"*&+#,*- . ! /$ %&&"0 1 2)3%#*3"0 ()"*&+#,*-"4 5- 6

7&%89 7*5 :)"#,-; . ! /<2)8,=,8%#,*-"0 <,>+&%#,*-0 ?-;,-))3,-; 4 % +,

-. /0 1. 2 34 5 /+65 5

7615 4 . 6

345/+655

7615 4 . 6

345/+655

7615 4 . 6

345/+655

7615 4 . 6

345/+655

7615 4 . 6

8 9:/; /:/6 5 - .< 96 55 65

8 9:/; /:/6 5 - .< 96 55 65

-. /0 1. 2 34 5 /+65 5

7615 4 . 6

345/+655

7615 4 . 6

345/+655

7615 4 . 6

345/+655

7615 4 . 6

345/+655

7615 4 . 6

8 9:/; /:/6 5 - .< 96 55 65

8 9:/; /:/6 5 - .< 96 55 65

! # ! $% & ' % ( ' % ) * % + ,

!"#$%&'($)# + ! ,- ". / &#'$0"1#2 34(#'()5 / &#'$0"1#2 6"7"8'(9" :1$;&8'#< 4) =

>(0&%?'($) + ! ,6"#(5)2 6?'?2 0$;"%()5< 4 ) =

-. /0 1 . 2 34 5 /+65 5

7615 4 . 6

345/+655

7615 4 . 6

345/+655

7615 4 . 6

345/+655

7615 4 . 6

345/+655

7615 4 . 6

8 9:/; /:/6 5 - .< 96 55 65

8 9:/; /:/6 5 - .< 96 55 65

! # ! $% & ' % ( ' % ) * % + ,

!"#$%&'($)# + ! ,- ". / &#'$0"1#2 34(#'()5 / &#'$0"1#2 6"7"8'(9" :1$;&8'#< 4) =

>(0&%?'($) + ! ,6"#(5)2 6?'?2 0$;"%()5< 4 ) =

-. /0 1 . 2 34 5 /+65 5

7615 4 . 6

345/+655

7615 4 . 6

345/+655

7615 4 . 6

345/+655

7615 4 . 6

345/+655

7615 4 . 6

8 9:/; /:/6 5 - .< 96 55 65

8 9:/; /:/6 5 - .< 96 55 65

-. /0 1 . 2 34 5 /+65 5

7615 4 . 6

345/+655

7615 4 . 6

345/+655

7615 4 . 6

345/+655

7615 4 . 6

345/+655

7615 4 . 6

8 9:/; /:/6 5 - .< 96 55 65

8 9:/; /:/6 5 - .< 96 55 65



48


The components are:

– Output unit (product/service) for external customer

– Primary business measure of output unit for project

– Baseline performance of primary business measure

– Gap in baseline performance of primary business measure from

business objective

Let

s get down to

business

The Business Case communicates the need for the project in

terms of meeting business objectives.

What is a Business Case?

Selecting Projects

The Business Caseis created to ensurethe strategic need

for your project. Itis the first step inproject descriptiondevelopment.

Business Case Example

During FY 2005, the 1st Time Call ResolutionEfficiency for New Customer Hardware Setupwas 89% .

This represents a gap of 8% from the industry

standard of 93% that amounts to US$2,000,000 of annualized cost impact.

As you review this statement remember the following format of what needs to be in a Business Case:WHAT is wrong, WHERE and WHEN is it occurring, what is the BASELINE magnitude at which it isoccurring and what is it COSTING me?

You must take caution to avoid under-writing a Business Case. Your natural tendency is to write toosimplistically because you are already familiar with the problem. You must remember that if you are toenlist support and resources to solve your problem, others will have to understand the context and thesignificance in order to support you.

The Business Case cannot include any speculation about the cause of the problem or what actionswill be taken to solve the problem. It’s important that you don’t attempt to solve the problem or biasthe solution at this stage. The data and the Six Sigma methodology will find the true causes andsolutions to the problem.

The next step is getting project approval.

Here is an example of anBusiness Case. This defines

the problem and providesevidence of the problem.



49


The Business Case Template

Business Case Exercise

You need to make sure that your own Business Case captures the units of pain, the business measures,the performance and the gaps. If this template does not seem to be clicking use your own or just freeform your Business Case ensuring that its well articulated and quantified.

Selecting Projects

!"## "% &'( ) #* %+ , -./ 0 .1 / 2/ .3(4&5

!"#$%& ((((((((((((((((((((((((((((((((((( ) *+, (((((((((((((((((((( -.#

!"#$ %&' &) *%+ # )&$ ,- .#/ %0# 1#$)&$+ -0 2#3 !"$ %+ -$4 ,5 .%0#.. + #- .5$#3

(((((((((((((((((((((((( /0 1 ((((((((((((((((( 2

!6 7 #4 ,5 .%0#.. 1$& 2#..3 !8-.# / %0# 1# $)&$+- 02#3

3+$1 &04 .- ((((((((((((((((((((((((((((

!85.%0#.. &, 9#2*%:# *-$;#* :.< ,- .#/ %0#3

-#.5 ((((((((((((((((((( #,4#,1,%*1 (((((((((((((((((((( .- 6.1* $5406*2

!8 5. %0 # .. & , 9# 2*%: # 3 != & .* %+ 1 - 2 * & ) ; - 1 3

Using the Excel file‘Define Templates.xls

’, Business Case, perform this exercise.



50


What is a Project Charter?

Project Charter - Definitions

Components:

Selecting Projects

The Charter expands on the Business Case, it clarifies the projects focus and measures ofproject performance and is completed by the Six Sigma Belt.

! "#$ &'()*$+

! &'(,$-. /-(0$

! &'(,$-. 1$.'2-3

! &'2+4'5 6 /$-(784'5

! 9 '40#2-4* :230*45 (; &'(,$-. 1$.'2-3

! &'2+4'5 6 /$-(784'5

! /.4784'8 0'(,$-. 27;('+4.2(7

! &'(,$-.< =$*. 6 &'(-$33 > ?7$'

74+$3

! /.4'. 84.$ 6 8$32'$8 @78 84.$

! :2A232(7 (' =B327$33 C72.

! /B00('.27D 143.$' =*4-E =$*.

F1$7.('G

! "$4+ 1$+)$'3

The Project Charter is an important document – it is the initial communication of the project. The firstphases of the Six Sigma methodology are Define and Measure. These are known as“Characterization” phases that focus primarily on understanding and measuring the problem at hand.Therefore some of the information in the Project Charter, such as primary and secondary metrics, canchange several times. By the time the Measure Phase is wrapping up the Project Charter should bein its final form meaning defects and the metrics for measuring them are clear and agreed upon.

As you can see some of the information in the Project Charter is self explanatory, especially the firstsection. We are going to focus on establishing the Problem Statement and determining ObjectiveStatement, scope and the primary and secondary metrics.

! !"#$%&' )*+*&'&,* " #$%&'()*%+, %.+ /* &0 12 %.+ 3+2+'% 1$ +$$1$ &0 %.+

/$1'+,,4

! - $.&/*01& )*+ *&' &,* 5 6%*%+, .17 8('. 12 *0 &8/$19+8+0% &, 3+,&$+3

2$18 %.+ /$1:+'%4

! )/#2& 5 # $%&'()* %+, %.+ ;1(03* $&+, 12 %.+ /$1:+'%4

! !" 0'+ "3 4&*" 0/ 5 <.+ *'%(*) 8+*,($+ 12 %.+ 3+2+'% 1$ +$$1$ &0 %.+ /$1'+,,4

! )&/#,5 + "3 4&*"0/678 5 =+* ,($+, 12 /1%+0%&*) '10,+>(+0'+, ?@ A "B *, *

$+,()% 12 '.*0C+, &0 %.+ /$1'+,,4

! 9:+"*7 5 D $*/.&'* ) 3&,/)*E, 12 %.+ F$&8*$E *03 6+' 103*$E =+%$&', 19+$ *

/+$&13 12 %&8+4



52


Pareto Analysis

The 80:20 Rule Examples

Assisting you in determining what inputs are having the greatest impact on your process is thePareto Analysis approach.

Here are someexamples of the 80:20Rule. Can you think ofany other examples?

! "#$ &' ()* (+,* *-.*/0*0 .1&023*0 4 #$ &' ()* 1*526(5

! 4#$ &' 7&21 .)&/* 38 665 9& (& "#$ &' ()* /8,*5 &/ 7&21 6+5(

! "#$ &' ()* 5(1**(5 )8/06* 4# $ &' ()* (18''+3

! 4#$ &' ()* ,*865 +/ 8 1*5(8218/( 3&,* '1&, "#$ &' ()* ,*/2

! "#$ &' ()* .8.*1 )85 4#$ &' ()* /*:5

! 4#$ &' ()* /*:5 +5 +/ ()* '+15( "#$ &' ()* 81(+36*

! "#$ &' ()* .*&.6* 3825* 4# $ &' ()* .1&;6*,5

! "#$ &' ()* '*8(21*5 &' 8/ 8..6+38(+&/ 81* 25*0 4#$ &' ()* (+,*

Selecting Projects



53


Pareto Chart - Tool

Let’s look at the following example.

By drilling down from the first level wesee that Department J makes upapproximately 60% of the scrap and partZ101 makes up 80% of Dept J’s scrap.

See how we are creating focus andestablishing a line of sight?

You many be eager to jump into trying tofix the problem once you have identifiedit, BE CAREFUL. This is what causesrework and defects in the first place.

Follow the methodology, be patient andyou will eventually be led to a solution.

Selecting Projects

Multi level Pareto Charts are used in a drill down fashion to get to Root Cause of the tallest bar.

The Pareto Charts are often referred to as levels. For instance the first graph is called the first level,the next the second level and so on. Start high and drill down. Let’s look at how we interpret this andwhat it means.



55


Pareto Chart – Example (Cont.)

Selecting Projects

Let’s look at the problem a little differently…

- Using a higher level scope for the first Pareto may help in providing focus.- Create another Pareto as shown below.

This gives a better picture of which product category produces the highest defect count.

Now we’ve got something to work with. Notice the 80% area…. draw a line from the 80%mark across to the cumulative percent line (Red Line) in the graph as shown here.

Which cards create the highest Defect Rates?

Now you are beginning to see what needs work to improve the performance of your project.



56


Pareto Chart – Example (cont.)

Remember to keep focused on finding the biggest bang for the buck.

This does not mean there is NO opportunity for improvements to be had; it simply means nothingobvious is sticking out at this level.

So let’s keep looking.

Selecting Projects



57


Project Charter – Primary Metric

Moving on to the nextelement of the ProjectCharter…, Using theExcel file ‘Define

Templates.xls’,Project Charter,perform the followingexercise:

Since we will benarrowing in on thedefect thru theMeasure Phase it iscommon for thePrimary Metric to

change several timeswhile we struggle tounderstand what ishappening in ourprocess of interest.

Project Charter – Secondary Metrics

Consider a projectfocused on improvingduration of call times(cycle time) in a callcenter. If we realize areduction in call timeyou would want toknow if anything elsewas effected.

Think about it…didovertime increase /reduce, did laborincrease / reduce, whathappened to customersatisfaction ratings?These are all thingsthat should bemeasured in order toaccurately capture thetrue effect of theimprovement.

The Primary Metric also serves as the gauge for when we can claim victory with the project.

SigmaXL® also has a Project Charter template. You can access it through, “SigmaXL>Templatesand Calculators>DMAIC and DFSS Templates>Team/Project Charter ”.

Selecting Projects



59


What is the Financial Evaluation?

The Financial Evaluation establishes the value of the project .

The components are: – Impact• Sustainable

• One-off

– Allocations• Cost Codes / Accounting System

– Forecast

• Cash flow

• Realization schedule

OK, let

s add it up

Benefits Capture - Calculation“

Template”

Standard financial principles should be followed at the beginning and end of the project to provide atrue measure of the improvement’s effect on the organization.

A financial representative of the firm should establish guidelines on how savings will be calculatedthroughout the Six Sigma deployment.

Sustainable Impact “One-Off” Impact

ReducedCosts

IncreasedRevenue

Costs Implemen-

tation Capital

C

O

S

T

C

O

D

E

S

F

O

R

E

C

A

S

T

I

M

P

A

C

T

Realization Schedule

(Cash Flow)

By Period(i.e. Q1,Q2,Q3,Q4)

Sustainable Impact “One-Off” Impact

ReducedCosts

IncreasedRevenue

Costs Implemen-

tation Capital

C

O

S

T

C

O

D

E

S

F

O

R

E

C

A

S

T

I

M

P

A

C

T

Realization Schedule

(Cash Flow)

By Period(i.e. Q1,Q2,Q3,Q4)

! "# $%&% ' ) *+' *', # -./# $.*-01 2'*$*3*4 5 # ) 6% $"%1% # 12% 3$1

1"*+ 47 6 % # 33*+-$%7 8*' 9 . $" .- # -) .52'* &%5 %-$ 2'*:%3$;

!"#$# &$# '() '*+#, )-

./+& 0'1 2 3# 2 -- 4

56,'&73&89#

: ),' : );#, & 99)0& '# '"#

7/+&0' ') '"#&++$)+$7&'# &$#& 73 '"#

<=))>,?

@)$#0&,', & 99)( -)$

+$)+#$ /&3&A#/#3' )-

+$)B#0', &3; $#,)6$0#,

Selecting Projects



60


•

Projects directly impact the Income Statement or Cash Flow

Statement.

• Projects impact the Balance Sheet (working capital).

•

Projects avoid expense or investment due to known or expectedevents in the future (cost avoidance).

•

Projects are risk management, insurance, Safety, Health,Environment and Community related projects which prevent or

reduce severity of unpredictable events.

D

A

B

C

You don

t want to take this one home

Benefits Capture - Basic Guidelines

When calculating project benefits you should follow these steps.

Benefits Capture - Categorization

Here is an example of how to categorize your project’s impact.

Selecting Projects



61


Benefits Calculation Involvement & Responsibility

Benefits Capture - Summary

It is highly recommended that you follow the involvement governance shown here.

Just some recommendations to consider when running your projects or program.

•

Performance tracking for Six Sigma Projects should use the

same discipline that would be used for tracking any other

high-profile projects.

• The A-B-C-D categories can be used to illustrate the impact of

your project or a portfolio

of projects.

•

Establish The Governess Grid for Responsibility &

Involvement.

It

s a wrap

!"#$%&& ( )*%"+ ,-./0#*

1

!"#$%&& ( )*%"

23-$4 2%35+ ,-./0#*

1

!"#$%&& ( )*%"

60*-*$0-3

7%/"%&%*5-508%

60*-*$0-3

7%/"%&%*5-508%

60*-*$0-3

7%/"%&%*5-508%

60*-*$0-3

7%/"%&%*5-508%

! # $ % &' ( ) * + &,-./0-0%&1& +$%23#3(3, 3456$708& 90/08&+$%

!"#$%&& ( )*%"+ ,-./0#*

1

!"#$%&& ( )*%"

23-$4 2%35+ ,-./0#*

1

!"#$%&& ( )*%"

60*-*$0-3

7%/"%&%*5-508%

60*-*$0-3

7%/"%&%*5-508%

60*-*$0-3

7%/"%&%*5-508%

60*-*$0-3

7%/"%&%*5-508%

! # $ % &' ( ) * + &,-./0-0%&1& +$%23#3(3, 3456$708& 90/08&+$%

Selecting Projects



62


Benefits Calculation Template

Selecting Projects

The Benefits Calculation Template facilitates and aligns with the aspects discussed for Project Accounting.

The Excel file ‘Define Templates.xls’, BENEFITS CALCULATION TEMPLATE.



63



You have now completed Define Phase – Selecting Projects.

Selecting Projects

! Understand the various approaches to project selection

!

Articulate the benefits of a “Structured Approach”

!

Refine and Define the business problem into a Project

Charter to display critical aspects of an improvementproject

! Make initial financial impact estimate

Notes



64


Lean Six Sigma

Black Belt Training

Now we will continue in the Define Phase with “Elements of Waste”.

Define PhaseElements of Waste



65


Elements of Waste

Overview

Definition of Lean

The core fundamentalsof this phase are the 7components of wasteand 5S.


! #$% &$ '(')* $ + , - *)(! #$% &$ '(')* $ + , - *)(

. /. /

0'1 (2*)- '1 3'4 /35 / 34 % -

/(6(7)3'4 82$9(7)*

:6(% (' )* $+ , - *)(

/35 / 34 % - ;<'1 - % (')- 6*

, 2- & 0& = > 7)3$' ?)(% *

! #$% &$ '(')* $ + , - *)(! #$% &$ '(')* $ + , - *)(

. /. /

0'1 (2*)- '1 3'4 /35 / 34 % -

/(6(7)3'4 82$9(7)*

:6(% (' )* $+ , - *)(

/35 / 34 % - ;<'1 - % (')- 6*

, 2- & 0& = > 7)3$' ?)(% *

!"#$% '%(#)*)+,# +, -$,#. /% (0# *)#1+,# (0$( $%230#)#

3/)4 +, -#+%5 ./%#6 3$,(# +, -#+%5 5#%#)$(#.7

80# "#$% '%(#)*)+,# ,##4, (/ /)5$%+9 # +(, *)/:#,,#, (/ (0#

/*(+1;1 <#=#<6 (0)/;50 (0# :/%(+%;$< >/:;, /% (0#

+.#%(+>+:$(+/% $%. #<+1+%$(+/% /> 3$,(#7?

! ! " # $ % # $ # ' ( ) # *



66


Lean – History

Lean Six Sigma

time is spent on value-added work, meaning as much as 90% of time is allocated to non value-addedactivities, or waste.

Forms of waste include: Wasted capital (inventory), wasted material (scrap), wasted time (cycle time),wasted human effort (inefficiency, rework) and wasted energy (energy inefficiency). Lean is aprescriptive methodology for relatively fast improvements across a variety of processes, fromadministrative to manufacturing applications. Lean enables your company to identify waste where itexists. It also provides the tools to make improvements on the spot.

The essence of Lean is to

concentrate effort on removingwaste while improving processflow to achieve speed and agilityat lower cost. The focus of Leanis to increase the percentage ofvalue-added work performed bya company. Lean recognizesthat most businesses spend arelatively small portion of theirenergies on the true delivery ofvalue to a customer. While all

companies are busy, it isestimated for some companiesthat as little as 10% of their

Elements of Waste

1885

Craft Production - Machine then harden

- Fit on assembly

- Customization

- Highly skilled workforce

- Low production rates

- High Cost

1955 - 1990

Toyota Production

System - Worker as problem

solver

- Worker as process

owner enabled by:

-- Training

-- Upstream quality

-- Minimal inventory

-- Just-in-time

- Eliminate waste

- Responsive to change

- Low cost

- Improving productivity

- High quality product

1993 -

Lean Enterprise - "Lean" applied to all

functions in enterprise

value stream

- Optimization of value

delivered to all

stakeholders and

enterprises in value chain

- Low cost

- Improving productivity

- High quality product

- Greater value for

stakeholders

1913

Mass Production - Part inter-changeability

- Moving production line

- Production engineering

- "Workers don't like to

think"

- Unskilled labor

- High production rates

- Low cost

- Persistent quality

problems

- Inflexible models

Lean Manufacturing has been going on for a very long time, however the phrase is credited toJames Womac in 1990. A small list of accomplishments are noted in the slide above primarilyfocused on higher volume manufacturing.



67


• Perhaps one of the most criminal employee performance issues in

todays organizations is generated not by a desire to cheat one’s

employer but rather by a lack of regard to waste.

• In every work environment there are multiple opportunities forreducing the non-value added activities that have (over time)

become an ingrained part of the standard operating procedure.

• These non-value added activities have become so ingrained in our

process that they are no longer recognized for what they are,

WASTE.

•

waste (v .) Anything other than the minimum amount of time,

material, people, space, energy, etc needed to add value to the

product or service you are providing.

• The Japanese word for waste is muda.

Get that stuff

outta here

Lean Six Sigma (cont.)

Employees at some level have been de-sensitized to waste:“That

’s what we

’ve always done.

”

Lean brings these opportunities for savings back into focus with specific approaches to findingand eliminating waste.

Project Requirements for Lean

Lean focuses on what calls the Value Stream, the sequence of activities and work required toproduce a product or to provide a service. It is similar to a Linear Process Flow Map, but itcontains its own unique symbols and data. The Lean method is based on understanding how theValue Stream is organized, how work is performed, which work is value added vs. non-value

added and what happens to products and services and information as they flow through the ValueStream. Lean identifies and eliminates the barriers to efficient flow through simple, effective tools.

Lean removes many forms of waste so that Six Sigma can focus on eliminating variability.Variation leads to defects, which is a major source of waste. Six Sigma is a method to makeprocesses more capable through the reduction of variation. Thus the symbiotic relationshipbetween the two methodologies.

Elements of Waste



68


Muda is classified into seven components:

– Overproduction

–

Correction (defects) – Inventory

– Motion

– Overprocessing

– Conveyance

– Waiting

Sometimes additional forms of muda are added:

– Under use of talent

–

Lack of safety

Being Lean means eliminating waste.

Seven Components of Waste

Overproduction

Elements of Waste

Overproduction is producing more than the next step needs or morethan the customer buys.

–

It may be the worst form of waste because it contributes to allthe others.

Waste of Overproduction relates to the excessiveaccumulation of work-in-process (WIP) or finished

goods inventory.

Examples are:

"

Preparing extra reports

"

Reports not acted upon oreven read

"

Multiple copies in data storage

"

Over-ordering materials

"

Duplication of effort/reports

Producing more parts than necessary to satisfy the customer ’s quantity demand thus leading toidle capital invested in inventory.

Producing parts at a rate faster than required such that a work-in-process queue is created –

again, idle capital.



69


Correction

Inventory

Inventory is a drain on an organization’s overhead. The greater the inventory, the higher theoverhead costs become. If quality issues arise and inventory is not minimized, defective materialis hidden in finished goods.

To remain flexible to customer requirements and to control product variation, we must minimizeinventory. Excess inventory masks unacceptable change-over times, excessive downtime,

operator inefficiency and a lack of organizational sense of urgency to produce product.

Elements of Waste

Correcting or repairing a defect in materials or parts adds unnecessary costs because ofadditional equipment and labor expenses. An example is the labor cost of schedulingemployees to work overtime to rework defects.

Correction of defects are as obvious as it sounds.

Eliminate erors

Waste of Correction includes the waste of handling andfixing mistakes. This is common in both manufacturing

and transactional settings.

Examples are:

"

Incorrect data entry

"

Paying the wrong vendor

"

Misspelled words in

communications

"

Making bad product

"

Materials or labor discarded

during production

Inventory is the liability of materials that are bought, invested in and

not immediately sold or used.

Waste of Inventory is identical to overproduction except thatit refers to the waste of acquiring raw material before the

exact moment that it is needed.

Examples are:

"

Transactions not processed

"

Bigger in box”

than outbox

”

"

Over-ordering materials

consumed in-house

"

Over-ordering raw materials

– just in case



71


Conveyance

Waiting

Idle time between operations or events, i.e. an employee waiting for machine cycle to finish or amachine waiting for the operator to load new parts.

Elements of Waste

Conveyance is the unnecessary movement of material and Goods.

– Steps in a process should be located close to each other somovement is minimized.

Waste of Conveyance is the movement of material.

Examples are:

"

Extra steps in the

process

"

Distance traveled

"

Moving paper from

place to place

Waiting is nonproductive time due to lack of material, people, or

equipment.

–

Can be due to slow or broken machines, material not arriving on time,etc.

Waste of Waiting is the cost of an idle resource.

Examples are:

"

Processing once each month

instead of as the work comes in

"

Showing up on time for ameeting that starts late

"

Delayed work due to lack of

communication from another

internal group

Conveyance is incidental, required action that does not directly contribute value to the product.Perhaps it must be moved however, the time and expense incurred does not produce product or service characteristics that customers see.

It’s vital to avoid conveyance unless it is supplying items when and where they are needed (i.e. just-in-time delivery).



72


Waste Identification Exercise

Elements of Waste

!" #$%&'# )* +#%,&-# . !" $%&'($)* +,-(& (.,( "//01- $'

*"01 21"/&--&-3

4 1$(& ,' &5,627& ") &,/. (*2& ") 60%, 8&7"+9

: ; <&121"%0/($"' ===================

: > "11&/($"' ===================

: ?'<&'("1* ===================

: @"($"' ===================

: ; <&121"/&--$'A ===================

: > "'<&*, '/& =================== : 4 ,$($'A ===================

Notes



73


5S – The Basics

The term “5S” derives from the Japanese words for five practices leading to a clean andmanageable work area. The five “S” are:

‘ Seiri' means to separate needed tools, parts and instructions from unneeded materials and toremove the latter.'Seiton' means to neatly arrange and identify parts and tools for ease of use.'Seiso' means to conduct a cleanup campaign.'Seiketsu' means to conduct seiri, seiton and seiso at frequent, indeed daily, intervals to maintain aworkplace in perfect condition.'Shitsuke' means to form the habit of always following the first four S’s.

Simply put, 5S means the workplace is clean, there is a place for everything and everything is in itsplace. The 5S will create a work place that is suitable for and will stimulate high quality and highproductivity work. Additionally it will make the workplace more comfortable and a place of which you

can be proud.Developed in Japan, this method assume no effective and quality job can be done without clean andsafe environment and without behavioral rules.

The 5S approach allows you to set up a well adapted and functional work environment, ruled bysimple yet effective rules. 5S deployment is done in a logical and progressive way. The firstthree S’s are workplace actions, while the last two are sustaining and progress actions.

It is recommended to start implementing 5S in a well chosen pilot workspace or pilot process andspread to the others step by step.

Elements of Waste

5S is a process designed to organize the workplace, keep it neat andclean, maintain standardized conditions, and instill the discipline

required to enable each individual to achieve and maintain a world

class work environment.

Seiri - Put things in order

Seiton - Proper Arrangement

Seiso – Clean

Seiketsu – Purity

Shitsuke - Commitment



74


English Translation

There have been many attempts to force 5 English “S” words to maintain the original intent of 5Sfrom Japanese. Listed below are typical English words used to translate:

1. Sort (Seiri)2. Straighten or Systematically Arrange (Seiton)

3. Shine or Spic and Span (Seiso)4. Standardize (Seiketsu)5. Sustain or Self-Discipline (Shitsuke)

Regardless of which “S” words you use, the intent is clear: Organize the workplace, keep it neatand clean, maintain standardized conditions and instill the discipline required to enable eachindividual to achieve and maintain a world class work environment.

Elements of Waste

5 S

Sort

Identify necessary items andremove unnecessary ones, use

time management

ShineVisual sweep of areas,eliminate dirt, dust andscrap. Make workplace

shine.

Place things in such away that they can be

easily reachedwhenever they are

needed

Straighten

Make 5S strong inhabit. Make

problems appear andsolve them.

Self - Discipline Standardize

Work to standards,

maintain standards,wear safety equipment.



75


5S Exercise

Elements of Waste

!" #$%&'# )* +#%,&-# . . !" $%&'($)* &+&,&'(- ") ./ $'

*"01 2"134+56&7

8 1$(& 5' &95,4+& )"1 &56: ") (:& ./;- <&+"2=

> /"1( ????????????????????

> /(15$@:(&' ????????????????????

> / :$'& ????????????????????

> /(5'%51%$A& ????????????????????

> /&+)BC$-6$4+$'& ????????????????????

Notes



76



You have now completed Define Phase – Elements of Waste.

Elements of Waste

! Describe 5S

!

Identify and describe the 7 Elements of Waste

!

Provide examples of how Lean Principles can affect your area

Notes



77


Lean Six Sigma

Black Belt Training

Now we will conclude the Define Phase with “Wrap Up and Action Items”.

Define PhaseWrap Up and Action Items



78


Wrap Up and Action Items

Define Phase Overview—The Goal

Define Action Items

The goal of the Define Phase is to:

•

Identify a process to improve and develop a specific Six Sigmaproject.

– Six Sigma Belts define critical processes, sub-processes and

elaborate the decision points in those processes.

• Define is the contract phase of the project. We are determining

exactly what we intend to work on and estimating the impact to

the business.

•

At the completion of the Define Phase you should have a

description of the process defect that is creating waste for the

business.

Goooooaaaaalllll!!

At this point you should all understand what is necessaryto complete these action items associated with Define.

–

Charter Benefits Analysis

–

Team Members

– Process Map – high level

– Primary Metric

–

Secondary Metric(s)

– Lean Opportunities

– Stakeholder Analysis

– Project Plan

–

Issues and Barriers Deliver the

Goods



79



Six Sigma Behaviors

Define Phase — The Roadblocks

•

Being tenacious, courageous

•

Being rigorous, disciplined

• Making data-based decisions

• Embracing change & continuous learning

• Sharing best practices

Each player

in the Six Sigma process must be A ROLE MODEL

for the Six Sigma culture.

Walk

the

Walk

Look for the potential roadblocks and plan to address them

before they become problems:

– No historical data exists to support the project.

– Team members do not have the time to collect data.

–

Data presented is the best guess by functional managers.

–

Data is communicated from poor systems.

– The project is scoped too broadly.

–

The team creates the ideal Process Map rather than the asis Process Map.

Clear the road –

I

m comin

through



80



DMAIC Roadmap

Define Phase Deployment

!"#$%&## ( )#&

*&+&,-&.

/ 0-$12 !&+-# )%. * -)3&40+.&5#

( 5&)-& 6$7489&:&+ ;50,&## <)=

>&-&5?$%& @==50=5$)-& ;50A&,- B0,"#

C;)5&-0D ;50A&,- >&#$5)E$+$-2F

>&1$%& G ( 4)5-&5 ;50A&,-

C;50E+&? *-)-&?&%-D H EA&,-$:&D ;5$?)52 <&-5$,D *&,0%.)52 <&-5$,F

I#-$?)-& ( H ;J

K&,0??&%. ;50A&,- B0,"#

( 5&)-& L&)?

( 4)5-&5 L&)?

K&).2 105 <&)#"5&

@==50:&.

;50A&,-

B0,"#

/

M

!"#$%&## ( )#&

*&+&,-&.

/ 0-$12 !&+-# )%. * -)3&40+.&5#

( 5&)-& 6$7489&:&+ ;50,&## <)=

>&-&5?$%& @==50=5$)-& ;50A&,- B0,"#

C;)5&-0D ;50A&,- >&#$5)E$+$-2F

>&1$%& G ( 4)5-&5 ;50A&,-

C;50E+&? *-)-&?&%-D H EA&,-$:&D ;5$?)52 <&-5$,D *&,0%.)52 <&-5$,F

I#-$?)-& ( H ;J

K&,0??&%. ;50A&,- B0,"#

( 5&)-& L&)?

( 4)5-&5 L&)?

K&).2 105 <&)#"5&

@==50:&.

;50A&,-

B0,"#

//

MM

The importance of the DefinePhase is to begin to understandthe problem and formulate itinto a project. Notice that if theRecommended Project Focus isapproved the next step wouldbe team selection.

Identify Problem Area

Assess Stability, Capability, and Measurement Systems

Identify and Prioritize All Xs

Prove/Disprove Impact Xs Have On Problem

Identify, Prioritize, Select Solutions Control or Eliminate Xs Causing Problems

Implement Solutions to Control or Eliminate Xs Causing Problems

Implement Control Plan to Ensure Problem Doesnt Return

Verify Financial Impact

Determine Appropriate Project Focus

Estimate COPQ

Establish Team

C h a m p i o n /

P r o c e s s O w n e r

D e f i n e

M e a s u r e

A n a l y z e

I m p r o v e

C o n t r o l



81


Action Items Support List

These are some additional questions to ensure all the deliverables are achieved.


Define Questions

Step One: Project Selection, Project Definition And Stakeholder Identification

Project Charter

• What is the problem statement? Objective?

• Is the business case developed?

• What is the primary metric?

• What are the secondary metrics?

• Why did you choose these?

• What are the benefits?

• Have the benefits been quantified? It not, when will this be done?

Date:____________________________

• Who is the customer (internal/external)?

• Has the COPQ been identified?

• Has the controller’s office been involved in these calculations?

• Who are the members on your team?

• Does anyone require additional training to be fully effective on the team?

Voice of the Customer (VOC) and SIPOC defined• Voice of the customer identified?

• Key issues with stakeholders identified?

• VOC requirements identified?

• Business Case data gathered, verified and displayed?

Step Two: Process Exploration

Processes Defined and High Level Process Map• Are the critical processes defined and decision points identified?

• Are all the key attributes of the process defined?

• Do you have a high level process map?

• Who was involved in its development?

General Questions

• Are there any issues/barriers that prevent you from completing this phase?

• Do you have adequate resources to complete the project?

• Have you completed your initial Define report out presentation?



83


Lean Six Sigma

Black Belt Training

Now that we have completed Define we are going to jump into the Measure Phase.

Here you enter the world of measurement, where you can discover the ultimate source ofproblem-solving power: data. Process improvement is all about narrowing down to the vital fewfactors that influence the behavior of a system or a process. The only way to do this is tomeasure and observe your process characteristics and your critical-to-quality characteristics.Measurement is generally the most difficult and time-consuming phase in the DMAICmethodology. But if you do it well, and right the first time, you will save your self a lot of troublelater and maximize your chance of improvement.

Welcome to the Measure Phase - will give you a brief look at the topics we are going to cover.

Measure PhaseWelcome to Measure



86


Lean Six Sigma

Black Belt Training

Now we will continue in the Measure Phase with “Process Discovery”.

Measure PhaseProcess Discovery



88


Overview of Brainstorming Techniques

1.

Agree on the category or condition to be considered.2. Encourage each team member to contribute.3.

Discourage debates or criticism, the intent is to generate ideas andnot to qualify them, that will come later.

4.

Contribute in rotation (take turns), or free flow, ensure every memberhas an equal opportunity.

5.

Listen to and respect the ideas of others.6.

Record all ideas generated about the subject.7.

Continue until no more ideas are offered.

8.

Edit the list for clarity and duplicates.

Process Discovery

!"#$%&' #"

)#*+,-,#*

./& 0

./& 123

4)563&37

! )5-&8#",&3"#$%&'#! "%#()&%*%+$ , +-'&.+*%+$

/ %.0!% "#12'+% "%$2.3

./&

!"#$%&'

) 563 & 5*+ 9 ::&;- <,58"5'

!"#$%&' #"

)#*+,-,#*

./& 0

./& 123

4)563&37

! )5-&8#",&3"#$%&'#! "%#()&%*%+$ , +-'&.+*%+$

/ %.0!% "#12'+% "%$2.3

./&

!"#$%&'

) 563 & 5*+ 9 ::&;- <,58"5'

!"#$%&' #"

)#*+,-,#*

./& 0

./& 123

4)563&37

! )5-&8#",&3"#$%&'#! "%#()&%*%+$ , +-'&.+*%+$

/ %.0!% "#12'+% "%$2.3

./&

!"#$%&'

) 563 & 5*+ 9 ::&;- <,58"5'

!"#$%&' #"

)#*+,-,#*

./& 0

./& 123

4)563&37

! )5-&8#",&3"#$%&'#! "%#()&%*%+$ , +-'&.+*%+$

/ %.0!% "#12'+% "%$2.3

./&

!"#$%&'

) 563 & 5*+ 9 ::&;- <,58"5'

You will need to use brainstorming techniques to identify all possible problems and their causes.

Brainstorming techniques work because the knowledge and ideas of two or more persons isalways greater than that of any one individual.

Brainstorming will generate a large number of ideas or possibilities in a relatively short time.Brainstorming tools are meant for teams, but can be used at the individual level also.Brainstorming will be a primary input for other improvement and analytical tools that you will use.

You will learn two excellent brainstorming techniques, cause and effect diagrams and affinitydiagrams. Cause and effect diagrams are also called Fishbone Diagrams because of theirappearance and sometimes called Ishikawa diagrams after their inventor.

In a brainstorming session, ideas are expressed by the individuals in the session and written down

without debate or challenge. The general steps of a brainstorming sessions are:



89


Cause and Effect Diagram

A cause and effect diagram is a composition of lines and words representing a meaningfulrelationship between an effect, or condition, and its causes. To focus the effort and facilitate

thought, the legs of the diagram are given categorical headings. Two common templates for theheadings are for product related and transactional related efforts. Transactional is meant forprocesses where there is no traditional or physical product; rather it is more like an administrativeprocess.

Transactional processes are characterized as processes dealing with forms, ideas, people,decisions and services. You would most likely use the product template for determining the causeof burnt pizza and use the transactional template if you were trying to reduce order defects fromthe order taking process. A third approach is to identify all categories as you best perceive them.

When performing a cause and effect diagram, keep drilling down, always asking why, until youfind the root causes of the problem. Start with one category and stay with it until you have

exhausted all possible inputs and then move to the next category. The next step is to rank eachpotential cause by its likelihood of being the root cause. Rank it by the most likely as a 1, secondmost likely as a 2 and so on. This make take some time, you may even have to create sub-sections like 2a, 2b, 2c, etc. Then come back to reorder the sub-section in to the larger ranking.This is your first attempt at really finding the Y=f(X); remember the funnel? The top X’s have thepotential to be the critical X’s, those X’s which exert the most influence on the output Y.

Finally you will need to determine if each cause is a control or a noise factor. This as you knowis a requirement for the characterization of the process. Next we will explain the meaning andmethods of using some of the common categories.

Process Discovery



90




Process Discovery



91



Process Discovery

!"# ! "#$ % ' ( ))%* + ,-"./"0 %& &%'()* + ,--) ,- .#/#0+,# -(%/%-/&

+1-2, (-&& %1)# 3+2&#& 4-0 5#4#3,& 6

7 -0 #+3" -4 ,"# 8 9& %5#/,%4%#5 %/ ,"# 7 %&"1-/# 5%+. 0+' 3)+&& %4* ,"#'

+& 4-))-:&;

< = -/,0-))+1)# < = >? /-:)#5.#@

< A 0-3#520+) < A >A #-()#B C *&,#'&@

< D-%& # < D >E F,#0/+ ) -0 G/3-/,0-))+1)#@

!"%/H -4 (0-3#520+) +& + & 21&#, -4 3-/,0-))+1)#6 G/4-0,2/+,#)*B '+/*

(0-3#520#& :%,"%/ + 3-'(+/* +0# /-, :#)) 3-/,0-))#5 +/5 3+/ 3+2& #

,"# 5#4#3, )#I#) ,- .- 2(6 !"# 3)+&& %4%3+,%-/ '#,"-5-)-.* %& 2& #5 ,-

&#(+0+,# ,"# 8 9& &- ,"#* 3+/ 1# 2&#5 %/ ,"# 8 JK L%+.0+' +/5 ,"#

7 ME N ,+2. ", )+,#0 %/ ,"%& '-52)#6

!" #$ " & '( $ ) *+ , - , . , $ / + 0

The Cause and Effect Diagram is an organized way to approach brainstorming. This approach

allows us to further organize ourselves by classifying the X’s into controllable, procedural or noise

types.

Classifying the X s



92


Chemical Purity Example

Cause & Effect Diagram – SigmaXL®

This example of the cause and effect diagram is of chemical purity. Notice how the input variables foreach branch are classified as Controllable, Procedural and Noise.

Process Discovery

Measurement

Incoming QC (P)

MeasurementMethod (P)

MeasurementCapability (C)

Manpower

Skill Level (P)

Adherence to procedure (P)

Work order variability (N)

Materials

Raw Materials (C)

Multiple Vendors (C)

Specifications (C)

Startup inspection (P)

Handling (P)

Purification Method (P)

Methods

Room Humidity (N)

RM Supply in Market (N)

Shipping Methods (C)

Mother Nature

Nozzle type (C)

Data collection/feedback(P)

Equipment

Column Capability (C)

Temp controller (C)

ChemicalPurity

Insufficient staff (C)

Training on method (P)

The Fishbone Diagram shown here for Surface Flaws was generated in SigmaXL®. We will nowreview the various steps for creating a Cause & Effect Diagram using the SigmaXL® statistical

software package.



93


Cause & Effect Diagram - SigmaXL®

Select “SigmaXL >Templates and Calculators>DMAIC and DFSS Templates>Cause & Effect(Fishbone) Template”.

Take a few moments to study the worksheet. Notice the six groups are the classic bones for aFishbone. Enter each Cause under the appropriate heading: People, Method, Material, Machine,Measurement, and Environment. You may enter up to 2 Sub-causes for each Cause.

Process Discovery



94


Cause & Effect Diagram - SigmaXL® (cont.)

Fill in the template as shown above. Click the “Fishbone Diagram” button to generate the Causeand Effect Diagram.

You may modify the results to add data, however due to the simplicity of the template it isrecommended that you add to the template and recreate the chart.

Process Discovery



95


Cause & Effect Diagram Exercise

Process Discovery

Exercise objective: Create a Fishbone Diagram.

1.

Retrieve the high level Process Map for your project

and use it to complete a Fishbone, if possible include

your project team.

Don t let the

big one get

away



96


Overview of Process Mapping

Process Discovery

Process Mapping, also called flowcharting, is a technique to visualize the tasks, activities and stepsnecessary to produce a product or a service. The preferred method for describing a process is toidentify it with a generic name, show the workflow with a Process Map and describe its purpose withan operational description.

Remember that a process is a blending of inputs to produce some desired output. The intent of eachtask, activity and step is to add value, as perceived by the customer, to the product or service we are

producing. You cannot discover if this is the case until you have adequately mapped the process.

There are many reasons for creating a Process Map:- It helps all process members understand their part in the process and how their process fits into thebigger picture.- It describes how activities are performed and how the work effort flows, it is a visual way of standingabove the process and watching how work is done. In fact, process maps can be easily uploadedinto model and simulation software where computers allow you to simulate the process and visuallysee how it works.- It can be used as an aid in training new people.- It will show you where you can take measurements that will help you to run the process better.

- It will help you understand where problems occur and what some of the causes may be.- It leverages other analytical tools by providing a source of data and inputs into these tools.- It identifies and leads you to many important characteristics you will need as you strive to makeimprovements.

Individual maps developed by Process Members form the basis of Process Management. Theindividual processes are linked together to see the total effort and flow for meeting business andcustomer needs.

In order to improve or to correctly manage a process, you must be able to describe it in a way thatcan be easily understood, that is why the first activity of the Measure Phase is to adequately describethe process under investigation. Process Mapping is the most important and powerful tool you will

use to improve the effectiveness and efficiency of a process.

!" $%&'% ($ )$%%')(*+ , - "- . ' - /%$)'00 1 + $2

, 20( 3' - 3*' ($ & '0)% 43' 4 ( 4" - 5 - + (6- ( )-" 3'

' - 0 4*+ 2 " & ' % 0 ($ $ & 7

! "#$ &'$($''$) *$+#,) (,' )$-.'/0/12 3 &',.$-- /-+, /)$1+/(4 /+ 5/+# 3 2$1$'/. 13*$6 -#,5 +#$

5,'7(8,5 5/+# 3 9',.$-- :3& 31) )$-.'/0$ /+-&;'&,-$ 5/+# 31 ,&$'3+/,138 )$-.'/&+/,1<

! "#$ (/'-+ 3.+/=/+4 ,( +#$ :$3-;'$ 9#3-$ /- +,

3)$>;3+$84 )$-.'/0$ +#$ &',.$-- ;1)$'/1=$-+/23+/,1<

84"4069('/ : ! "

0 /

' ) (9 ('/ ; 9 ('/ < 9('/ =9(-%( 84"4069('/ :

! " 0 /

' ) (9 ('/ ; 9 ('/ < 9('/ =9(-%(



97


1.

Process inputs (X’s)2.

Supplier requirements

3.

Process outputs (Y’s)

4. Actual customer needs

5.

All value-added and non-value added process tasks and steps

6.

Data collection points

• Cycle times

•

Defects

•

Inventory levels

• Cost of poor quality, etc.

7.

Decision points

8.

Problems that have immediate fixes

9. Process control needs

By mapping processes we can identify many importantcharacteristics and develop information for otheranalytical tools:

Information from Process Mapping

Process Mapping

Process Discovery

These are more reasonswhy Process Mapping isthe most important andpowerful tool you will

need to solve a problem.It has been said that SixSigma is the mostefficient problem solvingmethodology available.This is because workdone with one tool setsup another tool, very littleinformation and work iswasted. Later you willlearn to how to further

use the information andknowledge you gatherfrom Process Mapping.

!"#$# &$# '('&))* +"$## ,-#.( /0 & 1$/2#( ( 3

What you THINK it is..

11

What you THINK it is..

11

What it ACTUALLY is..

22

What it ACTUALLY is..

22 33

What it SHOULD be..

33

What it SHOULD be..

There are usually three viewsof a process: The first view is“what you think the processis” in terms of its size, how

work flows and how well theprocess works. In virtually allcases the extent and difficultyof performing the process isunderstated.

It is not until someone

Process Maps the processthat the full extent anddifficulty is known, and itvirtually is always larger than

what we thought, is moredifficult and it cost more tooperate than we realize. It is here that we discover the hidden operations also. This is the secondview: “what the process actually is”.

Then there is the third view: “what it should be”. This is the result of process improvement activities.It is precisely what you will be doing to the key process you have selected during the weeks betweenclasses. As a result of your project you will either have created the “what it should be” or will be wellon your way to getting there. In order to find the “what it should be” process, you have to learnprocess mapping and literally “walk” the process via a team method to document how it works. Thisis a much easier task then you might suspect, as you will learn over the next several lessons.

We will start by reviewing the standard Process Mapping symbols.



98


Standard Process Mapping Symbols

Standard symbols for Process Mapping:

(available in Microsoft Office™, Visio™, iGrafx™ , SigmaFlow™ and other products)

A RECTANGLE indicates an

activity. Statements within

the rectangle should begin

with a verb

A DIAMOND signifies a decision

point. Only two paths emerge from

a decision point: No and Yes

An ELLIPSE shows the start

and end of the process

A PARALLELAGRAM shows

that there are data

An ARROW shows the

connection and direction

of flow

1 A CIRCLE WITH A LETTER OR

NUMBER INSIDE symbolizesthe continuation of aflowchart to another page

Process Discovery

There may be several interpretations of some of the Process Mapping symbols; however, just abouteveryone uses these primary symbols to document processes. As you become more practiced youwill find additional symbols useful, i.e. reports, data storage etc. For now we will start with just thesesymbols.



99


Process Mapping Levels

Process Discovery

! "#"$ & ' ()" *+,-. / -.,"0 0 *+12 0 .3"453"0 , +$$"6 +

*+7+8"3"74 $"#"$ .- #5"91.574:

! "#"$ ; ' ()" *5,-. /-.,"00 *+12 0.3"453"0 ,+$$"6 4)" <31-.#"3"74

$"#"$ .- #5"91.574: = 535$+- 4. + $"#"$ >2 54 95$$ 0) .9 3. -" 0 4"1 0 +76 4+0 ?0

+76 .7 54 95$$ @" #+-5.A0 1"-B.-3+7," 6+4+C D5"$60 2 ,D, $" 453"2 #+$A" +76

7.7 #+$A" +66"6 453"2 6"B",402 "4,:

! "#"$ > ' ()" /-.,"0 0 *+12 0.3"453"0 ,+$$"6 4)" E.-?"- $"#"$ .-

#5"91.574: ()50 "F+31$" 50 B-.3 4)" 1"-0 1", 45#" .B 4)" 15GG + , )" B

!"##$

&'(

)(*+(

,-.."

! '((+/0

! 1$0'2+(

3145(6

7"8+

)(*+(

9"8+

,-.."

! ''8

,-.."

:';

,-.."

<+#-=+(

,-.."

! 1$0'2+(

> "0$

!"##$

&'(

)(*+(

,-.."

! '((+/0

! 1$0'2+(

3145(6

7"8+

)(*+(

9"8+

,-.."

! ''8

,-.."

:';

,-.."

<+#-=+(

,-.."

! 1$0'2+(

> "0$

Take Orderfrom Cashier

AddIngredients

Check

if Done

Place in

Oven

Place in

Box

Removefrom Oven

ObserveFrequently

Put onDelivery Rack

Yes

Yes

No

Pizza

Dough

Pizza

Correct

No

Scrap

Start NewPizza

Tape

Order on

Box

1

1

Take Orderfrom Cashier

AddIngredients

Check

if Done

Place in

Oven

Place in

Box

Removefrom Oven

ObserveFrequently

Put onDelivery Rack

Yes

Yes

No

Pizza

Dough

Pizza

Correct

No

Scrap

Start NewPizza

Tape

Order on

Box

1

1

Before Process Mapping starts, you have to learn about the different level of detail on a ProcessMap and the different types of Process Maps. Fortunately these have been well categorized andare easy to understand.

There are three different levels of Process Maps. You will need to use all three levels and youmost likely will use them in order from the macro map to the micro map. The macro map containsthe least level of detail, with increasing detail as you get to the micro map. You should think of anduse the level of Process Maps in a way similar to the way you would use road maps. For example,if you want to find a country, you look at the world map. If you want to find a city in that country,you look at the country map. If you want to find a street address in the city, you use a city map.This is the general rule or approach for using Process Maps.

The Macro Process Map, what is called the Level 1 Map, shows the big picture, you will use this toorient yourself to the way a product or service is created. It will also help you to better see whichmajor step of the process is most likely related to the problem you have and it will put the variousprocesses that you are associated with in the context of the larger whole. A Level 1 PFM,sometimes called the “management” level, is a high-level process map having the followingcharacteristics:

! Combines related activities into one major processing step!

Illustrates where/how the process fits into the big picture!

Has minimal detail!

Illustrates only major process steps!

Can be completed with an understanding of general process steps and the

purpose/objective of the process



100


Process Mapping Levels (cont.)

Types of Process Maps

There are four types of Process Maps that you will use. They are the Linear Flow Map, thedeployment or Swim Lane Flow Map, the S-I-P-0-C Map (pronounced sigh-pock) and the ValueStream Map.

Process Discovery

The next level is generically called the Process Map. You will refer to it as a Level 2 Map and itidentifies the major process steps from the workers point of view. In the pizza example above,these are the steps the pizza chef takes to make, cook and box the pizza for delivery. It gives you agood idea of what is going on in this process, but could can you fully understand why the process

performs the way it does in terms of efficiency and effectiveness, could you improve the processwith the level of knowledge from this map?

Probably not, you are going to need a Level 3 Map called the Micro Process Map. It is also knownas the improvement view of a process. There is however a lot of value in the Level 2 Map, becauseit is helping you to “see” and understand how work gets done, who does it, etc. It is a necessarystepping stone to arriving at improved performance.

Next we will introduce the four different types of Process Maps. You will want to use different typesof Process Maps, to better help see, understand and communicate the way processes behave.

While they all show how work gets done, they emphasize different aspects of process flow andprovide you with alternative ways to understand the behavior of the process so you can dosomething about it. The Linear Flow Map is the most traditional and is usually where most start themapping effort.

The Swim Lane Map adds another dimension of knowledge to the picture of the process: Now youcan see which department area or person is responsible. You can use the various types of maps

in the form of any of the three levels of a Process Map.

!"# % &'#()*+ ,-. /)-0#1 1 2(3

Calls

for

Order

Pizza

Correct

Customer

Hungry

Take

Order

Make

Pizza

Cook

Pizza

Box

Pizza

Deliver

Pizza

Customer

Eats

Calls

for

Order

Pizza

Correct

Customer

Hungry

Take

Order

Make

Pizza

Cook

Pizza

Box

Pizza

Deliver

Pizza

Customer

Eats

41 5"# '(6# 15(5#1 7 5"&1 8&(9)(6 1 "-.1 5"# 3)-0#1 1 15#31 &' ( 1# :;#'5&(, <,-.7 9#'#)(,,= -)8#)#8

<)-6 (' ;33#) ,#<5 0-)'#) -< 5"# 6(3 5-.()81 5"# )&9"5 1 &8#>

Calls for

Order

Customer

Hungry

Take

Order

Make

Pizza

Cook

Pizza

Box

Pizza

Deliver

Pizza

Customer

Eats

C u s t o m e r

C a s h i e r

C o o k

D e l i v e r e r

Pizza

Correct

Calls for

Order

Customer

Hungry

Take

Order

Make

Pizza

Cook

Pizza

Box

Pizza

Deliver

Pizza

Customer

Eats

C u s t o m e r

C a s h i e r

C o o k

D e l i v e r e r

C u s t o m e r

C a s h i e r

C o o k

D e l i v e r e r

Pizza

Correct

!"# ?#3,-=6#'5*+,-. -) @.&6 % ('# /)-0#1 1 2(3

!"# A(,;# -< 5"# @ .&6 % ('# 6(3 &1 5"(5 &1 1"-.1 =-; ."- -) ."&0" 8#3()56#'5 &1 )#13-'1 &B,# <-)5"# 15#31 &' ( 3)-0#1 1 > !"&1 0 (' 3)-A&8# 3-.#)<;, &'1&9"51 &' 5"# .(= ( 3)-0#11 3#)<-)61> 45&6#,&'# 0(' B# (88#8 5- 1"- . "-. ,-'9 &5 5(C#1 #(0" 9 )-;3 5- 3#)<-)6 5"#&) .-)C> 4,1- #(0 "5&6# .-)C 6-A#1 (0 )-11 ( 1 .&6 ,('#7 5"#)# &1 ( D@ ;33,&#) E F ;15-6#)G &'5#)(05&-'> !"&1 &1 ;1 ;(,,=."#)# B-55,#'#0C1 ('8 :;#;#1 <-)6>



102


Types of Process Maps

The Value Stream Map is a specialized map that helps you to understand numerous performancemetrics associated primarily with the speed of the process, but has many other important data. Whilethis Process Map level is at the macro level, the Value Stream Map provides you a lot of detailedperformance data for the major steps of the process. It is great for finding bottlenecks in the process.

Process Discovery

Process Mapping Exercise – Going to Work

! "# %& '%() # (* +",) #-#'. ,) # ,) +( / #0#1(% 2 3 #0#1 4 52.'(6 3 ,7# 2'

8 '(. #) ) 9 1(: 52% 27/ +"#7 . (70 #'+ +",) ;2% +( 2 < :,; 3 27# 52%=

! "#$ &'" ()**)+,-. /#0 1. 2)3-$ ()2 &'" "4"20,5 "6 ! "# %&'( )((* +"*+(,*(-

&)"#. /"#, &)010./ ." &,,0'( &. 2",3 "* .04( &*- &15" .%( &4"#*. "6 .04( 0. .&3(5

6,"4 .%( .04( /"#, &1&,4 7"(5 "66 #*.01 /"# &,,0'( &. 2",38 9 " %(1: /"# )(..(,

#*-(,5.&*- )".% .%( '&,0&.0"* 0* &,,0'&1 .04(5 &*- .%( .".&1 .04(; /"# -(+0-( ."

+,(&.( & < ('(1 = >&+," ? ,"+(5 5 >&:8 @ ", :#,:"5(5 "6 .%05 (A(,+05 (; .%( 5.&,. 05

2%(* /"#, &1&,4 7"(5 "66 .%( 60,5. .04( &*- .%( (*- 05 2%(* /"# &,,0'( &. /"#,2",3 5.&.0"*8

7#51 8 B >(*.&11/ .%0*3 &)"#. .%( '&,0"#5 .&5 35 &*- &+.0'0.0(5 .%&. /"# ,"#.0*(1/

-" 6,"4 .%( -(60*(- 5.&,. ." .%( (*- :"0*.5 "6 .%( (A(,+05(8

7#51 9 B C5 0*7 & :(*+01 &*- :&:(, +,(&.( & 10*(&, :,"+(5 5 4&: &. .%( 4&+ ,"

1('(1; )#. 20.% (*"#7% -(.&01 .%&. /"# +&* 5(( &11 .%( 4&D", 5.(:5 "6 /"#,

:,"+(558

7#51 : B @ ,"4 .%( < 0*(&, ? ,"+(5 5 >&:; +,(&.( & 5 204 1&*( 5./1( ? ,"+(5 5 >&:8

@ ", .%( 1&*(5 /"# 4&/ #5( .%( -066(,(*. :%&5 (5 "6 /"#, :,"+(55 ; 5 #+% &5 .%(

2&3( #: :%&5(; 7(..0*7 :,(:&,(-; -,0'0*7; (.+8



103


A Process Map of Process Mapping

Process Discovery

Process Mappingfollows a generalorder, but sometimes

you may find itnecessary, evenadvisable to deviatesomewhat. However,you will find this agood path to followas it has proven itself to generatesignificant results.

On the lessonsahead we will alwaysshow you where youare at in thissequence of tasks

for Process Mapping. Before we begin our Process Mapping we will first start you off with how todetermine the approach to mapping the process.

Basically there are two approaches: the individual and the team approach.

!"#$%" '(" )* +,"#+- '(" . "/"0 1 234

56"%'$#7 ) 8,,0$"-

-"98$-":"%')

56"%'$#7 ;00 <=) ;%6

> =)

!"'"-:$%";,,-+;*( '+ :;,

'(" ,-+*") )

? "0"*' '(" ,-+*"))

@ +:,0"'" . "/"0 A23 4 B+-C)(""'

@-";'" ."/"0 A 23 4

@ -";'" '(" ."/"0 1

2 3 4

56"%'$#7 DEFGDE

)'",)

2"-#+-: ? 52H@

@ -";'" ; ."/"0 I

2 3 4

E66 2"-#+-:;%*"

6;';

56"%'$#7 *8) '+:"-

-"98$-":"%')

!"#$%" '(" )* +,"#+- '(" . "/"0 1 234

56"%'$#7 ) 8,,0$"-

-"98$-":"%')

56"%'$#7 ;00 <=) ;%6

> =)

!"'"-:$%";,,-+;*( '+ :;,

'(" ,-+*") )

? "0"*' '(" ,-+*"))

@ +:,0"'" . "/"0 A23 4 B+-C)(""'

@-";'" ."/"0 A 23 4

@ -";'" '(" ."/"0 1

2 3 4

56"%'$#7 DEFGDE

)'",)

2"-#+-: ? 52H@

@ -";'" ; ."/"0 I

2 3 4

E66 2"-#+-:;%*"

6;';

56"%'$#7 *8) '+:"-

-"98$-":"%')

Process Mapping Approach

If you decide to do the individual approach, here are a few key factors: You must pretend that you arethe product or service flowing through the process and you are trying to “experience” all of the tasksthat happen through the various steps.

You must start by talking to the manager of the area and/or the process owner. This is where you willdevelop the Level 1 Macro Process Map. While you are talking to him, you will need to receive

permission to talk to various members of the process in order to get the detailed information you need.

!" #$% '() *)+, -../0+1(

!" # $%%$& ()* ! "#$ &''()#*+ ,) - ()*". . /#''012

!" #$% '() 2$3#4#35+6 -../0+1(!" + (,-( &.() ()* / *0*% ! 1,2-$ 3-$2*4 4 1,5"

6" 1**( &.() 5-$2*4 4 $&7*-849 : ;,7,< *-849" = -*,(* ,/ *0*% ! 1,5 , 7> $?(,.7 ,55-$0,% ($ .7(*-0.*&5-$2*44 ;*;?*-4"

@" + (,-(.7< &.() ()* ?*<.77.7< $A ()* 5-$2*4 4 B 5-*(*7>C$D ,-* ()* 5-$>D2( $- 4*-0.2* A%$&.7< ()-$D<) ()*5-$2*44 B .7(*-0.*& ($ <,()*- .7A$-;,(.$7"

E" F4 ()* .7(*-0.*& 5-$<-*44 B ,4 4*;?%* ()* >,(, .7($ ,/ *0*% 6 3# 1"

G" H*-.AC ()* ,22D-,2C $A ()* / *0*% 6 3 # 1 &.() ()*.7>.0.>D,%4 &)$ 5-$0.>*> .75D("

I" J5>,(* ()* /*0*% 6 3 # 1 ,4 7**>*>"

7)8#$) '()" 10.) 80/

'() 9)4)6 :; < =

7)')/,#$)+../0+1( '0

,+. '()./01)""

> )6)1' '()

./01)""

? 0,.6)')9 )4)6 @

;<=A0/B"())'

? /)+')

9 )4)6 @

; < =



104


Process Mapping Approach

Process Discovery

Where appropriate the team should include line individuals, supervisors, design engineers,process engineers, process technicians, maintenance, etc. The team process mappingworkshop is where it all comes together.

!" #$% '() *)+, -../0+1(

!" # $%&$ ()$* $*+ , +-+. ! /%0&1 2 &10+3 3 /%4"

5" /++$ ()$* 4&10+3 3 1(6+&738 9 :%6%; +&738" < &+%$+ %

,+-+. ! /%4 %6= 1>$%)6 %44&1-%. $1 0%.. % 4&10+33:%44)6; :++$)6; ()$* 4&10+33 :+:>+&3 7# ++ $+%:(1&?3*14 )63$&@0$)163 A1& =+$%).3 16 &@66)6; $*+:++$)6;8"

B" C &)6; ?+D :+:>+&3 1A $*+ 4&10+3 3 )6$1 $*+ 4&10+3 3A.1( (1&?3*14" EA $*+ 4&10+33 )3 .%&;+ )6 3014+F *1.=)6=)-)=@%. (1&?3*143 A1& +%0* 3@>3+0$)16 1A $*+$1$%. 4&10+3 3 " # $%&$ ()$* $*+ >+; )66)6; 3 $+43 "G&;%6)H+ :++$)6; $1 @3+ $*+ I413$J)$ 61$+ % 44&1%0*$1 ;%$*+& )6=)-)=@%. $%3?3 %6= %0$)-)$)+3F >%3+= 16$*+ :%0&1 :%4F $*%$ 01:4&)3+ $*+ 4&10+33"

K" E::+=)%$+.D %33 +:>.+ $*+ )6A1&:%$)16 $*%$ *%3>++6 4&1-)=+= )6$1 % 2&10+33 /%4"

L" M+&)AD $*+ 2 N / >D =)30 @33 )6; )$ ()$* 4&10+3 3 1(6+&3%6= >D 1>3+&-)6; $*+ %0$@%. 4&10+33 A&1: >+;)66)6;

$1 +6="

2)3#$) '()"10.) 30/

'() 4)5)6 78 9 :

2)')/,#$)+../0+1( '0

,+. '()./01)""

; )6)1' '()

./01)""

< 0,.6)')4 )5)6 =

89:>0/?"())'

< /)+')

4 )5)6 =

8 9 :

Process Mappingworks best with ateam approach. The

logistics ofperforming themapping aresomewhat different,but it overall it takesless time, the qualityof the output ishigher and you willhave more “buy-in” into the results. Inputshould come from

people familiar withall stages of process.

In summary, after adding to and agreeing to the Macro Process Map, the team process mappingapproach is performed using multiple post-it notes where each person writes one task per note and,when finished, place them onto a wall which contains a large scale Macro Process Map.

This is a very fast way to get a lot of information including how long it takes to do a particular task.Using the Value Stream Analysis techniques which you will study later, you will use this data toimprove the process. We will now discuss the development of the various levels of Process Mapping.

!" #$$ &' ()$ (*+,, ') -(.+' / +'.,00 -(1"

2" 30 4)* 5"6 7 !! 1(1,+ 8'+ ,(.9 :(.+' 1+'.,0 0 0&,1;

&(1, &9, 1+'.,00 &' &9, <(== 4) ( =4),(+ 0&>=,"?" / +'.,0 0 -,:@,+0 &9,) =40& (== A)'<) 1+'.,00 &(0 A0

&9(& &9,> $' ') ( / '0&B4& )'&,; '), 1+'.,00 &(0 A 1,+

)'&,"

CD).=E$, &9, (.&E(= &4:, 01,)& &' 1,+8'+: ,(.9(.&4F4&>; $' )'& 4).=E$, ()> <(4& &4:, '+ GE,E,

&4:,"

CH 40& ()> A)'<) 1,+8'+:()., $( &( &9(& $,0 .+4@,&9, GE(=4&> '8 &9, &(0A"

I" / =(., &9, 1'0&B4& )'&,0 ') &9, <(== E)$,+ &9,

(11+'1+4(&, :(.+' 0&,1 4) &9, '+$,+ '8 &9, <'+A 8='<"

6" J ,F4,< 1+'.,0 0 <4&9 <9'=, *+'E1; ($$ ($$4&4')(=

4)8'+:(&4') ()$ .='0, :,,&4)*"

K" D::,$4(&,=> .')0'=4$(&, 4)8'+:(&4') 4)&' ( H,F,= 2/ +'.,00 -(1"

L" M 'E <4== 0&4== 9(F, &' F,+48> &9, :(1 @> <(=A4)* &9,

1+'.,00"

!"# !#%& '()* #++ ,%--./0 1)(2+")-

Define thescope forthe Level 2

PFM

Determineapproach to

map theprocess

Select the

process

CompleteLevel 1

PFMworksheet

Create

Level 1

PFM



105


Process Discovery

Steps in Generating a Level 1 PFM

You may recall that thepreferred method fordescribing a process is toidentify it with a generic

name, describe its purposewith an operationaldescription and show theworkflow with a processmap. When developing aMacro Process Map, alwaysadd one process step in frontof and behind the area youbelieve contains yourproblem as a minimum. Toaid you in your start, we

have provided you with achecklist or worksheet. Youmay acquire this data fromyour own knowledge and/or with the interviews you do with the managers / process owners. Once youhave this data, and you should do this before drawing maps, you will be well positioned tocommunicate with others and you will be much more confident as you proceed.

A Macro Process Map can be useful when reporting project status to management. A macro-map canshow the scope of the project, so management can adjust their expectations accordingly. Remember,only major process steps are included. For example, a step listed as “Plating” in a manufacturingMacro Process Map, might actually consists of many steps: pre-clean, anodic cleaning, cathodicactivation, pre-plate, electro-deposition, reverse-plate, rinse and spin-dry, etc. The plating step in the

macro-map will then be detailed in the Level 2 Process Map.

!" $%&'()*+ , -&'&.)/ ',0& *1. (2& 3.1/&445

6 1. )'4(,'/&5 78 94(10&. 1.%&. 3.1/&4 4:

;" $%&'()*+ (2& <&-)'')'- ,'% &'%)'- 4(&34 1* (2& 3.1/&4 45

!"#$%%$%# = /94(10&. /,>>4 )'" &%'$%# ? <,@&% 3)AA, - )B&' (1

13&.,()1'4

C" D&4/.)<& (2& 3.)0,.+ 39.314& ,'% 1<E&/()B& 1* (2& 3.1/&44

F13&., ()1',> %&*)')()1'G5

H 2& 39.314& 1* (2& 3.1/&44 )4 (1 1<(,)' (&>&321'& 1.%&.4 *1.

3)AA, 4I 4& >> ,%%)()1',> 3.1%9/(4 )* 3144 )<>&I >&( (2& /94 (10&.

@'1J (2& 3.)/& ,'% ,33.1K)0,(& %&>)B&.+ ()0&I 3.1B)%& ,'

,//9.,(& /11@ 1.%&.I >1- (2& ()0& ,'% )00&%),(&>+ -)B& )( (1 (2&

3)AA, /11@&."

L" M&'(,>>+ 7J,>@: (2.19-2 (2& 0,E1. 4(&34 1* (2& 3.1/&44 ,'%

J.)(& (2&0 %1J'5

N &/&)B& (2& 1.%&. B), 321'& /,>> *.10 (2& /94 (10&.I /,>/9>,(&

(2& 3.)/&I /.&,(& , <9)>% 1.%&. ,'% 3.1B)%& (2& 1.%&. (1

13&.,()1'4

O" P4& 4(,'%,.% *>1J/2,.()'- 4+0<1>4 (1 1.%&. ,'% (1 )>>94(.,(&

(2& *>1J 1* (2& 0, E1. 3.1/&4 4 4(&34"

( )"*+$%# * - "."/ 0 12 3

4"5$%" +6"78 9:" 59)

+6" -"."/ ;

1 2 3

4"+")<$%"*::)9*86 +9

<*: +6":)98"77

= "/"8+ +6"

:)98"77

( 9<:/"+"- "."/ 0

123>9)?76""+

( )"*+"

- "."/ 0

1 2 3

Exercise – Generate a Level 1 PFM



108


Building a SIPOC

Process Discovery

The tool name prompts the team to consider the suppliers (the 'S' in SIPOC) of your process, theinputs (the 'I') to the process, the process (the 'P') your team is improving, the outputs (the 'O') ofthe process and the customers (the 'C') that receive the process outputs.

Requirements of the customers can be appended to the end of the SIPOC for further detail andrequirements are easily added for the suppliers as well.

The SIPOC tool is particularly useful in identifying:

Who supplies inputs to the process?What are all of the inputs to the process we are aware of? (Later in the DMAIC methodologyyou will use other tools which will find still more inputs, remember Y=f(X) and if we are going toimprove Y, we are going to have to find all the X’s.What specifications are placed on the inputs?What are all of the outputs of the process?Who are the true customers of the process?What are the requirements of the customers?

You can actually begin with the Level 1 PFM that has 4 to 8 high-level steps, but a Level 2 PFM is evenof more value. Creating a SIPOC with a process mapping team, again the recommended method is a

wall exercise similar to your other process mapping workshop. Create an area that will allow the team toplace post-it note additions to the 8.5 X 11 sheets with the letters S, I, P, O and C on them with a copy of the Process Map below the sheet with the letter P on it.

Hold a process flow workshop with key members. (Note: If the process is large in scope, hold anindividual workshop for each subsection of the total process, starting with the beginning steps).The preferred order of the steps is as follows:

1. Identify the outputs of this overall process.2. Identify the customers who will receive the outputs of the process.3. Identify customers’ preliminary requirements4. Identify the inputs required for the process.5. Identify suppliers of the required inputs that are necessary for the process to function.6. Identify the preliminary requirements of the inputs for the process to function properly.

Identify all X

sand Y s

Create theLevel 2 PFM

PerformSIPOC

Identifysupplier

requirements

Identifycustomer

requirements

Suppliers ATT Phones

Office Depot

TI CalculatorsNEC Cash Register

SIPOC diagram for customer-order process:

Process See Below

Customers

Call for

an Order

Answer

Phone

Write

Order

Sets

Price

Confirm

Order

Address

& Phone

Order to

Cook

Customer Order:

Level 1 process flow diagram

Outputs

Bake order

Price

Order confirmation

Data on cycle time

Order rate data

Order transaction

Delivery info

Cook

Accounting

Requirements

Order to Cook < 1 minute

Complete bake order

Correct bake order

Correct address

Correct Price

Complete call < 3 min

Inputs Pizza type

Size

QuantityExtra Toppings

Special orders

Drink types & quantities

Other products

Address

Phone number

Time, day and date

Name

Volume



109


You are now ready toidentify the customerrequirements for theoutputs you have defined.

Customer requirements,called VOC, determinewhat are and are notacceptable for each of theoutputs. You may find thatsome of the outputs do nothave requirements orspecifications. For a wellmanaged process, this isnot acceptable. If this is thecase, you must ask/

negotiate with the customeras to what is acceptable.

There is a technique for

determining the validity of

Process Discovery

Identifying Customer Requirements

customer and supplier requirements. It is called “RUMBA” standing for: Reasonable, Understandable,Measurable, Believable and Achievable. If a requirement cannot meet all of these characteristics, then itis not a valid requirement , hence the word negotiation. We have included the process for validatingcustomer requirements at the end of this lesson.

!"#$%&'( *++ ,-.

*$" /-.

0 1#*%# %2#

3#4#+ 5 678

6#1'91:

; !6<0

!"#$%&'(

.=>>+&#1

1#?=&1#:#$%.

!"#$%&'(

@=.%9:#1

1#?=&1#:#$%.

1 3 4 5 6 7 8 9 10 11 12 13

Value Data General Data/Information

Internal External Metric LSL Target USL Comments

Operational

Definition

Process Name

VA

or

NVA

Output Data Requirements Data Measurement Data

Process Output - Name (Y)

Customer (Name) Metric Measurement

System (How is it

Measured)

Frequency of

Measurement Performance Level Data

PROCESS OUTPUT

IDENTIFICATION AND ANALYSIS

The Excel spreadsheet is somewhat self explanatory. You will use a similar form for identifying the

supplier requirements. Start by writing in the process name followed by the process operationaldefinition. The operational definition is a short paragraph which states why the process exists, what itdoes and what its value proposition is. Always take sufficient time to write this such that anyone whoreads it will be able to understand the process. Then list each of the outputs, the Y ’s, and write in thecustomer ’s name who receives this output, categorized as an internal or external customer.

Next are the requirements data. To specify and measure something, it must have a unit of measure;called a metric. As an example, the metric for the speed of your car is miles per hour, for your weight itis pounds, for time it is hours or minutes and so on. You may know what the LSL and USL are but youmay not have a target value. A target is the value the customer prefers all the output to be centered at;essentially, the average of the distribution. Sometimes it is stated as “1 hour +/- 5 minutes”. One hour isthe target, the LSL is 55 minutes and the USL is 65 minutes. A target may not be specified by the

customer; if not, put in what the average would be. You will want to minimize the variation from thisvalue.

You will learn more about measurement, but for now you must know that if something is required, youmust have a way to measure it as specified in column 9. Column 10 is how often the measurement ismade and column 11 is the current value for the measurement data. Column 12 is for identifying if this isa value or non value added activity; more on that later. And finally column 13 is for any comments youwant to make about the output.

You will come back to this form and rank the significance of the outputs in terms of importance toidentify the CTQ’s.



110


Identifying Supplier Requirements

The supplier input orprocess input identificationand analysis form is nearly

identical to the output form just covered. Now you arethe customer, you willspecify what is required ofyour suppliers for yourprocess to work correctly;remember RUMBA – thesame rules apply.

You will notice a newparameter introduced incolumn 2. It asks if the input

is a controlled input or anuncontrolled input (noise).The next topic will discussthe meaning of these terms.

Process Discovery

!"#$%&'( *++ ,-.

*$" /-.

0 1#*%# %2#

3#4#+ 5 678

6#1'91:

;! 6 <0

!"#$%&'(

.=>>+&#1

1#?=&1#:#$%.

!"#$%&'(

@=.%9:#1

1#?=&1#:#$%.

1 2 3 4 5 6 7 8 9 10 11 12

V al ue D at a G en er al D at a/ In fo rm at io n

Internal External Metric LSL Target USL

Operational

Definition

NV

or

NVA

PROCESS INPUTIDENTIFICATION AND ANALYSIS

Process Name

Measurement

System (How is it

Measured)

Frequency of

Measurement

Performance

Level Data CommentsProcess Input- Name (X)

Controlled (C)

Noise (N)

Supplier (Name) Metric

Input Data Requirements Data Measurement Data

Later you will come back to this form and rank the importance of the inputs to the success of yourprocess and eventually you will have found the Critical X’s.

Controllable vs. Noise Inputs

For any process or processstep input, there are twoprimary types of inputs: Controllable - we can exertinfluence over them

Uncontrollable - theybehave as they want towithin some reasonableboundaries.Procedural - A standardizedset of activities leading toreadiness of a step.

Compliance to GAAP(Generally Accepted Accounting Principals).

However, even with theinputs we define ascontrollable, we never exert

! "# %&'("))

*+,-+,)

.'/)" 01-+,)

%&'("))

2''3 4"3-

5'/),+&" 6 '1,"1,

017&"8/"1, 9:&/:,/'1

%/;; : < /;"

017&"8/" 1, 4#-")=5/>")

9'?+3"

6 '1,&'??:@?"

01-+,)

%&'("8+&:?01-+,)

6 '&&"(, 017&"8/"1,)

%&'-"&?# 6''A"8

B', %/;;: CDEF 8"7

G H"&# /1-+, (:1 @" "/,I"&J

! "#$%"&&'(&) K6 L ! "#$%&' )*# +, *-.%'&,- /0 )/#&0/11,- 2341, &3, $0/),'' 4' 0%##4#5 6,7578 '$,,-89,,- 0*&,8 &,:$,0*&%0,8 *#- $0,''%0,;

*%"+),-%'& K% L ! "#$%&' )*# +, *-.%'&,- /0 )/#&0/11,- 2341, &3, $0/),'' 4' 0%##4#5 6,7578 '$,,-89,,- 0*&,8 &,:$,0*&%0,8 *#- $0,''%0,;

."/0) K. L M <34#5' 2, -/#=& &34#> 2, )*# )/#&0/18 2, *0, %#*2*0, /9 /0 ',,8 &// ,?$,#'4@, /0 &//-4994)%1& &/ )/#&0/1 6,7578 *:+4,#& &,:$,0*&%0,8 3%:4-4&A8 4#-4@4-%*1;

Screens in Place

Oven Clean

Ingredients prepared

complete control. We can control an input within the limits of its natural variation, but it will vary onits own based on its distributional shape - as you have previously learned. You choose to controlcertain inputs because you either know or believe they have an effect on the outcome of theprocess, it is inexpensive to do, so controlling it “makes us feel better ” or there once was a

problem and the solution (right or wrong) was to exert control over some input.



111


Exercise – Supplier Requirements

Process Discovery

You choose to not control some inputs because you think you cannot control them, you either knowor believe they don’t have much affect on the output, you think it is not cost justified or you just don’tknow these inputs even exist. Yes, that’s right, you don’t know they are having an affect on theoutput. For example, what effect does ambient noise or temperature have on your ability to be

attentive or productive, etc?

It is important to distinguish which category an input falls into. You know through Y=f(X), that if it is aCritical X, by definition, that you must control it. Also if you believe that an input is or needs to becontrolled, then you have automatically implied there are requirements placed on it and that it mustbe measured. You must always think and ask whether an input is or should be controlled or if it isuncontrolled.

Controllable vs. Noise Inputs (cont.)



112


The Level 3 Process Flow Diagram

Process Discovery

You have a decision at this point to continue with a complete characterization of the process you havedocumented at a Level 2 in order to fully build the process management system or to narrow the effortby focusing on those steps that are contributing to the problem you want solved.

In reality, usually just a few of the process steps are the root cause areas for any given higher levelprocess output problem. If your desire is the latter, there are some other Measure Phase actions andtools you will use to narrow the number of potential X’s and subsequently the number of process steps.

To narrow the scope so it is relevant to your problem consider the following: Remember using the pizzarestaurant as our example for selecting a key process? They were having a problem with overalldelivery time and burnt pizzas. Which steps in this process would contribute to burnt pizzas and howmight a pizza which was burnt so badly it had to be scrapped and restarted effect delivery time? It wouldmost likely be the steps between “place in oven” to “remove from oven”, but it might also include “addingredients” because certain ingredients may burn more quickly than others. This is how, based on theProblem Statement you have made, you would narrow the scope for doing a Level 3 PFM.

For your project, the priority will be to do your best to find the problematic steps associated with yourProblem Statement. We will teach you some new tools in a later lesson to aid you in doing this. You mayhave to characterize a number of steps until you get more experience at narrowing the steps that causeproblems; this is to be expected. If you have the time you should characterize the whole process.

Each step you select as the causal steps in the process must be fully characterized, just as you havepreviously done for the whole process. In essence you will do a “mini SIPOC” on each step of theprocess as defined in the Level 2 Process Map. This can be done using a Level 3 Micro Process Mapand placing all the information on it or it can be consolidated onto an Excel spreadsheet format or acombination of both. If all the data and information is put onto an actual Process Map, expect the mapto be rather large physically. Depending on the scope of the process, some people dedicate a wall

space for doing this; say a 12 to 14 foot long wall. An effective approach for this is to use a roll ofindustrial

1 2 3 4 5 6 7 8 9 10 11 12 13

V a lu e D at a G e ne ra l D at a/ In f or ma ti on

I nt er na l E xt er na l M etr ic L SL T ar ge t U SLFrequency of

Measurement

ProcessNamePROCESS STEP

INPUT IDENTIFICATION AND ANALYSIS

Performance

Level Data Comments

Controlled(C)

Noise(N)

Input Data

Metric

Requirements Data Measurement D ata

Measurement

System (Howisit

Measured)

VA

or

NVAProcessInput-Name(X)

Supplier(Nam e)

Step Name/Number

1 2 3 4 5 6 7 8 9 10 11 12 13

V a lu e D at a G en e ra l D at a/ In fo rm at io n

I nt ern al E xt ern al M et ri c L SL T arg et U SLFrequency of

Measurement

ProcessNamePROCESS STEP


Performance

Level Data Comments

Controlled(C)

Noise(N)

Input Data

Metric

Requirements Data Measurement D ata

Measurement

System (Howisit

Measured)

VA

or

NVAProcessInput-Name(X)

Supplier(Name)

Step Name/Number

1 3 4 5 6 7 8 9 10 11 12 13

ValueData General Data/ In format ion


Measurement

System (Howis it

Measured)

Frequency of

Measurement Performance Level Data Comments

VA

or

NVAProcessOutput - Name(Y)

Customer (Name) Metric

PROCESS STEP

OUTPUT IDENTIFICATION AND ANALYSIS


Process Name Step Name/Number

1 3 4 5 6 7 8 9 10 11 12 13

ValueData General Data/ In format ion

Internal External Metri c LSL Target USL

Measurement

System (Howisit

Measured)

Frequency of


VA

or

NVAProcessOutput - Name(Y)


PROCESS STEP




Take Order

from Cashier

Add

Ingredients

Check

if Done

Place in

Oven

Place in

Box

Remove

from Oven

Observe

Frequently

Put onDelivery Rack

Yes

Yes

No

Pizza

Dough

Pizza

Correct

No

Scrap

Start NewPizza

TapeOrder on

Box

1

1

Take Order

from Cashier

Add

Ingredients

Check

if Done

Place in

Oven

Place in

Box

Remove

from Oven

Observe

Frequently

Put onDelivery Rack

Yes

Yes

No

Pizza

Dough

Pizza

Correct

No

Scrap

Start NewPizza

TapeOrder on

Box

1

1



113


The Level 3 Process Flow Diagram (Cont.)

Process Inputs (X s) and Outputs (Y s)

You are now down at thestep level of the process,this is what we call theimprovement view of aprocess. Now you doexactly the same thingas you did for the overallprocess, you list all ofthe input and outputinformation for steps of

the process you haveselected for analysis andcharacterization to solveyour problem. To helpyou comprehend whatwe are trying toaccomplish we haveprovided you withvisualization for theinputs and outputs of thePizza restaurant.

Process Discovery

grade brown package wrapping paper, which is generally 4 feet wide. Just roll out the length you want,cut it, place this on the wall and then build your Level 3 Process Map by taping and writing variouselements onto the paper. The value of this approach is that you can take it off the wall, roll it up, take itwith you and then put it back on any wall; great for team efforts.

A Level 3 Process Map contains all of the process details needed to meet your objective: all of the flows,set points, standard operating procedures (SOPs), inputs and outputs; their specifications and if they areclassified as being controllable or non-controllable (noise). The Level 3 PFM usually contains estimatesof defects per unit (DPU), yield and rolled throughput yield (RTY) and value/non-value add. If processingcycle times and inventory levels (materials or work queues) are important, value stream parameters arealso included.

This can be a lot of detail to manage and appropriate tracking sheets are required. We have suppliedthese sheets in a paper and Excel spreadsheet format for your use. The good news is the approach andforms for the steps are essentially the same as the format for identifying supplier and customerrequirements at the process level. A spreadsheet is very convenient tool and the output from the

spreadsheet can then be fed directly into a C&E matrix and an FMEA (to be described later), also builtusing spreadsheets.

You will find the work you have done up to this point in terms of a Level 1 and 2 Process Maps and theSIPOC will be of use, both from knowledge of the process and actual data.

An important reminder of a previous lesson: You will recall when you were taught about project definitionwhere it was stated that you should only try to solve the performance of only one process output, at anyone time. Because of the amount of detail you can get into for just one Y, trying to optimize more thanone Y at a time can become overwhelming. The good news is that you will have laid all the ground workto focus on a second and a third Y for a process by just focusing on one Y in your initial project.

1 2 3 4 5 6 7 8 9 10 11 12 13

V al ue D ata General D ata/ In fo rmat ion

Inter nal Ext ernal Metric LSL T arget USLFrequency of

Measurement

Process NamePROCESS STEP


Performance

Level Data Comments

Controlled (C)

Noise (N)

Input Data

Metric

Requirements Data Measurement Data

Measurement

System (How is it

Measured)

VA

or

NVAProcess Input- Name (X)

Supplier (Name)

Step Name/Number

!"#$%&'(*+,-*+ .%#/.

0 1#2%# 2

3#4#5 6 789

+""

7#1':1;2$<#

"2%2

1 3 4 5 6 7 8 9 10 11 12 13

Value Data General Data/ Information


Measurement

System (How is it

Measured)

Frequency of


VA

or

NVAProcess Output - Name (Y)


PROCESS STEP






115


! # $% # $&'( )*+, -.*/ 0., 12/, -$/3.4*5 67$37 8 9/ (5* $':.5,(0, $0

( :5.3*// ;,7* 4$,(+ <*6=>

? @ 7* ,*(' 3.0/ $-*5/ (++ :.// $A+* 8 9/ ,7(, 3(0 3.0,5$A2,* .53(2/* ,7* :5.A+*' .A/*54*->

? @ 7* ,*(' 2/ */ B :5$'(5C / .253*/ .< 8 $-*0,$<$3(,$.0D

E F5.3*// G(::$0&

E H$/7A.0* !0(+C/$/

E )( /$3 I( ,( ! 0(+C/$/ ? J 5(:7$3(+ (0- # ,(,$/,$3(+

? ! K $/ , .< 8 9/ $/ */ ,(A+$/ 7*- (0- 3.':$+*->

? @ 7* ,*(' ,7*0 :5$.5$,$L*/ 67$37 8 9/ $, 6$++ *% :+.5* <$5/ ,M (0-

*+$'$0(,*/ ,7* N.A4$.2/ O +.6 $':(3, 8 9/ <5.' <25,7*5

3.0/$-*5(,$.0>

@ 7* 8 PQ I$(&5(' $/ ,7$/ F 5$.5$,$L(,$.0 @..+R

Definition of X-Y Diagram

The Vital Few

This is an important tool for the many reasons we have already stated. Use it to your benefit,leverage the team and this will help you progress you through the methodology to accomplish yourultimate project goal.

Process Discovery

The X-Y Diagram is a great tool tohelp us focus, again it is based onteam experience and “Tribal” knowledge. At this point in the

project that is great although itshould be recognized that this isNOT hard data. As you progressthrough the methodology don’t besurprised if you find out throughdata analysis that what the teamthought might be critical turns outto be insignificant.

The great thing about the X-YDiagram is that it is sort of an

unbiased way to approachdefinition around the process andWILL give you focus.

! "#$ &'( )*+,-+. */0

1 2 3445 6/ $) 34 *)$73*89:;455+3$ <43$73*+5 & =/ +7) + //$/ / 3#$*--$5+3*>$ *.<+;3 47 .653*<5$ ( =/ ?*7;56)$ +55 ( =/ 3#+3 +-$;6/34.$- 84;6/$)@

1 A +/ $) 47 3#$ 3$+ .=/ ;455$;3*>$ B4<*7*47/C

1 D -$+3$) 84- $>$-9 <-4E$;3

1 F$ >$- ;4.<5$3$)

1 G<)+3$) H#$7$>$- + <+-+.$ 3$- */ ;#+7,$)

! "4 /6..+-*I$J 3#$ & '( */ + 3$+.'K+/ $) <-*4-*3*I+ 3*47 3445 84- 3#$<43$73*+5 & =/

! L2M FNFO P " #*/ */ 743 -$+5 )+3+J 3#*/ */ 4-,+7*I$)

K-+*7/34-.*7,PP 23 3#$ ;47;56/ *47 48 3#$ <-4E$;3 946 .+9 -$+5*I $3#+3 3#$ 3#*7,/ 946 3#46,#3 H$-$ ;-*3*;+5 +-$ *7 8+;3 743 +/*.<4-3+73 +/ H+/ K$5*$>$)Q



116


The“

XY Diagram”

Using the Classified X s

Process Discovery

This is the X-Y Diagram. You should have a copy of this template. If possible open it and getfamiliar with it as we progress through this section.

! " #$%&'(#)*+( #$-*.#$/ 0$% 1.2+ 3#.4%#.15 6.'( 7)2'#)11%81$ 9 :/

.43%7'.2+ '($ ;< =>

! ?/ $ '($ 7)2'#)11%81$ 9 :/ @#)4 '($ A ./(8)2$ %2%15/ ./ ') .271*0$ .2 '($

9 B< C.%+#%4>

! D ($ +)%1 ./ ') ./)1%'$ '($ E.'%1 @$6 9 :/ @#)4 '($ '#.E.%1 4%25 9 :/ >

! F #)7$0*#$/ %20 G)./$ 9 :/ 6.11 8$ */$0 .2 '($ A HI J %' '($ $20 )@

'(./ 4)0*1$> K)6$E$#L

M J11 3#)7$0*#$/ 4*/ ' 8$ .2 ')'%1 7 )431.%27$>

! D(./ 4%5 #$-*.#$ /)4$ '53$ )@ $@@$7'.E$2$// 4$%/*#$>! D (./ 7)*10 #$0*7$ )# $1.4.2%'$ / )4$ )@ '($ 0$@$7'/ 7*##$2'15 /$$ 2 .2

'($ 3#)7$/ / N%11)6.2+ @)7*/ )2 7)2'#)11%81$ 9 :/O>

M G)./ $ '53$ .23*'/ .27#$%/$ #./& )@ 0$@$7'/ *20$# 7*##$2'

'$7(2)1)+5 )@ )3$#%'.)2 %20 '($#$@)#$L

! P27#$%/ $ Q F G )2 '($ A HI J 0)7*4$2' @#)4 %2 .23*'>

! K$13 .0$2'.@5 %#$%/ 2$$0.2+ .2E$/ '4$2' @)# % R*/'.@.$0 Q SP>

*Risk Priority Number



118


X-Y Diagram: Steps (cont.)

The template we haveprovided automaticallycalculates and sorts theranking shown here.

Process Discovery

For each X listed along theleft, rank its effect on eachcorresponding metric basedon a scale of 0, 1, 3 or 9.

You can use any scale youchoose however werecommend this on. If youuse a scale of 1 to 10 thiscan cause uncertaintywithin the team…is it a 6 ora 7, what’s the difference,etc.?

!"# %&' ( ) *+, -%./ #&01 +-, %22%'- "0 %&'( 3%-#+' 4&, %. "0 & , '& *% "2 5/ 6 "# 78

! " $ %&'()* +

! , $ -./' &0. 1

! 2 $ 340)

!" #$%&$' ( )*+,&-+&./ ,1. 2#$% 34 .#51 6 7 8 ,1. 9.&'1 , 34 .#51 :.,2&5;

<1. -23=* 5, 34 ,1#, &/ #==.= ,3'.,1.2 ,3 7.53 ). ,1. !" #$%&$' (;



120


Give me an F

give me an M

……

Failure Modes Effect Analysis (FMEA) is a structured approach to:

•

Predict failures and prevent their occurrence in manufacturing andother functional areas which generate defects.

• Identify the ways in which a process can fail to meet criticalcustomer requirements (Y).

• Estimate the Severity, Occurrence and Detection (SOD) of defects

• Evaluate the current Control Plan for preventing these failuresfrom occurring and escaping to the customer.

• Prioritize the actions that should be taken to improve and controlthe process using a Risk Priority Number (RPN).

Fishbone Diagram Exercise

Definition of FMEA

Failure Modes Effect Analysis or FMEA[*usually pronouncedas F-M-E-A (individualletters) or FEMA** (asa word)] is a structured

approach to: readbullets. FMEA at thispoint is developed withtribal knowledge with across-functional team.Later using processdata the FMEA can beupdated and betterestimates of detectionand occurrence can beobtained. The FMEA isnot a tool to eliminateX’s but rather controlthe X’s. It is only atool to identify potentialX’s and prioritize theorder in which the X’sshould be evaluated.

Process Discovery

!" #$%&'# )* +#%,&-# . ! "#$%# $' ()* +,$-"$.

/0,'- %1# ,'23".$%,3' 2"3. %1# 4,0153'#

$'$670,08

98 :0,'- %1# 4,0153'# ;,$- "$. <"#$%#+ #$"6,#"= <"#$%#

$' ()* +,$-"$.8

>8 ?"#0#'% "#0/6%0 %3 73/" .#'%3"8



121


System FMEA: Performed on a product or service product at the early concept/designlevel when various modules all tie together. All the module level FMEAs tie togetherto form a system. As you go lower into a system more failure modes are considered.

– Example: Electrical system of a car, consists of the following modules: battery,

wiring harness, lighting control module and alternator/regulator.

– System FMEA focuses on potential failure modes associated with the modulesof a system caused by design

Design DFMEA: Performed early in the design phase to analyze product fail modesbefore they are released to production. The purpose is to analyze how fail modesaffect the system and minimize them. The severity rating of a fail modeMUST becarried into the Process PFMEA.

Process PFMEA: Performed in the early quality planning phase of manufacturing toanalyze fail modes in manufacturing and transactional processes that may escape tothe customer. The failure modes and the potential sources of defects are rated andcorrective action taken based on a Pareto analysis ranking.

Equipment FMEA: used to analyze failure modes in the equipment used in a process todetect or make the part.

– Example: Test Equipment fail modes to detect open and short circuits.

History of FMEA

Types of FMEA

s

There are manydifferent types ofFMEA’s. The basicpremise is thesame.

Process Discovery

The “edge of your seat” info on the history of the FMEA! I’m sure you will all be sharing thiswith everyone tonight at the dinner table!

! "#$%&' %) *+,- .

! "#$%& (%)* #+ &,) -. /0 1% #+ &,) 2)$3%45 6) #+*(%&$7 *($#+8 &,)

243993 :#%%#3+%! ;+ -.<= &,) > 5?7 *)?)934)* @;ABCDEB- /F. $)85 $*#+8 &,) (%) 3G

"@H2

! ;+ &,) 95&) -. <0 1%I 5(&3:3&#?) 5449#65&#3+% *$#?)+ J7 9#5J#9#&7

63%&%I J)85+ &3 #+63$43$5&) "@H2 #+&3 &,) :5+58):)+& 3G &,)#$

4$36)%%)%

! 2(&3:3&#?) ;+*(%&$7 26&#3+ K $3(4 L2;2 K M +3N :5#+&5#+% &,)

"@H2 %&5+*5$* G3$ J3&, E)%#8+ 5+* O$36)%% "@H2 1%



122


Purpose of FMEA

Who Creates FMEAs and When?

FMEA’s are a team toollike most in this phase ofthe methodology. They areapplicable is most everyproject, manufacturing orservice based.

For all intensive purposesthey will be used inconjunction with yourproblem solving project to

characterize and measureprocess variables. In somecases the FMEA willmanifest itself as amanagement tool when theproject concludes and insome cases it will not beappropriate to be used inthat nature.

Process Discovery

!"#$%& '

! "#$%&'( *+( ,-./0*12 %(/0.30/0*12 .45 6.7(*1 &7 $%&5-8*6 9

! "48%(.6 ( 8-6*&#(% 6.*06 7.8*0&49

! : (5-8( $%&5-8* 5('(/&$#(4* *0#( .45 8&6*9

! ;&8-#(4* .45 *%.8< .8*0&46 *.<(4 *& %(5-8( %06< .450#$%&'( *+( $%&8(669

! = &8-6 &4 8&4*04-&-6 $%&3/(# $%('(4*0&4 4&* $%&3/(#

6&/'04>9

! "#$ &'()*$+ ,$-. /'01234

'3 - 50$-1,#0')4# 60'7$(,8

! 9:;<:= /#' #-+ '0 #-* -

0'>$ 23 +$ &23234? $@ $(),234?

'0 (#-34234 ,#$ 60'($** 8

! "#2* 23(>)+$*A

! 9 **'( 2- ,$ *

! "$(#32(-> = @6$0,*

! B )6$0C2*'0*

! D- 3- 4$ 0*

! = ,(8

! E0'($** FD= 9* *#')>+ 5$ *,-0,$+A

! 9, ,#$ ('3($6,)-> +$*243 6#-*$8

! E0'($** FD= 9* *#')>+ 5$ )6+-,$+A

! G#$3 -3 $@2*,234 +$*243 '0 60'($**

2* 5$234 (#-34$+8

! G#$3 (-00HI'C$0 +$*243* '0

60'($**$* /2>> 5$ )*$+ 23 3$/

-66>2(-,2'3* -3+ $3C20'3.$3,*8

! G#$3 - 60'5>$. *'>C234 *,)+H 2*('.6>$,$+ -3+ 3$$+* ,' 5$

+'().$3,$+8

! B H*,$. FD= 9* *#')>+ 5$ (0$-,$+ -&,$0

*H*,$. &)3(,2'3* -0$ +$&23$+ 5), 5$&'0$

*6$( 2&2( #-0+/-0$ 2* *$ >$(,$+8

! J$*243 FD= 9* *#')>+ 5$ (0$-,$+ /#$3

3$/ *H*,$.*? 60'+)(,* -3+ 60'($**$* -0$

5$234 +$*243$+8

!"#!"# !"$%!"$%



123


Why Create an FMEA?

The FMEA…

This is an FMEA. We have provided a template for you to use.

Process Discovery

FMEA’s help you manageRISK by classifying yourprocess inputs and monitoringtheir effects. This is extremely

important during the course ofyour project work.! "# $ %%%

!" $%&' '( %)(*+ ,%-.*&/ 0%*1-2". *& '3" 42(,".. %. $"11 %. '3"

42*5%26 7 8 ",(&+%26 9"'2*,. :

;. % 5"%&. '( 5%&%/"<

9

8

7

6

5

4

3

2

1

# ProcessFunctio

n

(Step)

PotentialFailure

Modes

(process

defects)

PotentialFailure

Effects

(Y's)

SE

V

Cl

a

s

s

PotentialCauses of

Failure

(X's)

OC

C

CurrentProcess

Controls

DE

T

RP

N

Recommend Actions Responsible Person &

Target

Date

TakenAction

s

SE

V

OC

C

DE

T

RP

N

9

8

7

6

5

4

3

2

1

# ProcessFunctio

n

(Step)

PotentialFailure

Modes

(process

defects)

PotentialFailure

Effects

(Y's)

SE

V

Cl

a

s

s

PotentialCauses of

Failure

(X's)

OC

C

CurrentProcess

Controls

DE

T

RP

N

Recommend Actions Responsible Person &

Target

Date

TakenAction

s

SE

V

OC

C

DE

T

RP

N



124


FMEA Components…#

FMEA Components…Process Step

The second column is the Name of the Process Step. The FMEA should sequentially follow thesteps documented in your Process Map.

! Phone!

Dial Number!

Listen for Ring!

Say Hello!

Introduce Yourself! Etc.

Process Discovery

The first columnhighlighted here is the“Process StepNumber ”.

!"# %&'() *+,-./ &( )"# 0'+*#(( 1 )#2 3-.4#'5

6

7

8

9

:

;)*5

R

P

N

D

E

T

O

C

C

S

E

V

Taken

Action

s

Responsibl

e Person &

Target

Date

Recommen

d Actions

R

P

N

D

E

T

Current

Process

Controls

O

C

C

Potential

Causes of

Failure

(X's)

C

l

a

s

s

S

E

V

Potential

Failure

Effects

(Y's)

Potential

Failure

Modes

(process

defects)

Process

Function

(Step)

# R

P

N

D

E

T

O

C

C

S

E

V

Taken

Action

s

Responsibl

e Person &

Target

Date

Recommen

d Actions

R

P

N

D

E

T

Current

Process

Controls

O

C

C

Potential

Causes of

Failure

(X's)

C

l

a

s

s

S

E

V

Potential

Failure

Effects

(Y's)

Potential

Failure

Modes

(process

defects)

Process

Function

(Step)

#

Enter the Name of the Process Step here. The FMEA shouldsequentially follow the steps documented in your Process Map.

Phone

Dial Number

Listen for Ring

Say Hello

Introduce Yourself

Etc.

# Process

Function

(Step)

Potential

Failure

Modes

(process

defects)

Potential

Failure

Effects

(Y's)

S

E

V

C

l

a

s

s

Potential

Causes of

Failure

(X's)

O

C

C

Current

Process

Controls

D

E

T

R

P

N

Recommen

d Actions

Responsibl

e Person &

Target

Date

Taken

Action

s

S

E

V

O

C

C

D

E

T

R

P

N



125


FMEA Components…Potential Failure Modes

FMEA Components…Potential Failure Effects

The fourthcolumnhighlightedhere is simplythe effect ofrealizing thepotentialfailure modeon the overallprocess andis focused onthe output ofeach step.

Thisinformation isusuallyobtained fromyour ProcessMap.

Process Discovery

The third column to the mode in which the process could potentially fail. These are the defectscaused by a C, P or N factor that could occur in the Process.

!"#$ &'('&$ )* )"' +*,' #- ."#/" )"' 0&*/'$$ /*12, 0*)'-)#3224 (3#25

! "'$ ' 3&' )"' ,'('/)$ /31$', 64 3 7 89 *& : (3/)*& )"3) /*12, *// 1&

#- )"' 9&*/'$$5

! "#$ #-(*&+3)#*- #$ *6)3#-', (&*+ ;#$)*&#/32 < '('/) <3)35

= > ?55@ (3#21&' +*,' #$ 3 (3-/ 4 -3+' (*& 3 ,'('/)5

R

PN

D

ET

O

CC

S

EV

Taken

Actions

Responsibl

e Person &Target

Date

Recommen

d Actions

R

PN

D

ET

Current

ProcessControls

O

CC

Potential

Causes ofFailure

(X's)

C

la

s

s

S

EV

Potential

FailureEffects

(Y's)

Potential

FailureModes

(process

defects)

Process

Function

(Step)

# R

PN

D

ET

O

CC

S

EV

Taken

Actions

Responsibl

e Person &Target

Date

Recommen

d Actions

R

PN

D

ET

Current

ProcessControls

O

CC

Potential

Causes ofFailure

(X's)

C

la

s

s

S

EV

Potential

FailureEffects

(Y's)

Potential

FailureModes

(process

defects)

Process

Function

(Step)

#

!"#$ #$ $#&'() *"+ +,,+-* ., /+0(#1#23 *"+ '.*+2*#0( ,0#(4/+

&.5+ .2 *"+ .6+/0(( '/.-+$ $ 7 8* ,.-4$ +$ .2 *"+ .4*'4*$

., +0-" $*+'7

!"#$ #2,./&0*#.2 -02 9+ .9*0#2+5 #2 *"+ :/.-+$$ ;0'7

R

P

N

D

E

T

O

C

C

S

E

V

Taken

Action

s

Responsibl

e Person &

Target

Date

Recommen

d Actions

R

P

N

D

E

T

Current

Process

Controls

O

C

C

Potential

Causes of

Failure

(X's)

C

l

a

s

s

S

E

V

Potential

Failure

Effects

(Y's)

Potential

Failure

Modes

(process

defects)

Process

Functio

n

(Step)

# R

P

N

D

E

T

O

C

C

S

E

V

Taken

Action

s

Responsibl

e Person &

Target

Date

Recommen

d Actions

R

P

N

D

E

T

Current

Process

Controls

O

C

C

Potential

Causes of

Failure

(X's)

C

l

a

s

s

S

E

V

Potential

Failure

Effects

(Y's)

Potential

Failure

Modes

(process

defects)

Process

Functio

n

(Step)

#



127


! " #$ &'()$*(+$, -.$, $+/$) 0+ /#$ -.$1(0', , *()$ 2$.$ )$1$*0-$) 30.

/#$ 4'/0 (+)', /.56

! " #(, 24, (+7*')$) 0+*5 4, 4 !"#$%&#'%(((()*+,"*& .%/ "&,/ 0*1 2*.1) 30.

50'. -.08$7/6! 9 0'. , $1$.(/5 :45 ;$ *(+<$) /0 (:-47 / 0+ /#$ ;',(+$, , 0. (:-47/ 0+

/#$ +$=/ 7',/0:$.> $/76

! "# %&'' ())* +" *),&() - "#. " %( / .&+).&0! "# %&'' ())* +" *),&() - "#. " %( / .&+).&011

0(* 2) / "(3 &3 +)(+ +4."#54"#+ -"#. 678 90(* 2) / "(3 &3+)(+ +4."#54"#+ -"#. 678 9

3 %,4/ 5.*#'/ ,6.0 768 8% 0#!7, $%9#'% ,7% 96&&68#'! : ; <; = >? @

&%2%&/ #' 6". 68' A.6B%+,/C

?> @> ?A

Applying Severity Ratings to Your Process

Sample Transactional Severities

Shown here is an example for severity guidelines developed for a financial services company.

Process Discovery

The actual definitions of the severity are not so important as the fact that the team remainsconsistent in its use of the definitions. The next slide shows a sample of transactional severities.

Effect Criteria: Impact of Effect Defined Ranking

Critical Business

Unit-wide

May endanger company’s ability to do business. Failure mode affects process

operation and / or involves noncompliance with government regulation.10

Critical Loss -

Customer

Specific

May endanger relationship with customer. Failure mode affects product delivered

and/or customer relationship due to process failure and/or noncompliance with

government regulation.

9

HighMajor disruption to process/production down situation. Results in near 100%

rework or an inability to process. Customer very dissatisfied.7

Moderate

Moderate disruption to process. Results in some rework or an inability to process.

Process is operable, but some work arounds are required. Customers experience

dissatisfaction.

5

Low

Minor disruption to process. Process can be completed with workarounds or

rework at the back end. Results in reduced level of performance. Defect is

noticed and commented upon by customers.

3

Minor


rework at the back end. Results in reduced level of performance. Defect noticed

internally, but not externally.

2

None No effect. 1


Critical Business

Unit-wide



Critical Loss -

Customer

Specific




9



Moderate



dissatisfaction.

5

Low




3

Minor




2

None No effect. 1


Critical Business

Unit-wide



Critical Loss -

Customer

Specific




9



Moderate



dissatisfaction.

5

Low




3

Minor




2

None No effect. 1



128


FMEA Components…Classification “Class”

Potential Causes of Failure (X

s)

The column “Potential Causes of the Failure”, highlighted here, refers to how the failure couldoccur.

This should also be obtained from the Fishbone Diagram.

Process Discovery

Recall the classifications of Procedural, Controllable and Noise developed when constructing yourProcess Map and Fishbone Diagram? Use those classifications from the Fishbone in the “Class” column, highlighted here, in the FMEA.

! "#$$ $&'(") *#+,-'./0, ,#*& $ +,1 #$ #2

! ! '3+.'""#4", 5! 6

! 7 .'*,)(.#" 57 6

! 8'/$, 586

9 &/$ /3:'.;#+/'3 *# 3 4, '4+#/3,) /3 +&, 7 .'*,$ $ <#1=

! "#$%"&&'(&) > ? :#*+'. +&#+ *#3 4, )/# ",) /3+' # $ 1,* /:/* $ ,++/3-@A#"(,= B '. ,C# ;1", 9 ,;1,.#+(., '.

B "'D=

*%"+ ),-%). > ? $ +#3)#.)/0,) $ ,+ ': #* +/A/+/,$ ",#)/3- +' .,#)/3,$$ ': # $ +,1= B '. ,C#;1", E #:,+F

! ';1"/#3*,G HI '*J KL(+ 9 #- KL(+=M

/"0.) K ? :#*+'. +&#+ *#3 3'+ 4, )/#",) /3 +' # $ 1,*/:/* $ ,++/3-@A#"(,= B '. ,C#;1", .#/3 /3 # ;/3,=

R

P

N

D

E

T

O

C

C

S

E

V

Taken

Action

s

Responsibl

e Person &

Target

Date

Recommen

d Actions

R

P

N

D

E

T

Current

Process

Controls

O

C

C

Potential

Causes of

Failure

(X's)

C

l

a

s

s

S

E

V

Potential

Failure

Effects

(Y's)

Potential

Failure

Modes

(process

defects)

Process

Functio

n

(Step)

# R

P

N

D

E

T

O

C

C

S

E

V

Taken

Action

s

Responsibl

e Person &

Target

Date

Recommen

d Actions

R

P

N

D

E

T

Current

Process

Controls

O

C

C

Potential

Causes of

Failure

(X's)

C

l

a

s

s

S

E

V

Potential

Failure

Effects

(Y's)

Potential

Failure

Modes

(process

defects)

Process

Functio

n

(Step)

#

!"#$%#&'( *'+,$, "- #.$ /'&(+0$ 0$-$0, #" ."1 #.$ -'&(+0$ 2"+(3 "22+04

5.&, &%-"06'#&"% ,."+(3 7$ "7#'&%$3 -0"6 #.$ /&,.7"%$ 8&'90'64

R

P

N

D

E

T

O

C

C

S

E

V

Taken

Action

s

Responsibl

e Person &

Target

Date

Recommen

d Actions

R

P

N

D

E

T

Current

Process

Controls

O

C

C

Potential

Causes of

Failure

(X's)

C

l

a

s

s

S

E

V

Potential

Failure

Effects

(Y's)

Potential

Failure

Modes

(process

defects)

Process

Functio

n

(Step)

# R

P

N

D

E

T

O

C

C

S

E

V

Taken

Action

s

Responsibl

e Person &

Target

Date

Recommen

d Actions

R

P

N

D

E

T

Current

Process

Controls

O

C

C

Potential

Causes of

Failure

(X's)

C

l

a

s

s

S

E

V

Potential

Failure

Effects

(Y's)

Potential

Failure

Modes

(process

defects)

Process

Functio

n

(Step)

#



129


FMEA Components…Occurrence“

OCC ”

Ranking Occurrence

The Automotive Industry Action Group, a consortium of the “Big Three”: Ford, GM and Chryslerdeveloped these Occurrence rankings.

Process Discovery

The column “Occurrence” highlighted here, refers to how frequently the specified failure isprojected to occur. This information should be obtained from Capability Studies or Historical DefectData in conjunction with the predetermined scale.

Probability of Failure Possible Failure Rates Cpk Ranking

Very High: Failure is almost

inevitable.

< 0.33 10

! 0.33 9

High: Generally associated with

processes similar to previous

processes that have often failed.

! 0.51 8

! 0.67 7

Moderate: Generally associated

with processes similar to previous

processes that have experienced

occasional failures but not in major

proportions.

! 0.83 6

! 1.00 5

! 1.17 4

Low: Isolated failures associated

with similar processes. !

1.33 3Very Low: Only isolated failures

associated with almost identical

processes.! 1.5 2

Remote: Failure is unlikely. No

failures ever associated with almost

identical processes.

! 1 in 2

1 in 3

1 in 8

1 in 20

1 in 80

1 in 400

1 in 2,000

1 in 15,000

1 in 150,000

" 1 in 1,500,000 ! 1.67 1



inevitable.

< 0.33 10

! 0.33 9




! 0.51 8

! 0.67 7





proportions.

! 0.83 6

! 1.00 5

! 1.17 4





processes.! 1.5 2




! 1 in 2

1 in 3

1 in 8

1 in 20

1 in 80

1 in 400

1 in 2,000

1 in 15,000

1 in 150,000

" 1 in 1,500,000 ! 1.67 1



inevitable.

< 0.33 10

! 0.33 9




! 0.51 8

! 0.67 7





proportions.

! 0.83 6

! 1.00 5

! 1.17 4





processes.! 1.5 2




! 1 in 2! 1 in 2

1 in 3

1 in 8

1 in 20

1 in 80

1 in 400

1 in 2,000

1 in 15,000

1 in 150,000

" 1 in 1,500,000" 1 in 1,500,000 ! 1.67 1

Potential Failure Mode and Effects Analysis (FMEA), Reference Manual, 2002. Pg. 35.. Chrysler Corporation, Ford

Motor Company, General Motors Corporation.

# Process

Function

(Step)

Potential

Failure

Modes

(process

defects)

Potential

Failure

Effects

(Y's)

S

E

V

C

l

a

s

s

Potential

Causes of

Failure

(X's)

O

C

C

Current

Process

Controls

D

E

T

R

P

N

Recommen

d Actions

Responsibl

e Person &

Target

Date

Taken

Action

s

S

E

V

O

C

C

D

E

T

R

P

N



130


FMEA Components…Current Process Controls

FMEA Components…Detection (DET)

Process Discovery

The column “Current Process Controls” highlighted here refers to the three types of controls that arein place to prevent a failures.

! "##$%& ( #)*$+ + ! )%&#),+ #$-$#+ &) &.$ &.#$$ &/0$+ )- *)%&#),+ &.1& 1#$

2% 0,1*$ &) 0#$3$%& 1 -12,"#$ 2% 42&. &.$ 5 6+ 7 8 .$ 9 &/0$+ )- *)%&#),+ 1#$:

;< ( ! =< &1&2+&2*1, (#)*$+ + ! )%&#),>

;( )?$@A )?$ B =C2+&1?$ ( #))-2%D>

;E$&$*&2)% 1-&$# F 12,"#$

R

P

N

D

E

T

O

C

C

S

E

V

Taken

Action

s

Responsibl

e Person &

Target

Date

Recommen

d Actions

R

P

N

D

E

T

Current

Process

Controls

O

C

C

Potential

Causes of

Failure

(X's)

C

l

a

s

s

S

E

V

Potential

Failure

Effects

(Y's)

Potential

Failure

Modes

(process

defects)

Process

Function

(Step)

# R

P

N

D

E

T

O

C

C

S

E

V

Taken

Action

s

Responsibl

e Person &

Target

Date

Recommen

d Actions

R

P

N

D

E

T

Current

Process

Controls

O

C

C

Potential

Causes of

Failure

(X's)

C

l

a

s

s

S

E

V

Potential

Failure

Effects

(Y's)

Potential

Failure

Modes

(process

defects)

Process

Function

(Step)

#

!"# %&'(")*+ !"#$ &# $' ( #)*+#, *"-. &'/'(*0 1

!"#"$#%&' %) *' * ))") )+"'# &, #-" ./&0*0%1%#2 #-*# #-" ./&.&)"3 #2."

&, $&'#/&1 4%11 3"#"$# * )50)"65"'# ,*%15/" +&3"7

8 -%) %',&/+*#%&' ) -&513 0" &0#*%'"3 ,/&+ 2&5/ 9"*) 5/"+"'# : 2) #"+

;'*12)%) : #53%") *'3 #-" < /&$") ) 9*.7 ; /*#%'= ) -&513 0" *) ) %=' %'

$&'>5'$#%&' 4%#- #-" ./"3"#"/+%'"3 )$*1"7

R

P

N

D

E

T

O

C

C

S

E

V

Taken

Action

s

Responsibl

e Person &

Target

Date

Recommen

d Actions

R

P

N

D

E

T

Current

Process

Controls

O

C

C

Potential

Causes of

Failure

(X's)

C

l

a

s

s

S

E

V

Potential

Failure

Effects

(Y's)

Potential

Failure

Modes

(process

defects)

Process

Functio

n

(Step)

# R

P

N

D

E

T

O

C

C

S

E

V

Taken

Action

s

Responsibl

e Person &

Target

Date

Recommen

d Actions

R

P

N

D

E

T

Current

Process

Controls

O

C

C

Potential

Causes of

Failure

(X's)

C

l

a

s

s

S

E

V

Potential

Failure

Effects

(Y's)

Potential

Failure

Modes

(process

defects)

Process

Functio

n

(Step)

#



131


Ranking Detection

Risk Priority Number“

RPN ”

The “The Risk PriorityNumber ” highlighted hereis a value that will be usedto rank order the concernsfrom the process.

We provided you with atemplate which willautomatically calculate thisfor you based on yourinputs for Severity,

Occurrence and Detection.

Process Discovery

The Automotive Industry Action Group, a consortium of the “Big Three”: Ford, GM and Chryslerdeveloped these Detection criteria.

Almost Impossible

DetectionCriteria: The likelihood that the existence of a defect will

be detected by the test content before the product

advances to the next or subsequent processRanking

Test content must detect < 80% of failures 10

Very Remote Test content must detect 80% of failures 9

Remote Test content must detect 82.5% of failures 8

Very Low Test content must detect 85% of failures 7

Low Test content must detect 87.5% of failures 6

Moderate Test content must detect 90% of failures 5

Moderately High Test content must detect 92.5% of failures 4

High Test content must detect 95% of failures 3

Very High Test content must detect 97.5% of failures 2

Almost Certain Test content must detect 99.5% of failures 1

Almost Impossible

DetectionCriteria: The likelihood that the existence of a defect will

be detected by the test content before the product

advances to the next or subsequent processRanking

Test content must detect < 80% of failures 10

Very Remote Test content must detect 80% of failures 9

Remote Test content must detect 82.5% of failures 8

Very Low Test content must detect 85% of failures 7

Low Test content must detect 87.5% of failures 6

Moderate Test content must detect 90% of failures 5

Moderately High Test content must detect 92.5% of failures 4

High Test content must detect 95% of failures 3

Very High Test content must detect 97.5% of failures 2

Almost Certain Test content must detect 99.5% of failures 1

Potential Failure Mode and Effects Analysis (FMEA), AIAG Reference Manual, 2002 Pg. 35.. Chrysler Corporation,

Ford Motor Company, General Motors Corporation.

!"# % &'( ) *&+*&,- ./01#* &' 2 324/# ,"2, 5&44 1# /'#6 ,+ *27( +*6#*

,"# 8+78#*7' 9*+0 ,"# :*+8#'';

!"# % ) . &' ,"# :*+6/8, +9< = #3#*&,-< >88 /**#78# 276 ? #,#8, 21&4&,-2' *#:*#' #7,#6 "#*#@

% ). A B= C DEFB>G G EFB?C !E

R

P

N

D

E

T

O

C

C

S

E

V

Taken

Action

s

Responsibl

e Person &

Target

Date

Recomme

nd Actions

R

P

N

D

E

T

Current

Process

Controls

O

C

C

Potential

Causes of

Failure

(X's)

C

l

a

ss

S

E

V

Potential

Failure

Effects

(Y's)

Potential

Failure

Modes

(processdefects)

Process

Functio

n

(Step)

# R

P

N

D

E

T

O

C

C

S

E

V

Taken

Action

s

Responsibl

e Person &

Target

Date

Recomme

nd Actions

R

P

N

D

E

T

Current

Process

Controls

O

C

C

Potential

Causes of

Failure

(X's)

C

l

a

ss

S

E

V

Potential

Failure

Effects

(Y's)

Potential

Failure

Modes

(processdefects)

Process

Functio

n

(Step)

#



132


FEMA Components…Actions

FMEA Components…Adjust RPN

Process Discovery

The columns highlighted here are a type of post FMEA. Remember to update the FMEA throughoutyour project, this is what we call a “Living Document” as it changes throughout your project.

! "# $%%"&'"' ) #*+$&, -"."-, *$ */" 0#*+1+*2 .$- */" 3-"1"&*+$& $. 0

'"."#*4

! ", 3$&,+56" 7 "-,$& 8 90*" -"."-, *$ */" &0%" $. */" :-$;3 $- 3"-,$&

-",3$&,+56" .$- #$%36"*+&: */" 0#*+1+*2 0&' </"& */"2 <+66 #$%36"*" +*4

= 0>"& ) #*+$& -"."-, *$ */" 0 #*+$& 0&' ".."#*+1" '0*" 0.*"- +* /0, 5""&

#$%36"*"'4

R

P

N

D

E

T

O

C

C

S

E

V

Taken

Action

s

Responsibl

e Person &

Target

Date

Recommen

d Actions

R

P

N

D

E

T

Current

Process

Controls

O

C

C

Potential

Causes of

Failure

(X's)

C

l

a

s

s

S

E

V

Potential

Failure

Effects

(Y's)

Potential

Failure

Modes

(process

defects)

Process

Function

(Step)

# R

P

N

D

E

T

O

C

C

S

E

V

Taken

Action

s

Responsibl

e Person &

Target

Date

Recommen

d Actions

R

P

N

D

E

T

Current

Process

Controls

O

C

C

Potential

Causes of

Failure

(X's)

C

l

a

s

s

S

E

V

Potential

Failure

Effects

(Y's)

Potential

Failure

Modes

(process

defects)

Process

Function

(Step)

#

!"#$ &'$ ($#)**$"+$+ ,#&-)"./ ($.0)".-12$ 3$4.)" 5 67&$/

879$" ,#&-)" '7:$ 1$$" #)*02$&$+ &'$ ; $:$4-&</ !##=44$"#$ 7"+

6$&$#&-)" .')=2+ 1$ 7+>=.&$+? 8 '-. @-22 4$.=2& -" 7 "$@ ( 3 A 47&-"B?

RP

N

DE

T

OC

C

SE

V

Taken Action

s

Responsible Person &

Target

Date

Recommend Actions

RP

N

DE

T

CurrentProcess

Controls

OC

C

PotentialCauses of

Failure

(X's)

Cl

a

s

s

SE

V

PotentialFailure

Effects

(Y's)

PotentialFailure

Modes

(process

defects)

ProcessFunction

(Step)

# RP

N

DE

T

OC

C

SE

V

Taken Action

s

Responsible Person &

Target

Date

Recommend Actions

RP

N

DE

T

CurrentProcess

Controls

OC

C

PotentialCauses of

Failure

(X's)

Cl

a

s

s

SE

V

PotentialFailure

Effects

(Y's)

PotentialFailure

Modes

(process

defects)

ProcessFunction

(Step)

#

The columns highlighted here are the adjusted levels based on the actions you have taken within theprocess.



133


FMEA Exercise

Process Discovery

! "#$%&' # )*+#%,&-#. !""#$%&# ()*+ ,#-$ ./ )+0#+

,) 1+#-,# - 2 34 ! *" ./5 ,6# ./7)+$-,.)/

5#/#+-,#0 7+)$ ,6# 8 +)1#" " 3-9: 2 ."6%)/#;.-5+-$ -/0 < => ;.-5+-$?

@? A # 9+#9-+#0 ,) 9+#" #/, +#" *&," ,) ()*+ $#/,)+?

/0 1#234 5#,6'7#, ,82, 9:! ;<

OK Team, let

s

get that FMEA



134



Notes

You have now completed Measure Phase – Process Discovery.

! Create a high-level Process Map

!

Create a Fishbone Diagram

!

Create an X-Y Diagram

! Create an FMEA

! Describe the purpose of each tool and when it should be used

Process Discovery



135


Lean Six Sigma

Black Belt Training

Now we will continue in the Measure Phase with “Six Sigma Statistics”.

Measure PhaseSix Sigma Statistics



136


Six Sigma Statistics

Overview

Purpose of Basic Statistics

Statistics is the basic language of Six Sigma. A solid understanding of Basic Statistics is thefoundation upon which many of the subsequent tools will be based.

Having an understanding of Basic Statistics can be quite valuable. Statistics however, like anything,

can be taken to the extreme.

In this module you will learn how yourprocesses speak to you in the form ofdata. If you are to understand thebehaviors of your processes, then you

must learn to communicate with theprocess in the language of data.

The field of statistics provides the toolsand techniques to act on data, to turndata into information and knowledgewhich you will then use to makedecisions and to manage yourprocesses.

The statistical tools and methods thatyou will need to understand and

optimize your processes are notdifficult. Use of Excel spreadsheets orspecific statistical analytical softwarehas made this a relatively easy task.

In this module you will learn basic, yet powerful analytical approaches and tools to increase yourability to solve problems and manage process behavior.

•

Provide a numerical summary of the data being analyzed.

– Data (n)

•

Factual information organized for analysis.

•

Numerical or other information represented in a form suitable for processing by

computer

•

Values from scientific experiments.

• Provide the basis for making inferences about the future.

•

Provide the foundation for assessing process capability.

•

Provide a common language to be used throughout an organization to

describe processes.

Relax….it won

t

be that bad

Basic Statistics purpose:



137


Purpose of Basic Statistics (Cont.)

Use this as a cheat sheet, don’t bother memorizing all of this. Actually most of the notation in Greekis for population data.

But it is not the need or the intent of this course to do that, nor is it the intent of Six Sigma. It canbe stated that Six Sigma does not make people into statisticians, rather it makes people intoexcellent problem solvers by using appropriate statistical techniques.

Data is like crude oil that comes out of the ground. Crude oil is not of much good use. However if the crude oil is refined many useful products occur; such as medicines, fuel, food products,lubricants, etc. In a similar sense statistics can refine data into usable “products” to aid indecision making, to be able to see and understand what is happening, etc

Statistics is broadly used by just about everyone today. Sometimes we just don’t realize it.Things as simple as using graphs to better understand something is a form of statistics, as arethe many opinion and political polls used today. With easy to use software tools to reduce thedifficulty and time to do statistical analyses, knowledge of statistics is becoming a commoncapability amongst people.

An understanding of Basic Statistics is also one of the differentiating features of Six Sigma and it

would not be possible without the use of computers and programs like MINITAB™. It has beenobserved that the laptop is one of the primary reasons that Six Sigma has become both popularand effective.


Statistical Notation – Cheat Sheet

An individual value, an observation

A particular (1st) individual value

For each, all, individual values

The mean, average of sample data

The grand mean, grand average

The mean of population data

A proportion of sample data

A proportion of population data

Sample size

Population size

An individual value, an observation

A particular (1st) individual value

For each, all, individual values

The mean, average of sample data

The grand mean, grand average

The mean of population data

A proportion of sample data

A proportion of population data

Sample size

Population size

Summation

The standard deviation of sample data

The standard deviation of population data

The variance of sample data

The variance of population data

The range of data

The average range of data

Multi-purpose notation, i.e. # of subgroups, #

of classes

The absolute value of some term

Greater than, less than

Greater than or equal to, less than or equal to

Summation

The standard deviation of sample data

The standard deviation of population data

The variance of sample data

The variance of population data

The range of data

The average range of data

Multi-purpose notation, i.e. # of subgroups, #

of classes

The absolute value of some term

Greater than, less than

Greater than or equal to, less than or equal to



138


Parameters vs. Statistics

The purpose of sampling is:To get a “sufficiently accurate” inference for considerably less time, money, and other resources,and also to provide a basis for statistical inference; if sampling is done well, and sufficiently, thenthe inference is that “what we see in the sample is representative of the population”

A population parameter is a numerical value that summarizes the data for an entire population, asample has a corresponding numerical value called a statistic .

The population is a collection of all the individual data of interest. It must be defined carefully,such as all the trades completed in 2001. If for some reason there are unique subsets of trades itmay be appropriate to define those as a unique population, such as, “all sub custodial markettrades completed in 2001” or “emerging market trades”.

Sampling frames are complete lists and should be identical to a population with every elementlisted only once. It sounds very similar to population… and it is. The difference is how it is used. A sampling frame, such as the list of registered voters, could be used to represent the populationof adult general public. Maybe there are reasons why this wouldn’t be a good sampling frame.Perhaps a sampling frame of licensed drivers would be a better frame to represent the generalpublic.

The sampling frame is the source for a sample to be drawn.

It is important to recognize the difference between a sample and a population because wetypically are dealing with a sample of the what the potential population could be in order to makean inference. The formulas for describing samples and populations are slightly different. In mostcases we will be dealing with the formulas for samples.


! "#$%&'(") ! &+&,-'-+./

! "#$%&'( %$) +( ,)#$-%$./, .0 1 -.-231%$./

! 45 ! 5 65 !75 8

Population

Sample

Sample

Sample

Population

SampleSample

SampleSample

SampleSample

0 &,#%- 0 '&'(. '(1 . /

! "#$%&'(%$) +( ,)#$-%$./, .0 1

,1'-3(

! 9 :;1 # 5 , 5 - 5 , 75 /

!"#$%&'(") < "33 %&( $%(', %&1% &1=( %&( >-#.-(#%? .0 $/%(#(,%@ 2/+(# , %2+?A

2+&,-< "/ $+(/%$0$1;3( ,2;,(% .0 %&( -.-231%$./A

0 &,#%-< " , $B/$0$)1 /%3? ,'133(# ,2;, (% .0 %&( -.-231%$./ 2,(+ %. '1C( 1/ $/0(#(/)(A



139


Types of Data

The nature of data is important to understand. Based on the type of data you will have the option toutilize different analyses.

Data, or numbers, are usually abundant and available to virtually everyone in the organization.Using data to measure, analyze, improve and control processes forms the foundation of the SixSigma methodology. Data turned into information, then transformed into knowledge, lowers the risksof decision. Your goal is to make more decisions based on data versus the typical practices of “Ithink”, “I feel” and “In my opinion”.

One of your first steps in refining data into information is to recognize what the type of data it is thatyou are using. There are two primary types of data, they are Attribute and Variable Data.

Attribute Data is also called qualitative data. Attribute Data is the lowest level of data. It is purelybinary in nature. Good or bad, yes or no type data. No analysis can be performed on Attribute Data. Attribute Data must be converted to a form of Variable Data called Discrete Data in order to becounted or be useful.

Discrete Data is information that can be categorized into a classification. Discrete Data is based oncounts. It is typically things counted in whole numbers. Discrete Data is data that can't be brokendown into a smaller unit to add additional meaning. Only a finite number of values is possible andthe values cannot be subdivided meaningfully. For example, there is no such thing as a half of

defect or a half of a system lockup.

Continuous Data is information that can be measured on a continuum or scale. Continuous Data,also called quantitative data can have almost any numeric value and can be meaningfullysubdivided into finer and finer increments, depending upon the precision of the measurementsystem. Decimal sub-divisions are meaningful with Continuous Data. As opposed to Attribute Datalike good or bad, off or on, etc., Continuous Data can be recorded at many different points (length,size, width, time, temperature, cost, etc.). For example 2.543 inches is a meaningful number,whereas 2.543 defects does not make sense.

Later in the course we will study many different statistical tests but it is first important to understand

what kind of data you have.


! ""#$%&"' )*"* +,&*-$"*"$. '/

! "# %&'% (# )*+%,(- ./0,0 %,0 1+&( .'1 21# # *)&0 3% &40# 56- 78

9 : 0# - ;1

9 <1- ;1 =1

9 >%## ?@%*&

0*#$*%-' )*"* +,&*1"$"*"$.'/

! A*#B,0.0 5C 14+.8 A%.%

9 C %+ )0 B%.0=1,*D0E *+ % B&%## *F*B%.*1+ %+E *# )%#0 E 1+ B14+.#G

! ;4H)0, 1F E0F0B .#

! ;4H)0, 1F E0F0B .*30 4+*.#

! ;4H)0, 1F B 4# .1H0, ,0.4,+#

! C 1+.*+414# A%.%

9 C %+ )0 H0%#4,0E 1+ % B1+.*+44H- *. /%# E0B*H%& #4)E*3*#*1+# ./%. %,0

H0%+*+=F4&

! I *H0- > ,0# # 4,0- C 1+30(1, J 200E- K%.0,*%& F00E ,%.0

! K1+0(

! > ,0# #4,0

! C 1+30 (1, J 200E

! K%.0,*%& F00E ,%.0



140


Discrete Variables

Continuous Variables


Shown here are additional Discrete Variables. Can you think of others within your business?

Shown here are additional Continuous Variables. Can you think of others within your business?

!"" $%&" '()*%$+ *%,-%%' .// &'0 !1 -2%$% ! 3+,2% "&$4%+, 4"(56+% $%&03'4 3' &"" +(52 3'03730(&"+

82% *"660 4"(56+% $%&03'4 96$ ,26+% 3'03730(&"+2&73'4 4"(56+% $%&03'4+ %:(&" ,6 6$ 4$%&,%$ ,2&'

.//

!"" ,2% $%&" '()*%$+ *%,-%%' " &'0 ;</1///1

-2%$% " 3+ ,2% + )&""%+, 26(+%26"0 3'56)% 3' ,2%

=6=("&,36'

82% 26(+%26"0 3'56)% 96$ 26(+%26"0+ -3,2

3'56)%+ "%++ ,2&' 6$ %:(&" ,6 ;</1///

!"" ,2% $%&" '()*%$+ *%,-%%' " &'0 !1 -2%$% " 3+

,2% + )&""%+, &)6(', 69 ,3)% + %$7%0 &'0 ! 3+ ,2%

"&$4%+,>

82% "%'4,2 69 =$3+6' ,3)% +%$7%0 96$ 3'03730(&"+

56'735,%0 69 93$+, 0%4$%% )($0%$

! "# # $%&' )*&+'# ,"- ./' )*-$*%&'0 "1.$1+"+# )*-$*%&'

!"" $%&" '()*%$+ *%,-%%' .// &'0 !1 -2%$% ! 3+,2% "&$4%+, 4"(56+% $%&03'4 3' &"" +(52 3'03730(&"+

82% *"660 4"(56+% $%&03'4 96$ ,26+% 3'03730(&"+2&73'4 4"(56+% $%&03'4+ %:(&" ,6 6$ 4$%&,%$ ,2&'

.//

!"" ,2% $%&" '()*%$+ *%,-%%' " &'0 ;</1///1

-2%$% " 3+ ,2% + )&""%+, 26(+%26"0 3'56)% 3' ,2%

=6=("&,36'

82% 26(+%26"0 3'56)% 96$ 26(+%26"0+ -3,2

3'56)%+ "%++ ,2&' 6$ %:(&" ,6 ;</1///

!"" ,2% $%&" '()*%$+ *%,-%%' " &'0 !1 -2%$% " 3+

,2% + )&""%+, &)6(', 69 ,3)% + %$7%0 &'0 ! 3+ ,2%

"&$4%+,>

82% "%'4,2 69 =$3+6' ,3)% +%$7%0 96$ 3'03730(&"+

56'735,%0 69 93$+, 0%4$%% )($0%$

! "# # $%&' )*&+'# ,"- ./' )*-$*%&'0 "1.$1+"+# )*-$*%&'



141


•

Nominal Scale – data consists of names, labels, or categories. Cannot bearranged in an ordering scheme. No arithmetic operations are performed

for nominal data.

• Ordinal Scale – data is arranged in some order, but differences between

data values either cannot be determined or are meaningless.

• Interval Scale – data can be arranged in some order and for which

differences in data values are meaningful. The data can be arranged in an

ordering scheme and differences can be interpreted.

• Ratio Scale – data that can be ranked and for which all arithmetic

operations including division can be performed. (division by zero is ofcourse excluded) Ratio level data has an absolute zero and a value of

zero indicates a complete absence of the characteristic of interest.

Understanding the nature of data and how to represent it

can affect the types of statistical tests possible.

Definitions of Scaled Data

Nominal Scale

Shown here are the four types of scales. It is important to understand these scales as they willdictate the type of statistical analysis that can be performed on your data.

Listed are someexamples ofNominal Data.The only analysisis whether theyare different ornot.


Qualitative Variable Possible nominal level data values for

the variable

Blood Types A, B, AB, O

State of Residence Alabama,!, Wyoming

Country of Birth United States, China, other

Time to weigh in



142


Ordinal Scale

Interval Scale

These are examples ofOrdinal Data.

These are examples of Interval Data.


! "#$$ &' ! "#$$ &&' ! "#$$ &&&'

(#)*+ , -#. /-

0#$-1#"" 2-#3 4"#$$5654#25*7

8 **+' .**9' -:4-""-728 +*9/42 +#257.

; /14*3<#42' 4*3<#4 2'

572-+3-95#2-' 6/"" $5=-' "/:/+>

&/2*3*15"- ; 5=-$

! "# # $%&' )*+$,-& &'.'& +-/-

.-&0'#

10- &$/-/$.' 2-*$-%&'

! "#$$ &' ! "#$$ &&' ! "#$$ &&&'

(#)*+ , -#. /-

0#$-1#"" 2-#3 4"#$$5654#25*7

8 **+' .**9' -:4-""-728 +*9/42 +#257.

; /14*3<#42' 4*3<#4 2'

572-+3-95#2-' 6/"" $5=-' "/:/+>

&/2*3*15"- ; 5=-$

! "# # $%&' )*+$,-& &'.'& +-/-

.-&0'#

10- &$/-/$.' 2-*$-%&'

!""#

$%&' )*++','-.' /'%0''- 1 .2,'1

*1 3'415,4/6' 4-) &41

3'4-*-7 /5% 4 )*++','-.' 2+ 8"

92*-%1 /'%0''- !"" 4-) !8"

)2'1 -2% *-)*.4%' %&4% 2-'

1%5)'-% *1 !:8 %*3'1 32,'

*-%'66*7'-% ;

<= 1.2,'1 2+ 1 %5)'-%1 *-

> 64.?> '6% @,4*-*-7

! "# # $%&' ) * "+'#,-.'+/0& 10+$0%&'

!""#

$%&' )*++','-.' /'%0''- 1 .2,'1

*1 3'415,4/6' 4-) &41

3'4-*-7 /5% 4 )*++','-.' 2+ 8"

92*-%1 /'%0''- !"" 4-) !8"

)2'1 -2% *-)*.4%' %&4% 2-'

1%5)'-% *1 !:8 %*3'1 32,'

*-%'66*7'-% ;

<= 1.2,'1 2+ 1 %5)'-%1 *-

> 64.?> '6% @,4*-*-7

! "# # $%&' ) * "+'#,-.'+/0& 10+$0%&'



143


•

Continuous Data is always more desirable

• In many cases Attribute Data can be converted to

Continuous

• Which is more useful?

– 15 scratches or Total scratch length of 9.25

– 22 foreign materials or 2.5 fm/square inch

–

200 defects or 25 defects/hour

Ratio Scale

Shown here is anexample of Ratio Data.

Converting Attribute Data to Continuous Data

Continuous Dataprovides us moreopportunity forstatistical analyses. Attribute Data can oftenbe converted toContinuous byconverting it to a rate.


! #

$%& '()*+, - .+,*/0(* 12 3)40* +& &45 4,6

'()*+, 7 .+,*/0(* 2! 3)40*8 9( .4, *4:

5;45 '()*+, 7 .+,*/0(* 59<.( 4* 0/.; &45

4* '()*+, -= %& 4 '()*+, > . +,*/0(* ?()+

3)40* +& &45 '() 64:8 9( .4, *4: 5;()( <* 4

.+0'@(5( 4 A*(,. ( +& &45 .+,*/0(6 +, 5;45

64:= B+5( 5;45 4 )45<+ <* <,5()')(54A@( 4,6

4, 4A*+@/5( ?()+ (C<*5*=D

E )40* +& &45 .+,*/0(6 '() 46/@5 <, 5;(

F,<5(6 G 545(*

!"# #$%&' ) *"+'#, -.$" /-+$-%&'

! #

$%& '()*+, - .+,*/0(* 12 3)40* +& &45 4,6

'()*+, 7 .+,*/0(* 2! 3)40*8 9( .4, *4:

5;45 '()*+, 7 .+,*/0(* 59<.( 4* 0/.; &45

4* '()*+, -= %& 4 '()*+, > . +,*/0(* ?()+

3)40* +& &45 '() 64:8 9( .4, *4: 5;()( <* 4

.+0'@(5( 4 A*(,. ( +& &45 .+,*/0(6 +, 5;45

64:= B+5( 5;45 4 )45<+ <* <,5()')(54A@( 4,6

4, 4A*+@/5( ?()+ (C<*5*=D

E )40* +& &45 .+,*/0(6 '() 46/@5 <, 5;(

F,<5(6 G 545(*

!"# #$%&' ) *"+'#, -.$" /-+$-%&'



144


!"#$ %&"$ () * (+ #,-(. /+ ".,&#0 ,".1". + 23

! "#$ %

! "#&'$ % ! ")&#

!"#$%&"$ () 4#&-#,-(. /1-$ 5"&$ -(.3

! * $%+#

! ,%-#./0$ .-'1# * $%+#

! 2 -$%&$.& &#3'$-')%

! 4$.'$%5 #

Descriptive Statistics


We will review theDescriptive Statistics shownhere which are the most

commonly used.

1) For each of the measuresof location, how alike ordifferent are they?

2) For each measure ofvariation, how alike ordifferent are they?

3) What do these similaritiesor differences tell us?

We are going to usethe worksheet shownhere to create graphs

and statistics. Openthe workbook“Measure DataSets.xls” and select the“Basic Statistics” worksheet.

Change the Start Pointand the Bin Width asshown and click UpdateChart. Typically onewould use the default

values but thesechanges produce acleaner histogram.




145


Measures of Location

The physical centerof a data set is theMedian andunaffected by largedata values. Thisis why people useMedian whendiscussing average

salary for an American worker,people like BillGates and WarrenBuffet skew theaverage number.


Mean are the most common measure of location. A “Mean”, implies that you are talking about thepopulation or inferring something about the population. Conversely, average, implies somethingabout sample data.

To produce chart, SigmaXL>Graphical Tools>Basic Histogram, Select Data, as “Numeric DataVariable (Y)”. Set Start Point to 4.97 and Bin width to 0.01 then click update chart. Please selectDescriptive Statistics. After clicking OK, the X axis should be modified to show 2 decimal places.

Note, that Descriptive Statistics are also available in SigmaXL>Statistical Tools>DescriptiveStatistics, and SigmaXL>Graphical Tools>Histograms & Descriptive Statistics.

Although thesymbol isdifferent,there is nomathematicaldifferencebetween theMean of asample andMean of apopulation.



146


Measures of Location (cont.)

The Trimmed Mean (highlighted above) is less susceptible to the effects of extreme scores.

SigmaXL® does not include Trimmed Mean, but Excel’s native function can be used as shownabove. We will explain each part of this formula next.




147


Measures of Location (cont.)


It is possible to have multiple Modes. When this happens it’s called Bi-modal Distributions. Herewe only have one; Mode = 5.



148


Measures of Variation


A range is typically used for small data sets which is completely efficient in estimating variation fora sample of 2. As your data increases the Standard Deviation is a more appropriate measure ofvariation.

The Standard Deviation for a sample and population can be equated with short and long-termvariation. Usually a sample is taken over a short period of time making it free from the typesof variation that can accumulate over time so be aware. We will explore this further at a laterpoint in the methodology.



149


Measures of Variation (cont.)

The Variance is the square of the Standard Deviation. It is common in statistical tests where it isnecessary to add up sources of variation to estimate the total. Standard Deviations cannot beadded, variances can.

Normal Distribution

The Normal Distribution is the most recognized distribution in

statistics.

What are the characteristics of a Normal Distribution?

–

Only random error is present –

Process free of assignable cause

– Process free of drifts and shifts

So what is present when the data is Non-normal?

We can begin to discuss the Normal Curve and its properties once we understand the basicconcepts of central tendency and dispersion.

As we begin to assess our distributions know that sometimes it’s actually more difficult to determinewhat is effecting a process if it is Normally Distributed. When we have a Non-normal Distributionthere is usually special or more obvious causes of variation that can be readily apparent uponprocess investigation.




150


The Normal Curve

The Normal Distributionis the most commonlyused and abused

distribution in statisticsand serves as thefoundation of manystatistical tools whichwill be taught later in themethodology.

Normal Distribution

The shape of theNormalDistribution is afunction of 2parameters, (theMean and theStandardDeviation).

We will convert theNormalDistribution to the

standard Normal inorder to comparevarious NormalDistributions andto estimate tailarea proportions.


By normalizing the Normal Distribution this converts the raw scores into standard Z-scores with aMean of 0 and Standard Deviation of 1, this practice allows us to use the Z-table.



151


Normal Distribution (cont.)

Empirical Rule

The area under the curve between any two points represents the proportion of the distribution. Theconcept of determining the proportion between 2 points under the standard Normal curve is a criticalcomponent to estimating Process Capability and will be covered in detail in that module.

The Empiricalrule allows us topredict or moreappropriatelymake anestimate of howour process isperforming. Youwill gain a greatdeal of

understandingwithin theProcessCapabilitymodule. Noticethe differencebetween +/- 1SD and +/- 6 SD.




153


Tools for Assessing Normality

Goodness-of-Fit

Anderson-Darling test assesses how closely actual frequency at a given value corresponds to the

theoretical frequency for a Normal Distribution with the same Mean and Standard Deviation.

The AndersonDarling test yields astatisticalassessment (called

a goodness-of-fittest) of Normalityand the SigmaXL®

version of theNormal Probabilitytest produces agraph to visuallydemonstrate justhow good that fit is.


Watch that curve



154


The Normal Probability Plot

graph shows you which values tend to deviate from the Normal Curve.



Open theworksheet tab“ Amount ”.

The graphshows theprobabilitydensity of yourdata plottedagainst theexpected densityof a Normalcurve. Noticethat the y-axis(probability)

does notincrease linearly.Normal data willlie on a straightline (the blackline) in thisanalysis. The

Open the worksheet tab “ Descriptive Statistics” .

Using SigmaXL®’s Histograms and Descriptive Statistics tool, select Anderson Darling and clickOK.



155



Anderson-Darling Caveat

If the Data Are Not Normal, Don

t Panic!

Once again, Non-normal Data is NOT abad thing, dependingon the type of process /metrics you are workingwith. Sometimes it caneven be exciting tohave Non-normal Databecause in some waysit represents

opportunities forimprovements.

Don’t touch that button



156


! "#$ %&' ) &*+ #, !"#$"%$&' $) *"+),- ./ 0'&1' 2"*%&#) %3"% #,)+4% $'

" '&'5#"'-&6 -$) %#$.+%$&' &2 &+%7+%8 94) & #,2,##,- %& ") :9) ) $;'".4,

< "+),=8

) -..- / ) &*+ #, !"#$"%$&' *"+),- ./ +'0'&1' 2"*%&#) #,)+4%$'; $'

" )%,"-/ .+% #"'-&6 -$)%#$.+%$&' &2 &+%7+% "#&+'- %3, ">,#";, &2

%3, -"%"8 ?% $) %3, >"#$"%$&' 4,2% &>,# "2%,# )7,*$"4 *"+), >"#$"%$&' 3")

.,,' #,6&>,- "'- %/7$*"44/ @'&% "41"/)A 2&44&1) " '&#6"4

-$)%#$.+%$&'8

?2 1, 0'&1 %3"% %3, .") $* ) %#+*%+#, &2 %3, -"%" )3&+4- 2&44&1 "

'&#6"4 -$)%#$.+%$&'B .+% 74&%) 2#&6 &+# -"%" )3&1) &%3,#1$),C 1,

0'&1 %3, -"%" *&'%"$' )7,*$"4 *"+),)8

! "#$ %&' ) &*+ #+ , -" "./0*1%02

Isolating Special Causes from Common Causes

Normality Exercise

Don’t get too worriedabout killing all variation,get the biggest bang for

your buck and startmaking improvements byfollowing themethodology. Manycompanies today canrealize BIG gains andreductions in variation bysimply measuring,describing theperformance and thenmaking common sense

adjustments within theprocess…recall the“ground fruit”?

Think about your data interms of what it should


Answers:1) Is Distribution A Normal? Answer > No2) Is Distribution B Normal? Answer > No

look like, then compare it to what it does look like. See some deviation, maybe some SpecialCauses at work?



157


Data sources are suggested by many of the tools that havebeen covered so far:

– Process Map

– X-Y Matrix

– Fishbone Diagrams

– FMEA

Examples are:

1. Time

Shift

Day of the week

Week of the month

Season of the year

2. Location/position

Facility

Region

Office

3. Operator

Training

Experience

Skill

Adherence to procedures

4. Any other sources?

Data Sources

Introduction to Graphing

Datademographicswill come out ofthe basic

Measure Phasetools such asProcess Maps,X-Y Diagrams,FMEAs andFishbones. Putyour focus onthe top X’s fromX-Y Diagram tofocus youractivities.


Passive datacollection meansdon’t mess with theprocess! We are

gathering data andlooking for patternsin a graphical tool. Ifthe data isquestionable, so isthe graph we createfrom it. For nowutilize the dataavailable, we willlearn a tool calledMeasurement

System Analysis later in this phase.

The purpose of Graphing is to:

• Identify potential relationships between variables.

• Identify risk in meeting the critical needs of the Customer,

Business and People.• Provide insight into the nature of the Xs which may or may

not control Y.

• Show the results of passive data collection.

In this section we will cover ! 1. Box Plots

2. Scatter Plots

3. Dot Plots

4. Time Series Plots

5.

Histograms



158


!"# % "&'&%(#')*()%* +, & -++. - '&/" )0%12.#3

! 4&')#(5 +, .&(&

! 6 #1#%()+0 +,

" 4&')&71#*

" 8'&/"

" 9&0-#

:0,+';&()+0 (+ )0(#'/'#( '#1&()+0* ")/*

< =/1+ '# >2&0 ()(&()?# '#1&()+0* ")/*

The Histogram

Graphical Concepts

A Histogram is a basicgraphing tool thatdisplays the relativefrequency or thenumber of times ameasured items falls

within a certain cellsize. The values for themeasurements areshown on the horizontalaxis (in cells) and thefrequency of each sizeis shown on the verticalaxis as a bar graph.The graph illustratesthe distribution of thedata by showing which

values occur most andleast frequently. AHistogram illustrates


The characteristics of a graph arecritical to the graphing process.The validity of data allows us tounderstand the extent of error inthe data. The selection ofvariables impacts how we cancontrol a specific output of aprocess. The type of graph willdepend on the datademographics while the rangewill be related to the needs of thecustomer. The visual analysis ofthe graph will qualify furtherinvestigation of the quantitativerelationship between the

variables.

the shape, centering and spread of the data you have. It is very easy to construct and an easy touse tool that you will find useful in many situations. This graph represents the data for the 20 daysof arrival times at work from the previous lesson page.

In many situations the data will form specific shaped distributions. One very common distributionyou will encounter is called the Normal Distribution, also called the bell shaped curve for itsappearance. You will learn more about distributions and what they mean throughout this course.



159


Variation on a Histogram

Histogram Caveat

The Histogram shown here looks to be very Normal.


As you can see inthe SigmaXL® filethe columns usedto generate the

Histograms aboveonly have 20 datapoints. It is easyto generate yourown samples tocreate Histogramsimply by usingthe SigmaXL® menu path: “Data

Manipulation>Ran

dom Subset ”



160


!"# %&"'( ()**+,-./ 0+'+ +1")' '2/ (2+3/4 0-(3/,(-"5 +50 6/5'/, "7 '2/

0+'+ +50 + &(" 2/ &3 (3"' ")'&-/,(8

!"# % &"'( ,/9)-,/ '2+' "5/ "7 '2/ :+ ,-+1&/( 4 ; ", < 4 1/ 6+ '/=",-6+ & ",

0-(6,/'/ +50 '2/ "'2/, 1/ 6"5'-5)")(8

> *-5-*)* "7 ?@ "1(/,:+'-"5( (2")&0 1/ -56&)0/0 -5 =/5/,+'-5= '2/ 1"#

3&"'8

Middle

50% ofData

50th Percentile (Median)

25th Percentile

75th Percentile

min(1.5 x Interquartile Range

or minimum value)

Outliers

Maximum Value

Mean

Middle

50% ofData

50th Percentile (Median)

25th Percentile

75th Percentile


or minimum value)

Outliers

Maximum Value

Mean50th Percentile (Median)

25th Percentile

75th Percentile


or minimum value)

Outliers

Maximum Value

Mean

Box Plot

Dot Plot

A Box Plot (sometimes called aWhisker Plot) is made up of a boxrepresenting the central mass of thevariation and thin lines, calledwhiskers, extending out on eitherside representing the thinning tailsof the distribution. Box Plotssummarize information about theshape, dispersion and center ofyour data. Because of their concisenature, it easy to compare multipledistributions side by side.

These may be “before” and “after”views of a process or a variable. Orthey may be several alternativeways of conducting an operation.Essentially, when you want toquickly find out if two or moredistributions are different (or thesame) then you create a Box Plot.They can also help you spot outliersquickly which show up as asterisks

on the chart.


Using the “Graphing Data ” tab,create a Dot Plot.

Histogram for the granular

distribution obscures thegranularity, whereas the Dot Plotreveals it.

Points could have SpecialCauses associated with them.

These occurrences should alsobe identified in the Logbook inorder to assess the potential for aSpecial Cause related to them.

You should look for potentialSpecial Cause situations byexamining the Dot Plot for both high frequencies and location.

If in fact there are Special Causes (Uncontrollable Noise or Procedural non-compliance) then theyshould be addressed separately and then excluded from this analysis.

Take a few minutes and create other Dot Plots using the columns in this worksheet.



161


What can you tellabout the data

expressed in a

Box Plots?

Eat this –

then

check the

Box Plot

Box Plot Examples

Box Plot Anatomy

The first BoxPlot shows thedifferences inglucose levelfor ninedifferentpeople.

The secondBox Plot

shows theeffects ofcholesterolmedicationover time for agroup ofpatients.


A Box Plot is based on quartiles andrepresents a distribution as shownon the left of the graphic. The linesextending from the box are called

whiskers. The whiskers extendoutward to indicate the lowest andhighest values in the data set(excluding outliers). The lowerwhisker represents the first 25% ofthe data in the Histogram (the lightgrey area). The second and thirdquartiles form the box, whichrepresents fifty percent of the dataand finally the whisker on the rightrepresents the fourth quartile. The

line drawn through the boxrepresents the median of the data. Extreme values, or outliers, are represented by asterisks. Avalue is considered an outlier if it is outside of the box (greater than Q3 or less than Q1) bymore than 1.5 times (Q3-Q1).

You can use the Box Plot to assess the symmetry of the data: If the data are fairly symmetric,the Median line will be roughly in the middle of the box and the whiskers will be similar in length.If the data are skewed, the Median may not fall in the middle of the box and one whisker willlikely be noticeably longer than the other.

Median

Upper Whisker

Lower Whisker

Upper Limit: Q3+1.5(Q3-Q1)

Lower Limit: Q1+1.5(Q3-Q1)

Q3: 75th Percentile

Q1: 25th Percentile

Q2: Median 50th Percentile

B ox

* Outlier

Median

Upper Whisker

Lower Whisker

Upper Limit: Q3+1.5(Q3-Q1)

Lower Limit: Q1+1.5(Q3-Q1)

Q3: 75th Percentile

Q1: 25th Percentile

Q2: Median 50th Percentile

B ox

* Outlier



162


Box Plot Examples

The data shows thesetup cycle time tocomplete “Lockout –

Tagout” for threepeople in thedepartment.

Looking only at theBox Plots, it appearsthat Brian should bethe benchmark forthe departmentsince he has thelowest median setup

cycle time with thesmallest variation.On the other hand,Shree’s data has 3outlier points thatare well beyondwhat would be


Use the “Graphing Data” worksheet tab.

expected for the rest of the data and his variation is larger.

Be cautious drawing conclusions solely from a Box Plot. Shree may be the expert who is brought infor special setups because no one else can complete the job.



163


Attribute Y Box Plot

Multi-Vari Chart Enhancement

Open the “Graphing Data” tab.

To create this Box Plotfollow the SigmaXL® menupath “SigmaXL>Graphical

Tools>Boxplots”

If the output is pass/fail, itmust be plotted on the yaxis. Use the data shown tocreate the transposed BoxPlot. The reason we do thisis for consistency and

accuracy.


The Multi-Vari Chart shows theindividual data points that arerepresented in the Box Plot.

Open the workbook “MeasureData Sets” and select the“Graphing Data” tab.

The individual value plotshown here was createdusing SigmaXL®’s Multi-Vari Chart tool.



164


Individual Value Plot

Attribute Y Box Plot

Open the “Graphing Data” worksheet, select “Graphical Tools > Boxplots” . Select Data as theNumeric Data Variable (Y), and Distribution Type as the Group Category (X).

The Multi-Vari Chart was created and modified using “Graphical Tools > Multi-Vari Options” using the

same variables as the Box Plot. Note, if these options are saved they will be used in“Graphical Tools

> Multi-Vari Charts”.


SigmaXL® does notpermit transposedvalue and categoryscales so the aboveBox Plot showspass/fail on the x-axis and HydrogenContent on the Y-axis.



165


Time Series Plot

Multi-Vari Individuals

Using the“Graphing Data” worksheet.

A Run Chart iscreated byfollowing theSigmaXL® menupath“SigmaXL>Graphic

al Tools>Run

Chart ” . Run charts,also known asTime Series Plotsare very useful inmost projects.Every projectshould provide RunChart data to lookfor frequency,magnitude andpatterns. What Xwould cause theseissues?


Go to the Multi-Vari Individualsworksheet.

Note, SigmaXL® does not supportJitter, a featureused to spreadthe individualdata points.



166


Time Series Example

Now, using the “Graphing Data” worksheet…..

Now let’s lay 2 Time Series on top of each other. This can be done by following the SigmaXL® menupath “Graphical Tools > Overlay Run Chart ” (use variables Time 2 and Time 3).

What is happening within each plot? What’s the difference between the two plots? Time 3 appears tohave wave pattern.


Looking at the TimeSeries Plot, theresponse appearsto be very dynamic.

What othercharacteristic ispresent?

The benefit of thisapproach tocharting is you can

Note: SigmaXL® does not include Lowess Smoothing, however an advanced user could utilizeexponential smoothing in Excel’s Data Analysis Toolpak.

see every data point as it is gathered over time. Some interesting occurrences can be revealed.



167



You have now completed Measure Phase – Six Sigma Statistics.

! Explain the various statistics used to express location and spreadof data

!

Describe characteristics of a Normal Distribution

! Explain Special Cause variation

! Use data to generate various graphs and make interpretations

based on their output


Notes



168


Lean Six Sigma

Black Belt Training

Now we will continue in the Measure Phase with “Measurements System Analysis”.

Measure PhaseMeasurement System Analysis



169


Measurement System Analysis

Overview

Introduction to MSA

In order to improve your processes, it is necessary to collect data on the "critical to" characteristics.When there is variation in this data, it can either be attributed to the characteristic that is beingmeasured and to the way that measurements are being taken; which is known as measurement error.When there is a large measurement error, it affects the data and may lead to inaccurate decision-making.

Measurement error is defined as the effect of all sources of measurement variability that cause an

observed value (measured value) to deviate from the true value.

Measurement System Analysis is one of thosenon-negotiable items!MSA is applicable in

98% of projects and italone can have amassive effect on thesuccess of your projectand improvementswithin the company.

In other words, LEARNIT & DO IT. It is veryimportant.

! "# $% # '( )* +! "#$% # '( )* +

,"-$"./0# )* +,"-$"./0# )* +

+11-$.2 10 )* ++11-$.2 10 )* +

3-"4 54 6 +% 1$'7 8109#3-"4 54 6 +% 1$'7 8109#

: -'% 0## ; "4".$/$1<:-'%0# # ; "4".$/$1<

)0"#2-09071 * <# 109 + 7"/<#$#)0"#2-09071 * <# 109 + 7"/<# $#

* $= * $>9" * 1"1$#1$%#* $= * $>9" * 1"1$#1$% #

:-'%0## ?$# %'@0-<:-'%0## ?$# %'@0-<

30/% '90 1' )0"# 2-030/%'90 1' )0"# 2-0

! "# $% # '( )* +! "#$% # '( )* +

,"-$"./0# )* +,"-$"./0# )* +

+11-$.2 10 )* ++11-$.2 10 )* +

3-"4 54 6 +% 1$'7 8109#3-"4 54 6 +% 1$'7 8109#

: -'% 0## ; "4".$/$1<:-'%0# # ; "4".$/$1<

)0"#2-09071 * <# 109 + 7"/<#$#)0"#2-09071 * <# 109 + 7"/<# $#

* $= * $>9" * 1"1$#1$%#* $= * $>9" * 1"1$#1$% #

:-'%0## ?$# %'@0-<:-'%0## ?$# %'@0-<

30/% '90 1' )0"# 2-030/%'90 1' )0"# 2-0

So far we have learned that the heart and soul of Six Sigma is

that it is a data - driven methodology.

– How do you know that the data you have used is accurate andprecise?

– How do know if a measurement is a repeatable and

reproducible?


or MSA

Measurement System Analysisor

MSA

How good are these?



170


Introduction to MSA (Cont.)


The measurement system is the complete process used to obtain measurements, such as theprocedures, gages and personnel that are employed to obtain measurements. Each componentof this system represents a potential source of error. It is important to identify the amount of errorand, if necessary, the sources of error. This can only be done by evaluating the measurement

system with statistical tools.

There are several types of measurement error which affect the location and the spread of thedistribution. Accuracy, linearity and stability affect location (the average). Measurement accuracydescribes the difference between the observed average and the true average based on a masterreference value for the measurements. A linearity problem describes a change in accuracythrough the expected operating range of the measuring instrument. A stability problem suggeststhat there is a lack of consistency in the measurement over time. Precision is the variability in themeasured value and is quantified like all variation by using the standard deviation of thedistribution of measurements. For estimating accuracy and precision, multiple measurements ofone single characteristic must be taken.

The primary contributors to measurement system error are repeatability and reproducibility.Repeatability is the variation in measurements obtained by one individual measuring the samecharacteristic on the same item with the same measuring instrument. Reproducibility refers tothe variation in the average of measurements of an identical characteristic taken by differentindividuals using the same instrument.

Given that Reproducibility and Repeatability are important types of error, they are the object of aspecific study called a Gage Repeatability & Reproducibility study (Gage R&R). This study canbe performed on either attribute-based or variable-based measurement systems. It enables anevaluation of the consistency in measurements among individuals after having at least twoindividuals measure several parts at random on a few trials. If there are inconsistencies, then the

measurement system must be improved.

Measurement System Analysis isthe entire system, NOT justcalibration or how good themeasurement instrument is. Wemust evaluate the entireenvironment and MeasurementSystem Analysis gives us a way toevaluate the measurementenvironment mathematically.

All these sources of variationcombine to yield a measurementthat is different than the true value.

It is also referred to as “GageR&R” studies where R&R is:Repeatability & Reproducibility.


!" # %& ' (')*+(')%,'- ./0,+12/+ )0 32'4)%56 7'/%')%04 %4)/012,+1 )0 '

./0,+&& 0/ ./012,) 86 )*+ ',) 05 (+'&2/%49:

!+'&2/+(+4)

;/0,+&&

<47%/04(+4)

!"#$%&"'"()

*)"' ), -"

!"#$%&".

=+5+/+4,+

<32%.(+4)

;/0,+12/+

>.+/')0/ !+'&2/+(+4)

;/0,+&&

<47%/04(+4)

!"#$%&"'"()

*)"' ), -"

!"#$%&".

=+5+/+4,+

<32%.(+4)

;/0,+12/+

>.+/')0/

?*+ %)+( )0 8+ (+'& 2/+1 ,'4 8+ ' .*6&%,' - .'/)@ 10,2(+4) 0/ ' &, +4'/%0 50/ ,2&)0(+/ &+/7%,+:

>.+/')0/ ,'4 /+5+/ )0 ' .+/&04 0/ ,'4 8+ 1%55+/+4) %4&)/2(+4)& (+'&2/%49 )*+ & '(+ ./012,)&:

= +5+/+4,+ %& ' &)'41'/1 )*') %& 2& +1 )0 ,'-%8/')+ )*+ +32%.(+4):

;/0,+12/+ %& )*+ (+)*01 2&+1 )0 .+/50/( )*+ )+&):

< 32%.(+4) %& )*+ 1+7%,+ 2&+1 )0 (+'& 2/+ )*+ ./012,):

< 47%/04(+4) %& )*+ &2//0241%49& A*+/+ )*+ (+'&2/+& '/+ .+/50/(+1:



171


Measurement Purpose

The purpose ofconducting an MSAis tomathematicallypartition sources ofvariation within themeasurement

system itself. Thisallows us to createan action plan toreduce the biggestcontributors ofmeasurement error.

Purpose

The types and sophistication of measurement vary almost infinitely. It is becoming increasinglypopular or cost effective to have computerized measurement systems. The quality ofmeasurements also varies significantly - with those taken by computer tending to be the best. Insome cases the quality of measurement is so bad that you would be just as well off to guess atwhat the outcome should be. You will be primarily concerned with the accuracy, precision andreproducibility of measurements to determine the usability of the data.


Measurement is a processwithin itself. In order tomeasure something you mustgo through a series of tasks

and activities in sequence.Usually there is some from ofset-up, there is an instrumentthat makes the measurement,there is a way of recording thevalue and it may be done bymultiple people. Even when youare making a judgment callabout something, there is someform of setup. You become theinstrument and the result of adecision is recorded someway;even if it is verbal or it is a setof actions that you take.

Measurement Systems must provide value!

Value = Accurate Information = Usable

Knowledge

Key Question!

What do I need to know?

Too often, organizations build

complex data collection and

information management systems

without truly understanding how the

data collected and metrics calculated

can actually benefit the organization.

The error can be partitioned into specific sources:

– Precision

•

Repeatability - within an operator or piece of equipment

•

Reproducibility - operator to operator or attribute gage toattribute gage

– Accuracy

•

Stability - accuracy over time

• Linearity- accuracy throughout the measurement range

•

Resolution

• Bias – Off-set from true value

– Constant Bias

–

Variable Bias – typically seen with electronic equipment,amount of Bias changes with setting levels

MSA Objective Reduce Error



172


Accuracy and Precision


!"" #$%&' )#& *+& ,$'"-. ' / ! "

$%&'$(&) *+& ,+-*, $'& ." *+&

/&"*&' -0 *+& *$'(&* 12* *+&'& ., $

3-* -0 %$'.$1.3.*4

!" "# $%&' )#& *+& ,$'"-. ' / ! "

$%&'$(&) *+& ,+-*, $'& ." *+&

/&"*&' -0 *+& *$'(&* 12* *+&'& ., $

3-* -0 %$'.$1.3.*4

0$'"-.' )#& *+& %""#$%&' / 5+&

$%&'$(& ., "-* -" *+& /&"*&') 12*

*+& %$'.$1.3.*4 ., ,6$33

0$'"-.' )#& *+& %""#$%&' / 5+&

$%&'$( & ., "-* -" *+& / &"*&') 12*

*+& %$'.$1.3.*4 ., ,6$33

Measurement systems, likeall things, generate someamount of variation in theresults/data they output. In

measuring, we are primarilyconcerned with 3characteristics:

1. How accurate is themeasurement? For arepeated measurement,where is the averagecompared to some knownstandard?. Think of thetarget as the measurement

system, the knownstandard is the bulls eye inthe center of the target. Inthe first example you can

see the “measurements” are very dispersed, there is a lot of variability as indicated by the Histogramcurve at the bottom. But on average, the “measurements” are on target. When the average is ontarget, we say the measurement is accurate. However, in this example they are not very precise.

2. How precise is the measurement? For a repeated measurement, how much variability exists? Asseen in the first target example, the “measurements” are not very precise, but on the second targetthey have much less dispersion. There is less variability as seen in the Histogram curve. However, wenotice that the tight cluster of “measurements” are off target, they are not very accurate.

3. The third characteristic is how reproducible is the measurement from individual to another? What isthe accuracy and precision from person to person. Here you would expect each person that performsthe measurement to be able to reproduce the same amount of accuracy and precision as that of otherperson performing the same measurement.

Ultimately, we make decisions based on data collected from measurement systems. If themeasurement system does not generate accurate or precise enough data, we will make the decisionsthat generate errors, waste and cost. When solving a problem or optimizing a process, we must knowhow good our data are and the only way to do this is to perform a Measurement System Analysis.



173


MSA Uses


!"# %& ' () *+), -./

! "#$%&' )*+'&*%, )*-$'.+)"* -+%*/%&/- 0)+1 +1' -+%*/%&/- "2 3"4&

.4-+"#'&5

6)71,)71+ %&'%- 01'&' .%,)8&%+)"* +&%)*)*7 )- &'94)&'/5

:&";)/' % #'+1"/ +" ';%,4%+' )*-$'.+"& +&%)*)*7 '22'.+);'*'-- %- 0',,%- -'&;'- %- %* '<.',,'*+ +&%)*)*7 +"",5

:&";)/' % 7&'%+ 0%3 +"=

>! "#$% &' '<)-+)*7 #'%-4&'#'*+ '94)$#'*+5

>? 4%,)23 *'0 )*-$'.+)"* '94)$#'*+5

The measurement system always has some amount of variation and that variation is additive tothe actual amount of true variation that exists in what we are measuring. The only exception iswhen the discrimination of the measurement system is so poor that it virtually sees everything thesame.

This means that you may actually be producing a better product or service than you think you are,

providing that the measurement system is accurate; meaning it does not have a bias, linearity orstability problem. It may also mean that your customer may be making the wrong interpretationsabout your product or service.

The components of variation are statistically additive. The primary contributors to measurementsystem error are Repeatability and Reproducibility. Repeatability is the variation in measurementsobtained by one individual measuring the same characteristic on the same item with the samemeasuring instrument. Reproducibility refers to the variation in the average of measurements ofan identical characteristic taken by different individuals using the same instrument.

Why MSA?

Why is MSA so important?MSA is was allows us to trustthe data generated from ourprocesses. When you chartera project you are taking on asignificant burden which willrequire Statistical Analysis.What happens if you have agreat project, with lots of datafrom measurement systemsthat produce data with nointegrity?

!"#$ %&"' "() +, $ ) "' -(#., $ /$ !" !$%&'()*( (&+

, -(./0 (12 3 &4 5)'!) (!&* !* &.' %'&62"" (1)( !" 6)."2/ 70 &.'

$2)".'2$2*( "0"(2$8

, 9 &$%)'2 $2)".'2$2*(" 72(:22* &%2')(&'"8

, 9 &$%)'2 $2)".'2$2*(" 72(:22* (:& ;&' $&'2< $2)".'2$2*(

/25!62"8

, ='&5!/2 6'!(2'!) (& )66 2%( *2: $2)".'2$2*( "0"(2$" ;6&*"!/2' *2:

2>.!%$2*(<8

, ?5)@.)(2 ) "."%26( A) A28

, ?5)@.)(2 ) A)A 2 724&'2 )*/ )4(2' '2%)!'8

, B2(2'$!*2 ('.2 %'&62"" 5)'!)(!&*8

, ?5) @.)(2 24426(!52*2"" &4 (')!*!*A %'&A ')$8



174


Appropriate Measures

Poor Measures

Contextual means they are necessary to gather information on other relevant information that actually

would help to explain sources of variation.

It is very commonwhile working projectsto discover that thecurrent measurementsystems are poor.

Have you ever comeacross a situationwhere the data fromyour customer orsupplier doesn’tmatch yours? Ithappens often. It islikely a problem withone of themeasurementsystems. We have

worked MSA projectsacross criticalmeasurement pointsin various companies,


! " " #$ " #%& '( *( & + , #( + !"#$

% &'(()*)#+, - !.! )/!0/# ,2 0# 3#!4'"#5 "#6'/!"/7

% 8#/#.!+, -9#/: ,2 '+5#"4,!+5; )42/!,# ,9# :"20/#34

% 8#:"#4#+,!,).# < 2( ,9# :"2*#44 !*"244 49)(,4 !+5 :#2:/#

% = 2+,#>,'!/ - *2//#*,#5 ?),9 2,9#" "#/#.!+, )+(2"3!,)2+ ,9!,

3)69, #>:/!)+ :"2*#44 .!")!0)/),7@

Sufficient, means that aremeasures are available tobe measured regularly, ifnot it would take too long

to gather data.

Relevant, means that theywill help to understandand isolate the problems.

Representative measuresmean that we can detectvariation across shifts andpeople.

! " " # % & ' ( ) # & ( !"# %&'()* +%,-.

/ 0,,% ,% #,#1&23'*&#* ,4&%"*3,#") 5&+3#3*3,#'

/ 63++3!()* -&"'(%&'

/ 0,,% '"-4)3#7

/ 8"!9 ,+ (#5&%'*"#53#7 ,+ *:& 5&+3#3*3,#'

/ ;#"!!(%"*&< 3#'(++3!3&#* ,% #,#1!")3=%"*&5 -&"'(%&-&#*

5&>3!&'

%& ' ( ) #& * & + , -# #" # !,-4%,-3'&' 5&!3'3,#' *:"* "++&!*.

? @ ('*,-&%'

? 0%,5(!&%'

? A(44)3&%'

it’s not uncommon for more than 80% of the measurements to fail in one way or another.



175


Examples of What to Measure

Components of Variation

At this point you shouldhave a fairly good ideaof what to measure,listed here are some

ideas to get youthinking…

We are going to strive to have the measured variation be as close as possible to the true variation.In any case we want the variation from the measurement system to be a small as possible. We are

now going to investigate the various components of variation of measurements.


!" # $ % &'( * + , - # . # / 0 , - ' / .* $ ' # ( 1 2' 3

! "#$%&#' &)* +,-.)*&#' %,/#$-+

! 0,-$+$.) 1.$)/+ $) "#.-,++ 2&1+

! 3 )' &)* & 44 5&65,+7 %,&+6#,%,)/ *,8$-,+7 $)+/#6%,)/+7 ,/-

! 9:;+< $) /=, 1#.-,++

! "#$.# /. >'1./=,+$+ ?,+/$)5

! "#$.# /. %.*,4$)5

! "#$.# /. 14&))$)5 *,+$5),* ,@1,#$%,)/+

! A,B.#, &)* &B/,# 1#.-,++ -=&)5 ,+

! ?. C6&4$B' .1,#&/.#+

456 7( # 5 -*, 5.*% %'2888

! "#$#% #& ( )* +#, -*&# , $( ."/$0 1 ."# % , & /,./)$ .", . ( )*

)2 -#&% # 3, $ 2 # -#0 + #$.#4 /$.) ."# 5)6 6)7 /$0 3)+8 )$# $.-9

! "" $%&'()%$%*+ ','+%$' -&.% %))/)0 12 ,/( 3/*4+ 5*/6 -/6 $(7- /2 +-%.&)8&+8/* ,/( /9'%).% 8' 7/*+)89(+%3 9, ,/() $%&'()%$%*+ ','+%$: ,/(7& **/+ $&5% 7/*283%*+ 3%78'8/*'0

! " $% & ' ()( % *( +,(( -.*/ 0. 12 (0 3' 3$ " )%4 5%+ .*/ $ %&) 5 .1(*+(67%' "3+0 ' %& 5- $ %& 8( ' . 55 .*/ 0% - ) .9( .* 3 +17% %5 :% *(;

!77()&7,;)%78'8/*

<%=%&+&98"8+, <%=)/3(7898"8+,

>%&'()%$%*+ ?,'+%$ @))/)A*8+B+/B(*8+ C+)(%D E&)8&+8/*

: 2- #&%#4 ;, & /, ./)$

?+&98"8+, F8&' G8*%&)8+,

!77()&7,;)%78'8/*

<%=%&+&98"8+, <%=)/3(7898"8+,

>%&'()%$%*+ ?,'+%$ @))/)A*8+B+/B(*8+ C+)(%D E&)8&+8/*

: 2- #&%#4 ;, & /, ./)$

?+&98"8+, F8&' G8*%&)8+,



176


Precision

The spread of thedata is measured byPrecision. This tells

us how well ameasure can berepeated andreproduced.

Repeatability

Measurements will bedifferent…expect it! Ifmeasurement arealways exactly thesame this is a flag,sometimes it isbecause the gaugedoes not have theproper resolution,meaning the scaledoesn’t go down far

enough to get anyvariation in themeasurement.

For example, wouldyou use a football fieldto measure the gap in aspark plug?


! #$%&'(% )%*$'& '( +,% *-.* $%*/$,( *-% (.)% 0.1/% +2 . 3'0%,

.**$'4/*% %0%$5 *')% ., %(*').*% '( ).6%7

8$%&'(% 6.*. .$% ',6%#%,6%,* +2 9-+ %(*').*%( *-%) +$ 9-%,

*-% %(*').*% '( ).6%7

8$%&'('+, &., 4% #.$*'*'+,%6 ',*+ *9+ &+)#+,%,*(:

; <%#%. *.4'1'*5

; <%#$+6/&'4' 1'*5

!"#"$ %$ &' (' %) $ +, !"#-., /0'&' (' %) 1 2 $ 3 " !4 !

!"#"$%$&' ( ' %) !" $%& '()!($!*+ !+ ,&("-)&,&+$" *.$(!+&/ 0!$% ! " #

%#& '()#%#"* +"'*)(%#"* -"&/ "&'&)(1 $!,&" .2 *+& (33)(!"&)

0%!1& ,&("-)!+4 $%& !/&+$!5(1 5%()(5$&)!"$!5 *+ $%& ' & % # , & )* -

!"# %&'()*%+

6 7( +-8(5$-)!+49 : +& 3&)"*+ ,&("-)&" $%& 3-)!$2 *8 ,-1$!31& "(,31&"

*8 $%& "(,& '!(1 (+/ 4&$" /!88&)&+$ 3-)!$2 ,&("-)&";

6 <)(+"( 5$!*+(19 : +& 3&)"*+ &'( 1-($&" ( 5*+$)(5$ ,-1$!31& $!,&" =*'&) (

3&)!*/ *8 $!,&> (+/ ,(?&" /!88&)&+$ /&$&),!+($!*+" *8 &))*)";

Repeatability

Y



177


!"#$%&'()*)+ ),- !" $%& '()!($!*+ !+ $%& ('&)(,& *- $%&

.&("/)&.&+$" .(0& 12 !"##$%$&' (33)(!"&)" /"!+, $%& ) * + $

+$*),%"&- "&)'%,+$&' 4%&+ .&("/)!+, $%& !0&+$!5(6

5%()(5$&)!"$!5 *+ $%& ) * + $ . * % '/

!"# %&'()*%+

7 8( +/-(5$/)!+,9 :!--&)&+$ 3&*36& 3&)-*). 3/)!$2 $&"$ *+ "(.36&" -)*.

$%& "(.& '!(6 (+0 ,&$ 0!--&)&+$ )&"/6$";

7 <)(+"( 5$!*+( 69 :!--&)&+$ 3&*3 6& &'( 6/($& $%& "(.& 5*+$)(5$ ( +0

.(=& 0!--&)&+$ 0&$&).!+($!*+";

0$.%1!,2"3"4 "'5

> 3&)($*) ?

> 3&)($*) @

6

0$.%1!,2"3"4 "'5

> 3&)($*) ?

> 3&)($*) @

6

Reproducibility

Time Estimate Exercise

Reproducibility willbe present when it ispossible to havemore than oneoperator or morethan one instrumentmeasure the samepart.


!" #$%&'# )* +#%,&-#. !"#$%&'()'" +$, ,"-- .$/ 0)%

"&'1#)'" ) 23 &"0$%4 '1#" 1%'"(5)-6

26 7)1( /8 ,1'+ )% )&&$01)'"6

9 6 : %" 8"(&$% ,1-- &). &')(' )%4 &'$8 '$ 1%410)'" +$,

-$%; '+". '+1%< '+" 23 &"0$%4& -)&'6 !$ '+1& = '1#"&6

>6 ?+" $'+"( 8"(&$% ,1-- +)5" ) ,)'0+ ,1'+ ) &"0$%4

+)%4 '$ )0'/)--. #")&/(" '+" 4/()'1$% $@ '+" "&'1#)'"6

A"0$(4 '+" 5)-/" ,+"(" .$/( 8)('%"( 0)%B' &"" 1'6

C6 D,1'0+ ')&<& ,1'+ 8)('%"( )%4 4$ 1' = '1#"& )-&$6

E6 A"0$(4 )-- "&'1#)'"&F ,+)' 4$ .$/ %$'10"G



178


Accuracy Against a Known Standard

Accuracy


!" $ %%&'$() *)$+&')*)"( ,+ (-) .,//)')"%) 0)(1))" (-) 20+)'3). $ 3)'$4 ) 2/

(-) *)$+&')*)"( $". $ ')/)')"%) 3$5&)6

7 8 -)" $ *)(',% 2' *)$+&')*)"( +9+()* %2"+,+()"(59 23)' 2' &".)' )+(,*$()+ (-)

3$5&) 2/ $" $((',0&(): ,( ,+ +$,. (2 0) ;,"$%%&'$()<

!%%&'$%9 %$" 0) $++)++). ," +)3)'$5 1$9+=

7 >)$ +&')*)"( 2/ $ ?"21" +($ ".$ '.

7 @ 2*A$ ',+2" 1 ,(- $ "2(-)' ?"21" *)$+&')*)"( *)(-2.

7 B').,%(,2" 2/ $ (-)2')(,%$5 3$ 5&)

8 -$( -$AA)"+ ,/ 1) .2"C( -$3) +($".$'.+: %2*A$',+2"+ 2' (-)2',)+D

!"#$

% & $ " ' ( $

%))#"')*

+ $ ' , # " $ - $ . /

!"#$

% & $ " ' ( $

%))#"')*

+ $ ' , # " $ - $ . /

0 '".1.( 2 45 .5/ ',,# -$ *5 #"

- $/"565( * "$7$"$. )$ 1, ( 5,8 $69

Accuracy and theaverage are related.Recall in the BasicStatistics module we

talked about theMean and thevariance of adistribution.

Think of it thisway….If theMeasurement Systemis the distribution thenaccuracy is the Meanand the precision is

the variance.

In Transactional Processes the measurement system can

consist of a database query.

! For example, you may be interested in measuring product returns

where you will want to analyze the details of the returns over some

time period.

! The query will provide you all the transaction details.

However, before you invest a lot of time analyzing the data, you

must ensure the data has integrity.

! The analysis should include a comparisonwith known reference points.

! For the example of product returns, the

transaction details should add up to thesame number that appears on financial

reports, such as the income statement.



179


Accuracy vs. Precision

Bias is a component of Accuracy. Constant Bias is when the measurement is off by a constantvalue. A scale is a prefect example, if the scale reads 3 lbs when there is no weight on it then

there is a 3lb Bias. Make sense?

Bias


!""#$!%& '$&"()&

* &(%+&$

,-%+

+ =

!""#$%"& $()%*(+ *, -,. "),+( *-(

%/($%0( ,1 *-( +-,*+ %$( *, *-(

2%+*($ ,$ 3#))4+5(&(6

7$("8+8,9 $()%*(+ *, *-( +:$(%; ,1

*-( +-,*+ ,$ <%$8%9"(6

Most Measurement Systems are accurate but not at all precise.

!"#$ !" $%&!'%$ (" )*% $%+!()!,' ,& )*% -%("./%$ +(0.% &/,- )*%

(1).(0 +( 0.%2

3 (0!4/()!,' 5/,1%$./%" 1(' -!'!-!6% ('$ 1,')/,0 4!( " 7!)*!'

(11%5)(40% 0!-!)"2 8$%(009: ;!(" 1(' '%+%/ 4% %0!-!'()%$ $.% ),

-()%/!(0 7%(/ ('$ )%(/<

Bias BiasBias Bias



180


Stability

Stability just looksfor changes in theaccuracy or Biasover time.

Linearity

Linearity just evaluates if any Bias is consistent throughout the measurement range of theinstrument. Many times Linearity indicates a need to replace or maintenance measurementequipment.


!"#$%&%"' !" $ %$&%' () *'"(+'* $) ',,!, -.'$)&,'* (+ /',.) !"

)/$+*$,* *'0($ /(!+1 $) $ "&+2/(!+ !" /(.'3 4+0(,!+.'+/$5 2!+*(/(!+)

)&26 $) 25'$+5(+'))7 +!()'7 0(8,$/(!+7 5(%6/(+%7 26'.(2$57 9'$, $+*

/'$, !, !/6', "$2/!,) &)&$55: (+"5&'+2' %$ &%' (+)/$8(5(/:3 ;*'$ 55:7%$&%') 2$+ 8' .$(+/$(+'* /! %(0' $ 6(%6 *'%,'' !" )/$8(5(/: 8&/ 2$+

+'0', 8' '5(.(+$/'* &+5(<' ,'=,!*&2(8( 5(/:3 > $&%' )/$8(5(/: )/&*(')

9!&5* 8' /6' "(,)/ '?',2()' =$)/ 2$5(8,$/(!+ =,!2'*&,')3

@ !+/,!5 @ 6$,/) $,' 2!..!+5: &)'* /! /,$2< /6' )/$8(5(/: !" $

.'$)&,'.'+/ ):)/'. !0', /(.'3

!"#$% & % "' %) *%#) +,#-#+".- %/.0

#) # 123+"%43 41 " %5.6

Drift Drift

!"#$%&"'( !" $%&!'%$ (" )*% $!&&%+%',% !' -!(" .(/0%" )*+102*10) )*%

3%("0+%3%') +('2% !' 4*!,* )*% 2(02% !" !')%'$%$ )1 5% 0"%$6 7*!" )%//" 810

*14 (,,0+()% 810+ 3%("0+%3%')" (+% )*+102* )*% %9:%,)%$ +('2% 1& )*%

3%("0+%3%')"6 ;) ('"4%+" )*% <0%")!1'= > ?1%" 38 2 (2% *(.% )*% "( 3%

(,,0+(,8 &1+ (// "!@%" 1& 15A%,)" 5%!'2 3%("0+%$B>

C!'%(+!)8 D EF/1:%E G H+1,%"" I(+!()!1'

J C!'%(+!)8 D EF/1:%E G KLL

Nominal HighLow

* **

Reference Value (x)

B i a s ( y )

0.00

+ e

- e

y = a + b.xy: Bias, x: Ref. Value

a: Slope, b: Intercept

Nominal HighLow

* **

Reference Value (x)

B i a s ( y )

0.00

+ e

- e

y = a + b.xy: Bias, x: Ref. Value

a: Slope, b: Intercept



181


Types of MSA s

Variable Data isalways preferred over Attribute because itgive us more to work

with.

Now we are gong toreview Variable MSAtesting.

Variable MSA s

MSA’s use a random effects model meaning that the levels for the variance components are notfixed or assigned, they are assumed to be random.


!" # $% '( ) ) *+,- ,. - /( ,01 -2*0%3

! #,,2*45,0

! 6 ( 2 * ( 4 ) 0

72( +%( /,*-+() 8 2-90/,% ,:8*/( ) ): ;( < 0 ( ,,2 *45,0 4( %0=

>0(%520>0+, %:%,0>%?

!(+ 5'(/,52 *+1 82-90/,% 1 0+02( ) ): 5 %0 < ( 2 *(4)0 % ,5=*0% >-20

-',0+@ 4 5, =- 5 %0 ( ,,2 *45,0 %,5= *0% ,- ( )0%%02 = 01 200?

#,,2*45,0

! A ( % % B C ( * )

! D -B E - D -

! F-/5>0+, A208( 2(, *-+

! "52'(/0 *>802'0/,*-+%

! G5%,->02 " 02< */0

H 0 % 8 - + % 0

6 ( 2 * ( 4 ) 0

! G-+, *+5-5% %/( )0

! F*%/20,0 %/()0

! G2 *, */() =*>0+%*-+%

! A5 )) %,20+1 ,;

! I ( 28



182


Cheat Sheet

Notice the calculation method explained here for Distinct Categories.

Traditionally NDC is truncated to an integer value, but SigmaXL® reports a more informative onedecimal place.


SigmaXL®’sdefault is 6 *StDev. Select“5.15 * StDev”

in the dialogbox. SigmaXL®

uses thisdefault to beconsistent with6 * StDev usedin processcapability .

The 5.15multiplier is

common in theautomotiveindustry (AIAGMSAHandbook).

The worksheet used for this example is “ Gage AIAG 2 -SigmaXL Template” . The above slide is fordemonstration purposes, this dataset will be used in a later exercise.



183


Number of Distinct Categories

Here is a rule of thumb for distinct categories.

AIAG Standards for Gage Acceptance


!"# %&' (#) *+ , -./-%0/ 01/#2 *)-#. /#3 3. 4 *& "*5 '1 %4 .#61 )1 /#

2 )*&6 . *+ 6 1 )/. /"# . 4 ./#' -. 1 (3# /* ,-./-%2 &-."7

1 Data Category1 Data Category

2 - 4 Categories2 - 4 Categories

5 or more Categories5 or more Categories

8%1 00#6/1(3# +*)

#./ -'1/-%2 6)*0#..

6 1 ) 1 ' # /# ) . 1 % , - % , -0 # .

9 %34 -%,-01/#. 5 "#/"#)

/"# 6)*0#.. -. 6)*,&0-%2

0*%+*)'-%2 *)

%*%0*%+*)'-%2 61)/.

: #%#)13 34 &%1 00#6/1(3#

+*) #./ -' 1 /-%2 6 )*0#..

6 1 ) 1 ' # /# ) . 1 % , - % , -0 # .

9 %34 6 )*; -,#. 0*1 ).#

#./ -'1/#.

< # 0 * ' ' # % , # ,

8%1 00#6/1(3# +*)

#./ -'1/-%2 6)*0#..

6 1 ) 1 ' # /# ) . 1 % , - % , -0 # .

9 %34 -%,-01/#. 5 "#/"#)

/"# 6)*0#.. -. 6)*,&0-%2

0*%+*)'-%2 *)

%*%0*%+*)'-%2 61)/.

: #%#)13 34 &%1 00#6/1(3#

+*) #./ -' 1 /-%2 6 )*0#..

6 1 ) 1 ' # /# ) . 1 % , - % , -0 # .

9 %34 6 )*; -,#. 0*1 ).#

#./ -'1/#.

< # 0 * ' ' # % , # ,

8%1 00#6/1(3# +*)

#./ -'1/-%2 6)*0#..

6 1 ) 1 ' # /# ) . 1 % , - % , -0 # .

9 %34 -%,-01/#. 5 "#/"#)

/"# 6)*0#.. -. 6)*,&0-%2

0*%+*)'-%2 *)

%*%0*%+*)'-%2 61)/.

8%1 00#6/1(3# +*)

#./ -'1/-%2 6)*0#..

6 1 ) 1 ' # /# ) . 1 % , - % , -0 # .

9 %34 -%,-01/#. 5 "#/"#)

/"# 6)*0#.. -. 6)*,&0-%2

0*%+*)'-%2 *)

%*%0*%+*)'-%2 61)/.

: #%#)13 34 &%1 00#6/1(3#

+*) #./ -' 1 /-%2 6 )*0#..

6 1 ) 1 ' # /# ) . 1 % , - % , -0 # .

9 %34 6 )*; -,#. 0*1 ).#

#./ -'1/#.

: #%#)13 34 &%1 00#6/1(3#

+*) #./ -' 1 /-%2 6 )*0#..

6 1 ) 1 ' # /# ) . 1 % , - % , -0 # .

9 %34 6 )*; -,#. 0*1 ).#

#./ -'1/#.

< # 0 * ' ' # % , # ,< # 0 * ' ' # % , # ,

! #$%&'()*&

$ '

! + , - . / 0( ' 1() *&

! 2$),'13-,1$) + / 4, & 5 146

7 8 ! $ ' %&44

7 8 ! 9 : 8 !

: 8 ! 9 ; 8 !

; 8 ! $ ' < '& ( ,& '

7! $' %&44

7 ! 9 = !

> ! 9 ? !

7 8 ! $ ' < '& ( ,& '

@ . & ( %

A**&B,(3%&

C ( ' < 1 ) ( %

D$ $ '

! #$%&'()*&

$ '

! + , - . / 0( ' 1() *&

! 2$),'13-,1$) + / 4, & 5 146

7 8 ! $ ' %&44

7 8 ! 9 : 8 !

: 8 ! 9 ; 8 !

; 8 ! $ ' < '& ( ,& '

7! $' %&44

7 ! 9 = !

> ! 9 ? !

7 8 ! $ ' < '& ( ,& '

@ . & ( %

A**&B,(3%&

C ( ' < 1 ) ( %

D$ $ '

!"#" %#" &'" !"#$%$#&'( *+,"-#./ ! 0#&$+ 1 .$"2() *"+,-,&,.-) +.#

/ %0 " %11"2&%-1"3



184


SigmaXL® Graphic Output Cheat Sheet


This chart may be recreated by taking the following steps:

1. Copy the “% Total Variation (TV)” column.2. Paste the column to the right of the “% Contribution of Variance Component” column.3. Highlight the entire table which the “% Total Variation (TV)” was added.4. From Excel, Insert> (Chart) Column>2-D Clustered Column.

5. Delete the“Variance Component

“ column from this chart.

This chart may be found in the “ Gage R&R - X-Bar & R (1)” worksheet.



185


SigmaXL® Graphic Output Cheat Sheet (cont.)


SigmaXL® produces these Multi-Vari Charts as part of the Gage R&R report. Select the “ Gage

R&R - X-Bar & R (1)” worksheet.

Currently the Gage R&R report in SigmaXL® does not include an Interaction Plot. The followingsteps show how to create the Interaction Plot using Two-Way ANOVA:

1. Select the datawhich will be used forthe chart.2. Select“ SigmaXL>Statistical

Tools>Two-Way

ANOVA”

3. This chart wasgenerated from the“Gage AIAG2 -

SigmaXL Format ”

worksheet. Select“Response” as“Numerical DataVariable (Y)”, “Part” as “Group CategoryFactor (X1)”, and“Operator ” as “GroupCategory Factor(X2)”.The operator by part interaction plot is given in the Two-Way ANOVA output worksheet.



187


Practical Conclusions


Repeatability and Reproducibility Problems

! " #" $ %$& ' (' %) + ,-&( " . /0! " #$%&'#() +' '),$#-) .#. )/

! 01 +2$3 +--4''%2. 5%(6 +2) +,)'#(+'7 ')8('#%2/

! " #,-1 23 '& ' (' %) + ,-&( " ./ 0! 9)#:4');)2( ;#-6%2):

< = %;%$#' ;#-6%2):

! >2:4') #$$ 6#?) &))2 - #$%&'#()@ #2@ (6#( (6) :(#2@#'@ ;)#:4');)2(;)(6+@ %: &)%2. 4(%$%A)@/

< B%::%;%$#' ;#-6%2):

! C 2) ;#- 6%2) %: :4,)'%+'/

! C ,)'#(+':

< D'#%2%2. #2@ :E%$$ $)?)$ +1 (6) +, )'#(+': ;4:( &) #::)::)@ /

< C ,)'#(+': :6+4$@ &) +&:)'?)@ (+ )2:4') (6#( :(#2@# '@ ,'+-)@4'): #')1+$$+5)@/

! C ,)'#(+'F ;#-6%2) &3 ,#'( %2()'#-(%+2:

< G2@)':(#2@ 563 (6) +,)'#(+'F ;#-6%2) 6#@ ,'+& $);: ;)# :4'%2. :+;) ,# '(:

#2@ 2+( +(6)':/! H)8;)#:4') (6) ,'+&$); ,#'(:

! I'+&$); -+4$@ &) # '):4$( +1 .# .) $%2)#'%(3

! I'+&$); -+4$@ &) 1%J(4') ,'+&$);

! I'+&$); -+4$@ &) ,++' .# .) @):%.2

For Repeatability Problems:If all operators have the sameRepeatability and it is too big,

the gage needs to be repairedor replaced.If only one operator or in thecase where there are nooperators, but several gagesand only one gage is showingRepeatability problems, re-train the one operator orreplace the one gage.

For Reproducibility Problems:

In the case where onlymachines are used and themultiple machines are allsimilar in design, check thecalibration and ensure that the

standard measurement method is being used. One of the gages maybe performing differently thanthe rest, the graphs will show which one is performing differently. It may need to go in for repair or itmay simply be a setup or calibration issue. If dissimilar machines are used it typically means thatone machine is superior. In the case where multiple operator are the graphs will show who will needadditional training to perform at the same level as the rest. The most common operator/machineinteractions are either someone misread a value, recorded the value incorrectly or that the fixture

holding the part is poor.



188


Design Types


Crossed Designs arethe workhorse ofMSA. They are themost commonly

used design inindustries where it ispossible to measuresomething more thanonce. Chemical andbiological systemscan use CrossedDesigns also as longas you can assumethat the samplesused come from a

homogeneoussolution and there isno reason they canbe different.

Nested Designs must be used for destructive testing. In a Nested Design, each part is measured byonly one operator. This is due to the fact that after destructive testing, the measured characteristicis different after the measurement process than it was at the beginning. Crash testing is an exampleof destructive testing.

If you need to use destructive testing, you must be able to assume that all parts within a singlebatch are identical enough to claim that they are the same part. If you are unable to make that

assumption then part-to-part variation within a batch will mask the measurement system variation.

If you can make that assumption, then choosing between a Crossed or Nested Gage R&R Study fordestructive testing depends on how your measurement process is set up. If all operators measureparts from each batch, then use Gage R&R Study (Crossed). If each batch is only measured by asingle operator, then you must use Gage R&R Study (Nested). In fact, whenever operators measureunique parts, you have a Nested Design. Your Master Black Belt can assist you with the set-up ofyour design.

! " # $ $ % & ( % $ ) * +! " $ %&''() )('*+ , *' -'() &,./ *, ,&,0)('1%-$1*2( 1('1*,+ 3 ,) 3''-4(' 1531 3 ..

15( 63%1' $3, 7( 4(3'-%() 4-.1*6.( 1*4(' 7/ (*15(% &6(%31&%' &% 4-.1*6.(43$5*,('8

9 : *2(' 15( 37*.*1/ 1& '(63%31( 63 %101&063 %1 23%*3 1*&, ;%&4 4(3'-%(4(,1'/'1(4 23%*31*&,8

9 "''(''(' %(6(3 137*.*1/ 3 ,) %(6%&)-$*7 *.*1/8

9 "''(''(' 15( *,1(%3$1*&, 7(1<((, 15( &6(%31&% 3,) 15( 63 %18

, %$-%& (%$)*+

! " ,('1() )('*+ , *' -'() ;&% )('1%-$1*2( 1('1*,+ =<( <*.. .(3%, 3 7&-1 15*' *,>?? 1%3*,*,+@ 3,) 3 .'& '*1-31*&,' <5(%( *1 *' ,&1 6&''*7.( 1& 53 2( 3..&6(%31&%' &% 43$5*,(' 4(3'-%( 3.. 15( 63%1' 4-.1*6.( 1*4('8

9 A('1%-$1*2( 1('1*,+ 3''-4(' 1531 3 .. 15( 63 %1' <*15*, 3 '*,+ .( 731$5 3%(*)(,1*$3. (,&-+5 1& $.3*4 15(/ 3%( 15( '34(8

9 B ('1() )('*+,' 3%( -'() 1& 1('1 4(3'-%(4(,1 '/'1(4' <5(%( *1 *' ,&16&''*7.( =&% )('*%37.(@ 1& '(,) &6(%31&%' <*15 63%1' 1& )*;;(%(,1 .&$31*&,'8

9 A& ,&1 *,$ .-)( 3 .. 6&''*7 .( $&47*,3 1*&,' &; ;3$ 1&%'8

9 C'(' '.*+ 51./ )*;;(%(,1 4315(431*$3. 4&)(. 153, 15( $%&''() )('* +,8



189


Gage R & R Study

template to record your study and then to perform the calculations for the result of the study.

Variable Gage R & R Steps


A Gage R&R, like any study,requires careful planning. Thecommon way of doing an Attribute Gage R&R consistsof having at least two peoplemeasure 20 parts at random,twice each. This will enableyou to determine howconsistently these peopleevaluate a set of samplesagainst a known standard. Ifthere is no consistencyamong the people, then themeasurement system mustbe improved, either by

defining a measurementmethod, training, etc. You usean Excel spreadsheet

!"# $ & ' ! " ## " %&"' '&&%()* ")+ ()%,-+./& %0& /-)/&1 %2 -3 %0& 4 "*& 565

!"# $ ( ' 7&#&/% 1",%2 3-, %0& 2%.+8 "/,-22 %0& ,")*& -3 ()%&,&2%

9 :3 %0& ()%&)% (2 %- &;" #."%& %0& '&"2.,&'&)% 282%&' %0,-.* 0-.% %0& 1,-/&22 ,")*&<

2&#&/% 1",%2 %0,-.*0-.% %0& ,")*&

9 :3 -)#8 " 2'"## ('1,-;&'&)% (2 =&()* '"+& %- %0& 1,-/ &22< %0& ," )*& -3 ()%&,&2% (2)-> %0& ('1,-;&'&)% ,")*&

!"# $ ) ' :+&)%(38 %0& ()21&/%-,2 -, &?.(1'&)% 8-. 1#" ) %- .2& 3-, %0& " )" #82(2

9 :) %0& / "2& -3 ()21&/%-,2< &@1#" () %0& 1.,1-2& -3 %0& ")"#82(2 " )+ %0"% %0&

()21&/%(-) 282%&' (2 =&()* &;"#."%&+ )-% %0& 1&-1#&

!"# $ * ' ! "#(=," %& %0& *" *& -, *"* &2 3-, %0& 2%.+8

9 5&'&'=&, #()&" ,(%8< 2%"=( #(%8 " )+ =("2

!"# $ + ' A";& %0& 3(,2% ()21&/%-, '&"2.,& "## %0& 2"'1#&2 -)/& () ,")+-' -,+&,

!"# $ , ' A";& %0& 2&/-)+ ()21&/%-, '&"2.,& "## %0& 2"'1#&2 () ,")+-' -,+&,

9 ! -)%().& %0(2 1,-/ &22 .)%(# " ## %0& -1&,"%-,2 0";& '&"2.,&+ "## %0& 1" ,%2 -)& %('&

9 B0(2 /-'1#&%&2 %0& 3(,2% ,&1#(/" %&

!"# $ - ' 5&1&"% 2%&12 C ")+ D 3-, %0& ,&?.(,&+ ).'=&, -3 ,&1#(/"%&2

9 E)2.,& %0&,& (2 "#>" 82 " +&#" 8 =&%>&&) %0& 3(,2% ")+ 2&/-)+ ()21 &/%(-)!"# $ . ' E)%&, %0& +" %" ()%- F:G :BHI BF ")+ ")" #8J& 8-., ,&2.#%2

!"# $ / ' K,"> /-)/#.2(-)2 ")+ '"L& /0")*&2 (3 )&/&22",8

The parts selected forthe MSA are notrandom samples. Wewant to be sure the

parts selectedrepresent the overallspread of parts thatwould normally be seenin manufacturing. Donot include parts thatare obviously grosslydefective, they couldactually skew yourmathematical resultsand conclude that the

MSA is just fine. Forexample, an enginemanufacturer was usinga pressure tester to

check for leaks in engine blocks. All the usual ports were sealed with plugs and the tester wasattached and pressure was applied. Obviously, they were looking for pin hole leaks that would causeproblems later down the line. The team performing the MSA decided to include an engine block thathad a hole in the casting so large you could insert your entire fist. That was an obvious gross defectand should never been included in the MSA. Don’t be silly saying that once in a while you get a partlike that and it should be tested. NO IT SHOULDN’T - you should never have received it in the firstplace and you have got much bigger problems to take care of before you do an MSA.

Gage R&R Study

• Is a set of trials conducted to assess the Repeatability andReproducibility of the measurement system.

•

Multiple people measure the same characteristic of the same set ofmultiple units multiple times (a crossed study)

•

Example: 10 units are measured by 3 people. These units are then

randomized and a second measure on each unit is taken.

A Blind Study is extremely desirable.

• Best scenario: operator does not know the measurement is a part of a

test

•

At minimum: operators should not know which of the test parts they are

currently measuring.

NO, not that kind of R&R



190


Gage R & R Study

This is the mostcommonly usedCrossed Design.

10 parts are eachmeasure by 3different operators2 different times.

To get the totalnumber of datapoints in the studysimply multiplythese numberstogether. In thisstudy we have 60measurements.

This and the next few slides show how to create a data collection table in SigmaXL ®.


!" #$ & ''()" $*(+ ,#(- & +. !(/ 0'"$*(+

1 2 3 4 3 5 6#(7789 :87 *; + *7 7<(= +

& - *+*-0 - (> $= ( - 8" 70#8-8+$7?/" #$?(/ 8#"$(# *7 #8@0*#89

A<#88 *7 B8$$8#C

! " # $ % & ' ( ) ! *

D /8#" $(# 1

D /8#" $(# 5

D /8#" $(# 4

A#*"' 1

A#*"' 5

A#*"' 1

A#*"' 5

A#*"' 1

A#*"' 5

!

"

#

$

7

Data Collection Sheet



192


Gage R & R

Graphical Output


We will now repeat theanalysis of theprevious Gage R&Rdata with a StandardDeviation Multiplier of6 and a Tolerancevalue of 1. Recall thatthe previous analysisused a StandardDeviation Multiplier of5.15. Change Alpha toremove interaction to0.25. This will preventSigmaXL® fromremoving the part by

operator interactionterm.

Select “SigmaXL>Measurement Systems Analysis > Analyze Gage R&R (Crossed)” and enter thevalues as shown above.

This chart may be recreated by taking the following steps:

1. Copy the “% Total

Variation (TV)” column.2. Paste the column to theright of the “%Contribution of VarianceComponent” column.3. Copy the “%Tolerence” column.4. Paste the column to theright of the “% TotalVariation (TV)” column.5. Highlight the entire

table which the“% TotalVariation (TV)” was

added.6. From Excel, Insert>(Chart) Column>2-DClustered Column.7. Delete the “VarianceComponent “ columnfrom this chart.



193


Graphical Output (cont.)


This Multi-Vari Chart was created withSigmaXL®’s Multi-Vari tool:

1.

Select the data which will be used for thechart.2.

Select “ SigmaXL>Graphical Tools>Multi-

Vari Chart ”

3. This chart was generated from the“Gage AIAG2 - SigmaXL Format ” worksheet. Select “Response” as“Numerical Data Variable (Y)”, “Operator ” as “Group Category Factor (X1)”, and“Part” as “Group Category Factor (X2)”.

The ANOVA table values are utilized to calculate % Contribution and Standard Deviation. To

calculate % study variation and % tolerance, you will need to know values for the StandardDeviation and tolerance ranges. SigmaXL® defaults to a value of 6 (the number of StandardDeviations within which about 99.7 % of your values should fall). Tolerance ranges are based onprocess tolerance and are business values specific to each process.

This output tells us the Tolerance is 19.40, the output is 17.05. Therefore, this gage is acceptable.

I can see clearly now



195


Signal Averaging Example (cont.)


Paper Cutting Exercise

We now use it in theCentral LimitTheorem equationto estimate theneeded number ofrepeated measuresto do this we will usethe StandardDeviation estimatedpreviously.

Determine sample size:

Using the average of 6

repeated measures will

reduce the Repeatability

component of

measurement error to the

desired 15% level.

This method should be considered temporary!



196


Attribute MSA


The Discrete MeasurementStudy is a set of trialsconducted to assess the abilityof operators to use anoperational definition orcategorize samples, an Attribute MSA has:

1 . Multiple operators measure(categorize) multiple samples amultiple number of times. Forexample: 3 operators eachcategorize the same 50samples, then repeat themeasures at least once.

2. The test should be blind. Itis difficult to run this without theoperator knowing it is acalibration test, but the

When a Continuous MSA is not possible an Attribute MSA can be performed to evaluate the qualityof the data being reported from the process.

! #$%&'(')'*+ ,-$( %' .--$-- ! %%/01,%$ 2$. -,/$#$3% 4+-%$#-5

6 7&$+ ./$ ,-$( 03 -0%,.%0'3- 8&$/$ . 9'3%03,',- #$.-,/$ 9. 33'%

1$ '1%.03$(5

6 :% /$;,0/$- . #030#,# '< = > .- #.3+ -.#?)$- .- . 9'3%03,',-

-%,(+5

6 @0-.*/$$#$3%- -&',)( 1$ ,-$( %' 9). /0<+ '?$/.%0'3. ) ($<030%0'3-

<'/ %&$ 9.%$*'/0$-5

A ! %%/01,%$ (. %. . /$ ,-,.))+ %&$ /$-,)% '< &,#.3 B,(*#$3% C8&09&

9.%$*'/+ ('$- %&0- 0%$# 1$)'3* 03D5

A E &$3 9.%$*'/0F 03* 0%$#- C*''(G 1. (H %+?$ '< 9.))H /$.-'3 <'/

)$.I03*D +', 3$$( . &0*& ($*/$$ '< .*/$$#$3% '3 8&09& 8.+ .3

0%$# -&',)( 1$ 9. %$*'/0F $(5

! %%/01,%$ J .*$ K//'/! %%/01,%$ J .*$ K//'/

L$?$.%.10)0%+L$?$.%.10)0%+ L$?/'(,9010)0%+L$?/'(,9010)0%+ M .)01/.%0'3M .)01/.%0'3

! %%/01,%$ J .*$ K//'/! %%/01,%$ J .*$ K//'/

L$?$.%.10)0%+L$?$.%.10)0%+ L$?/'(,9010)0%+L$?/'(,9010)0%+ M .)01/.%0'3M .)01/.%0'3

samples should be randomized and their true categorization unknown to each operator.

The test is analyzed based on correct (vs. incorrect) answers to determine the goodness of themeasuring system.

Attribute MSA Purpose

!"# %&'%()# (* +, ! ""# $% & "' )* ! -).

/ !( 0#1#'2-,# -* + 33 -,)%#41(') &)# 1"# )+2# 4'-1#'-+ 1( 0#1#'2-,# 5%+))6 *'(2 5*+-367

/ !( +))#)) 8(&' -,)%#41-(, )1+,0+ '0) +9+-,)1 8(&' 4&)1(2#':) '#;&-'#2#,1)7

/ !( 0#1#'2-,# "(< <#33 -,)%#41(') + '# 4(,*('2-,9 1( 1"#2)#3=#)7

/ !( -0#,1-*8 "(< -,)%#41(') + '# 4(,*('2-,9 1( + 5>,(<, 2+)1#'?6 <"-4" -,43&0#).

@ A(< (*1#, (%#'+1(') )"-% 0#*#41-=# %'(0&417

@ A(< (*1#, (%#'+1(') 0-)%()# (* +44#%1+B3# %'(0&417

/ C-)4(=#' +'#+) <"#'#.

@ !'+-,-,9 -) '#;&-'#07

@ D'(4#0&'#) 2&)1 B# 0#=#3(%#07

@ E1+,0+'0) +'# ,(1 +=+ -3+B3#7

F, F11'-B&1# GE F -) )-2-3+' -, 2+,8 <+8) 1( 1"# 4(,1-,&(&) GE F? -,43&0-,9 1"#

%&'%()#)7 C( 8(& "+=# +,8 =-)&+3 -,)%#41-(,) -, 8(&' %'(4#))#)H I, 8(&' #J%#'-#,4#

"(< #**#41-=# "+=# 1"#8 B##,H



197


Visual Inspection Test


Take 60 Seconds and count the number of times “F” appears in this paragraph?

Tally the answers? Did everyone get the same answer? Did anyone get 36? That’s the rightanswer!

Why not? Does everyone know what an “F” (defect) looks like? Was the lighting good in theroom? Was it quite so you could concentrate? Was the writing clear? Was 60 seconds longenough?

This is the nature of visual inspections! How many places in your process do you have visual

inspection? How good do you expect them to be?

How can we Improve Visual Inspection?

!"# % #&#''()* +, !-.(/(/0 1.-2 3./4' ,+- 1(-') 5 6.'' 1.-2'(/ )"# 1.)"#-6* 3./46(/0 +, 1.-2 7(8# 9)+&: (' 1+-#2+') (/

)"# ;*#' +, 1.-2 < =/#-'> 9(/&# )"# 1+-#,.)"#-' +, )"# 1.-2

< =/#-' !-.(/#4 )"# 1.-2 3./4' ,+- 1(-') 5 6.'' 1.-2' (/

)"# 1.)"#-6* 3./46(/0 +, 1.-2 7(8# 9)+&:? )"# 1.-2 < =/#-'

1##6 )"#* '"+@64 &.--* +/ =()" )"# 1.2(6* !-.4()(+/ +,

!-.(/(/0 1.-2 3./4' +, 1(-') 5 6.'' 1.-2#-' (/ )"# 1.)"#-6*

3./46(/0 +, 1.-2 7(8# 9)+&: A#&.@'# )"#* A#6(#8# () (' )"#

A.'(' +, B ++4 1@/4.2#/).6 1.-2 C./.0 #2#/)>

! "#$% & ()# *+ ,-".) ! " # % & '( ) * + , & - % . /

! 0 )& *" 1+* 2*"'#'#3 4 5& *1'6 '!" 1'+#

! 7 & , & 8+ ) 9 ' :; " 8 < '- : = > + ; # - " * . ? " ( ) 8 & :

! @ : 1" % 8 ': A ?1" #-" * -:

! @:1"%8 ':A ?&1BC) D*+!&-;*&:

! @:1"%8 ':A @,"8;"1 '+# D*+!&-;*&:

" @,"8;"1 '+# +6 1A& :"(& 8+!"1 '+# +# &"!A )"*1 E

" @"!A &, " 8;"1 '+# )&*6+*( &- ;#- &* 1A& :" ( & 8 '3 A1'#3 E

" @#: ;* & " 88 &," 8;" 1'+#: " * & ( " -& F ' 1A 1A& : " ( &

: 1 " # - " * - E

G ++H !8+:&8. #+FILook closely now



198


Attribute Agreement Analysis




199


Attribute Agreement Analysis (cont.)


Fleiss’ Kappa statistic is a “correlation coefficient” for discrete data. Kappa ranges from -1 to +1. AKappa value of +1 indicates perfect agreement. If Kappa = 0, then agreement is the same as wouldbe expected by chance. If Kappa = -1, then there is perfect disagreement. Kappa values > 0.9

indicate a very good measurement system; Kappa values > 0.7 indicate an acceptablemeasurement system.

The Between Appraiser Agreement and All Appraisers vs. Standard Agreement are also known as“System Effectiveness Scores”, with > 95% considered very good, 90-95% acceptable, 80 to < 90% marginal, and < 80 % unacceptable.

Clearly this measurement system needs to be improved, but we should not be quick to judge Appraiser C. The confidence intervals are quite wide and overlap. It is a good practice to “blamethe process not the people”. Look for unclear or confusing operational definitions, inadequatetraining, operator distractions or poor lighting. Consider the use of pictures to clearly define adefect. Use Attribute MSA as a way to “put your stake in the ground” and track the effectiveness of

improvements to the measurement system.



200


Exercise objective: Perform and Analyze an Attribute MSA Study.

•

You will need the following to complete the study: – A bag of M&Ms containing 50 or more pieces

– The attribute value for each piece.

–

Three or more inspectors.

• Judge each M&M as pass or fail.

– The customer has indicated that they want a bright and shiny M&M

and that they like Ms.

•

Pick 50 M&Ms out of a package.

• Enter results into SigmaXL®s Attribute MSA Template and

draw conclusions.

• The instructor will represent the customer for the Attribute

score.

Part AttributeNumber

M&M

M&M

M&M

1

2

3

Pass

Fail

Pass


To complete this study you will need, a bag of M&Ms containing 50 or more “pieces”. The

Attribute Value for each piece, which means the “True” value for each piece, in addition to beingthe facilitator of this study you will also serve as the customer, so you will have the say as to if thepiece is actually a Pass or Fail piece. Determine this before the inspectors review the pieces.You will need to construct a sheet as shown here to keep track of the “pieces” or “parts” in ourcase M&Ms it is important to be well organized during these activities. Then the inspectors willindividually judge each piece based on the customer specifications of bright and shiny M&M withnice M’s.

M&M Exercise



201



You have now completed Measure Phase – Measurement System Analysis.

! Understand Precision & Accuracy

!

Understand Bias, Linearity and Stability

!

Understand Repeatability & Reproducibility

! Understand the impact of poor gage capability on

product quality.

! Identify the various components of variation

!

Perform the step by step methodology in variable,and attribute MSA’s


Notes



202


Lean Six Sigma

Black Belt Training

Now we will continue in the Measure Phase with “Process Capability”.

Measure PhaseProcess Capability



205


Process Output Categories

As you have learned, variation exists in everything. There will always be variability in every processoutput. You can’t eliminate it completely, but you can minimize it and control it. You can toleratevariability if the variability is relatively small compared to the requirements and the processdemonstrates long-term stability, in other words the variability is predictable and the processperformance is on target meaning the average value is near the middle value of the requirements.

The output from a process is either: capable or not capable, centered or not centered. The degreeof capability and/or centering determines the number of defects generated. If the process is notcapable, you must find a way to reduce the variation.

And if it is not centered, it is obvious that you must find a way to shift the performance. But what doyou do if it is both incapable and not centered? It depends, but most of the time you must minimizeand get control of the variation first, this is because high variation creates high uncertainty, youcan’t be sure if your efforts to move the average are valid or not. Of course, if is just a simpleadjustment to shift the average to where you want it, you would do that before addressing thevariation.

Problem Solving Options – Shift the Mean

Two output behaviorsdetermine how well we meetour customer or processoutput expectations. The first

is the amount of variationpresent in the output and thesecond is how well the outputis centered relative to therequirements. If the amount ofvariation is larger than thedifference between the upperspec limit minus the lowerspec limit, our product orservice output will alwaysproduce defects, it will not be

capable of meeting thecustomer or process outputrequirements.

Our efforts in a Six Sigmaproject that is examining a

process that is performing at alevel less than desired is toShift the Mean of performancesuch that all outputs are withinan acceptable range.

Our ability to Shift the Meaninvolves finding the variablesthat will shift the process overto the target. This is theeasiest option.

Process Capability

LSL USLAverage

Target

Capable andon target

LSL USLAverage

Target

Capable andon target

C e n t e r

p r o c e

s s

R e d u c e s p r e a d

LSL USLAverage

Target

Off target

LSL USLAverage

Target

Off target

LSL USLAverage

Target

Incapable

LSL USLAverage

Target

Incapable

!"! #" !

"$%&' !"!

#" !

"$%&'

!"#$ #&'()'*$ +#&,#&- ."* '/0#/1)*$ ."/. 2#)) $"#+. ."* 30(4*$$ ('*0 .( ."*

./0- *.5 !"#$ #$ 6$6/))7 ."* */$#*$. (3.#(&5



206


Problem Solving Options – Reduce Variation

Problem Solving Options – Shift Mean & Reduce Variation

Reducing the variation meansfewer of our outputs failfurther away from the target.Our objective then is to

reduce variation of the inputsto stabilize the output.

Process Capability

!"##"##"#

!"#$ #$ &'(#)*++' ,-& $- .*$' &- *))-/(+#$" *,0 -))12$ -3&., #, 4#5

4#6 /* (2-7.)&$8

!"!#" !

"$%&' ) *+,-.+!"!#" !

"$%&' ) *+,-.+

!"#$ &''()$ &*+,- #- .#/ .#012 3)&4,'+$5Combination of shifting theMean and reducing variation –This is the primary objective ofSix Sigma projects.

Problem Solving Options

!"! #" ! #" !

$%&' ")'*

!"! #" ! #" !

$%&' ")'*

! "#$%&'() +,$' $-.($/' -01$23 +,/- 4$5/67 2%+ 2066%4/68 9 &'+%-/6'

&'&0(() 5% 2%+ 3% :%6 +,$' %.+$%2 "&+ $: +,/) 5%; $+<' +,/ /0'$/'+=

Move the specification limits –Obviously this implies making

them wider, not narrower.Customers usually do not gofor this option.



207


Capability Studies

Steps to Capability

A stable process is one that isconsistent with time. TimeSeries Plots are one way tocheck for stability, Control

Charts are another. Yourprocess may not be stable atthis time. One of the purposesof the Measure Phase is toidentify the many X’s possiblefor the defects seen, gatherdata and plot it to see if thereare any patterns to identifywhat to work on first.

When performing Capability

Analysis, try to get as much

Process Capability

! "# "$ % &% '( * '+,%-. /

! " #$ &'($')$) (* +$ #$,-./#0 1$#&*)&2 0 $3(&4/(&*'3 *5 / 1#*2$3363 /+ &.&(7

(* 4$$( &(3 #$8-&#$4$'(39

! : /' +$ 2*')-2($) *' +*(; )&32#$($ /') 2*'(&'-*-3 )/(/9

! " #$ 4*3( 4$/'&', 5-. <;$' 2*')-2($) *' 3(/+.$0 1#$)&2(/+.$

1#*2$33$39

! " #$ 2*44*'.7 #$1*#($) /3 =&, 4/ >$?$. <;&2; &3 *1(&4/. @3;*#( ($#4A

1$#5*#4/'2$9

! B$8-&#$ / (;*#*-,; -')$#3(/')&', *5 (;$ 5*..*<&',C

D : -3(*4$#63 *# +-3&'$3363 31$2&5&2/ (&*' .&4&(3

D E /(-#$ *5 .*', ($#4 ?39 3;*#( ($#4 )/ (/

D F$/ ' / ') =(/')/#) G$?&/ (&*' *5 (;$ 1#*2$33

D " 33$334$'( *5 (;$ '*#4/.&(7 *5 (;$ )/ (/ @2*'(&'-*-3 )/ (/ *'.7A

D H#*2$)-#$ 5*# )$($#4&'&', = &, 4/ .$?$.

data as are possible, back as far in time as possible, over a reference frame that is generallyrepresentative of your process.

Select Output forImprovement

Verify CustomerRequirements

ValidateSpecification

Limits

Collect SampleData

DetermineData Type

(LT or ST)

Check datafor normality

CalculateZ-Score, PPM,

Yield, CapabilityCp, Cpk, Pp, Ppk

#1

#2

#3

#4

#5

#6

#7



208


Verifying the Specifications

Specifications must beverified beforecompleting the

Capability Analysis. Itdoesn’t mean that youwill be able to changethem, but on occasionsome internalspecifications havebeen made muchtighter than thecustomer wants.

Data Collection

You must know if the datacollected from processoutputs is a short-term ora long-term representationof how well the processperforms. There are

several reasons for this,but for now we will focuson it from the perspectiveof assessing the capabilityof the process.

To help you understandshort-term vs. long-termdata, we will start bylooking at a manufacturingexample first. In thisscenario the manufacturer

Process Capability

! "# $%&'( $ %' *'($ &+#, -

! " #$% '( %#) (*+,-) *. %#) (/)-'.'-$%'*0(1

2 3 +(%*4), ,)5 +',)4)0%( 678 3 9

2 :+('0)(( ,)5+',)4)0%( 6%$,;)%< =)0-#4$,>9

2 3 *4/?'$ 0-) ,)5+',)4)0%( 6,);+?$%'*0(9

2 @)('; 0 ,)5 +',)4)0%( 6=?+)/,'0%< (A(%)49

! B ,) %#)A -+,,)0%1 C'>)?A %* -#$0;)1

! B ,) %#)A +0D),(%**D $0D $ ;,))D +/*01

2 8 /),$ %'*0$ ? D ).'0'%'*0(

2 @)/ ?*A)D %* %#) E*,> .*,-)

is filling bottles with a certain amount of fluid. Assume that the product is built in lots. Each lot is builtusing a particular vendor of the bottle, by a particular shift and set of employees and by one of manymanufacturing lines. The next lot could be from a different vendor, employees, line, shift, etc.

Each lot is sampled as it leaves the manufacturing facility on its way to the warehouse. The resultsare represented by the graphic where you see the performance data on a lot by lot basis for theamount of fill based on the samples that were taken. Each lot has its own variability and average asshown. The variability actually looks reasonable and we notice that the average from lot to lot isvarying as well.

What the customer eventually experiences in the amount of fluid in each bottle is the value acrossthe full variability of all the lots. It can now be seen and stated that the long-term variability will alwaysbe greater than the short-term variability.

Lot 1

Lot 2

F i l l Q u a n t i t y Lot 3

Lot 4

Lot 5

Short-term studies

Long-term study

Capability Studies should include all

observations (100% sampling) for a specified period.

Long-term data:

• Is collected across a broader inference

space.

• Monthly, quarterly; across multiple

shifts, machines, operators, etc

• Subject to both common and special

causes of variation.

• More representative of process

performance over a period of time.

•

Typically consists of at least 100 – 200data points.

Short-term data:

• Collected across a narrow

inference space.

• Daily, weekly; for one shift,

machine, operator, etc.

• Is potentially free of special cause

variation.

• Often reflects the optimal

performance level.

•

Typically consists of 30 – 50 datapoints.



209


Baseline Performance

automatically implies long-term performance. To not use long-term data to describe the BaselinePerformance would be dangerous.

As an example, imagine you reported that the process performance Baseline was based ondistribution 3 in the graphic, you would mislead yourself and others that the process had excellent ontarget performance. If you used distribution 2, you would be led to believe that the averageperformance was near the USL and that most of the output of the process was above the spec limit. To

resolve these potential problems, it is important to always use long-term data to report the Baseline.

How do you know if the data you have is short or long-term data? Here are some guidelines. Asomewhat technical interpretation of long-term data is the process has had the opportunity toexperience most of the sources of variation that can impact it. Remembering the outputs are a functionof the inputs, what we are saying is that most of the combinations of the inputs, each with their fullrange of variation has been experienced by the process. You may use these situations as guidelines.

Short-term data is a “snapshot” of process performance and is characterized by these types ofconditions:

One shift One lineOne batch One employee

One type of service One or only a few suppliers

Long-term data is a “video” of process performance and is characterized by these types of conditions:Many shifts Many batchesMany employees Many services and linesMany suppliers

Long-term variation is larger than short-term variation because of : material differences, fluctuations intemperature and humidity, different people performing the work, multiple suppliers providing materials,equipment wear, etc.

As a general rule, short-term data consist of 20 to 30 data points over a relatively short period of timeand long-term data consist of 100 to 200 data points over an extended period of time. Do not be

Here is another way to lookat long-term and short-termperformance. The “road” appearing graphic actuallyrepresents the target (centerline) and the upper and lowerspec limits. Here again yousee the representativeperformance in short-termsnapshots, which result inthe larger long-termperformance.

Process Baseline is a term

that you will use frequently

as a way to describe theoutput performance of aprocess. Whenever you hearthe word “Baseline” it

Process Capability

!"#$%&& ()&%* +,%- !"#

%&#'%(#) *+,(-.#'/ 0#'1+'/%,2#

*#&#* +1 % 0'+2#33 4"#, %** 5,06.&%'5%7*#3 %'# 6,2+,3.'%5,#89

!"#$%&& ()&%* +,%- !"#

%&#'%(#) *+,(-.#'/ 0#'1+'/%,2#

*#&#* +1 % 0'+2#33 4"#, %** 5,06.

&%'5%7*#3 %'# 6,2+,3.'%5,#89

`

./#"0 1%"2

!%"3#"2) ,$%

./#"0 1%"2

!%"3#"2) ,$%

TARGET USLLSL

1

2

3

4

4#,5 60%"2

7) &%*+,%

4#,5 60%"2

7) &%*+,%



210



Baseline Performance (cont.)

There are many waysto look at thedifference betweenshort-term and long-term data.

First keep on mindthat you never havepurely short-term or

purely long-term data.It is always somethingin between.

Short-term databasically representyour “entitlement” situation: you arecontrolling all thecontrollable sourcesof variation.

misled by the volume of product or service produced as an indicator of long and short-termperformance. Data that represents the performance of a process that produces 100,000 widgets a dayfor that day will be short-term performance. Data the represents the performance of a process thatproduces 20 widgets a day over a 3 month period will be long-term performance.

While we have used a manufacturing example to explain all this, it is exactly the same for a service oradministrative type of process. In these types of processes, there are still different people, differentshifts, different workloads, differences in the way inputs come into the process, different software,computers, temperatures, etc. The same exact concepts and rules apply.

You should now appreciate why, when we report process performance, we need to know what the datais representative of. Using such data we will now demonstrate how to calculate process capability andthen we will show how it is used.

Process Capability

!"#$ &'()*# +,-.#&&#& /0** 1,02' ($1 &302' -"#, '04# )5 (& 46.3 (& 789

:'($1(,1 ;#"0('0-$& -$ '3# ("#,(<#8

!"#$% '($)

* +%"+, - $#./ 01 $+1%+#,

!"#$% '($)

2(%3 ((, - $#./ 01 $+1%+#,

4#,5 '($)

6 7($1 8 8 01 $+1% +#,

Long-term data includes (in theory) all the variation that one can expect to see in the process.Usually what we have is something in between. It is a judgment call to decide which type of data youhave: it varies depending on what you are trying to do with it and what you want to learn from it.

In general one or more months of data are probably more long-term than short-term; two weeks orless is probably more like short-term data.



212


Measures of Capability

Capability Formulas

Process Capability

Note: Consider the “K” value the penalty for being off center

!"# % "&'( %)' (*& +,'

!%*-.*/. 0'1 "*% "2-

LSL – Lower specification limit

USL – Upper specification limit

! * & + , ' 3' * -

4)/'' % "&'( %)' (*&+,'

!%*-.*/. 0'1 "*% "2-

Cp and Pp:

• What is Possible if your process is perfectly Centered

•

The Best your process can be

• Process Potential (Entitlement)

Cpk and Ppk:

• The Reality of your process performance

•

How the process is actually running

• Process Capability relative to specification limits

ope

eality



213


SigmaXL ® Example

There are twocolumns of data thatshow the length ofcamshafts from two

different suppliers.Check the Normalityof each supplier.

In order to useProcess Capabilityas a predictivestatistic, the datamust be Normal forthe tool we areusing in SigmaXL®.

SigmaXL® alsoincludes advancedcapabilities for Non-normal data.

At this point in time we are only attempting to get a baseline number that we can compare to at theend of problem solving. We are not using it to predict a quality, we want to get a snapshot. DO NOTtry and make your process STABLE BEFORE working on it! Your process is a project becausethere is something wrong with it so go figure it out, don’t bother playing around with stability.

Ensure that X-Bar & S Charts are selected. SigmaXL® will compute the short term StDev using the

within subgroup variation calculated for the X-Bar & S Charts. Note that SigmaXL® defaults to usinga pooled StDev to calculate short term StDev.

Process Capability



214


SigmaXL® Example (cont.)

Looking below, 600.06 is theprocess Mean for Supplier 2 andis very close to the targetalthough both tails of thedistribution fall outside of thespecification limits. The Cpk

index is very similar to Supplier 1but this infers that we need towork on reducing variation.When making a comparisonbetween Supplier 1 and 2 elativeto Cpk vs Ppk we see thatSupplier 2 process is more proneto shifting over time. That couldbe a risk to be concerned about.

Again, Compare the PPM levels?

What does this tell us? Hint lookat PPM < LSL.

So what do we do. In lookingonly at the means you may claimthat Supplier 2 is the best. Although Supplier 1 has greaterpotential as depicted by the Cpmeasure and it will likely beeasier to move their Mean thandeal with the variation issues ofSupplier 2. Therefore we will

work with Supplier 1.

Process Capability

599.548 is the process Meanwhich falls short of the target(600) for Supplier 1, and the lefttail of the distribution falls outside

the lower specification limits.From a practical standpoint whatdoes this mean? You will havecamshafts that do not meet thelower specification of 598 mm.

Next we look at the Cp index.This tells us if we will produceunits within the tolerance limits.Supplier 1 Cp index is .66 whichtells us they need reduce the

process variation and work oncentering.

Look at the PMM levels? Whatdoes this tell us?



215



SigmaXL® doesnot includeBenchmark Z’s(sigma level) in

ProcessCapability. Tocompute sigmalevel, use theProcess SigmaLevel Calculatoras shown above.

This slide shows Sigma Shift as 0, resulting in sigma levels that match Benchmark Z’s. This isoptional. If the Sigma Shift is kept at 1.5 this will be added to the Sigma Level Values.

The overall long term sigma level is 1.86 for Supplier 1. If you enter the short term StDev of .556the potential Process Sigma Level will be 2.16.

Process Capability



216



Continuous Variable Caveats

Well this is one way to lie with

Statistics…When used as a predictivemodel, Capability makes assumptionsabout the shape to the data. Whendata is Non-normal, the model’sassumptions don’t work and would beinappropriate to predict.

It’s actually good news to have datathat looks like this because yourproject work will be easy!!! Why?Clearly there is something occurring inthe process that should be fairly

obvious and is causing these very twodistinct distribution to occur. Take a

The overall Long Term sigma level is 1.4. for Supplier 2. If you enter the short term StDev of 1.0 thepotential Process Sigma Level will be 1.72.

Process Capability

look at each of the distributions individually and determine what is causing this. DON’T fuss orworry about Normality at this point, hop out to the process and see what is going on.

Here in the Measure Phase stick with observed performance unless your data are Normal. Thereare ways to deal with Non-normal data for predictive capability but we’ll look at that once you haveremoved some of the Special Causes from the process. Remember here in the Measure Phase weget a snapshot of what we’re dealing with, at this point don’t worry about predictability, we’lleventually get there.

Please note, the Normal Distribution shown in blue has been added manually to illustrate the shortterm variation.



217


Capability Steps

Process Capability

When we follow the steps in performing a capability study on Attribute Data we hit a wall at step 6. Attribute Data is not considered Normal so we will use a different mathematical method to estimatecapability.

#7




Limits

Collect SampleData

DetermineData Type

(LT or ST)

Check datafor Normality

CalculateZ-Score, PPM,

Yield, Capability

Cp, Cpk, Pp, Ppk

#1

#2

#3

#4

#5

#6

We can follow the stepsfor calculating capability

for Continuous Data until

we reach the question

about data Normality !




Limits

Collect Sample

Data

CalculateDPU

Find Z-Score

Convert Z-Scoreto Cp & Cpk

#1

#2

#3

#4

#5

#6

#7

Notice the difference

when we come to step 5 !



219


Z Table

Attribute Capability

Stable process can shift and drift by as much as 1.5 Standard Deviations. Want the theory behindthe 1.5…Google it! It doesn’t matter.

In our case we haveto lookup theproportion for the Zscore of 1.33. This

means thatapproximately 9.1%of our data fallsbeyond the upperspec limit of 54. Ifwe are interested indetermining partsper million defectivewe would simplymultiply theproportion .09176 by

one million. In thiscase there are91,760 parts permillion defective.

Process Capability

! ""#$%&"' )*"* $+ ! " # ! $ % ,-./ "'#0 $. "1' +1$2"') 3-.)$"$-. +$.3' $" #'4&$#'+ +-

0*.5 +*06,'+ "- /'" * /--) '+"$0*"' 7$"1 #'*+-.*%,' 3-.2$)'.3'8

91-#" "'#0 3*6*%$,$"5 $+ "56$3*,,5 #'6-#"'): +- * +1$2"$./ 0'"1-) 7$,, %' '06,-5')

"- '+"$0*"' +1-#" "'#0 3*6*%$,$"58

Add

1.5

Long Term

CapabilityZLT

Subtract

1.5

Short Term

CapabilityZST

Long Term

Capability

Short Term

Capability

ZLTZST

Add

1.5

Long Term

CapabilityZLT

Subtract

1.5

Short Term

CapabilityZST

Long Term

Capability

Short Term

Capability

ZLTZSTYou Want to Estimate :

Your Data Is :

3.40.06

232.70.35

6209.731.74

66807.21350.03

308537.522750.12

691462.5158655.31

Long-Term

DPMO

Short-Term

DPMO

Sigma

Level

3.40.06

232.70.35

6209.731.74

66807.21350.03

308537.522750.12

691462.5158655.31

Long-Term

DPMO

Short-Term

DPMO

Sigma

Level



220


Attribute Capability (cont.)

Attribute Capability Example

We will use this example to demonstrate the capability of a customer service call group.

Some people like touse sigma level(SigmaXL® reportsthis as “Z-bench”),

other like to use Cpk,Ppk. If you are usingCpk and Ppk youcan easily translatethat into a Z score orsigma level bydividing by 3.

Process Capability

!" $%&'%() *+&,& -./0123, ".1 43( ,&& *+&/& %, 3 /&23*%.(,+%5 6&*'&&( *+&07

8- '& 9%$%9& .1/ : ,+./*;*&/0 6" < '& 43 ( 9&*&/0%(& .1/ = 5> 3(9 %- '& 9%$%9&

.1/ : 2.();*&/0 6" < '& 43( 9&*&/0%(& .1/ ?5>7

A customer service group is interested in estimating the Capability of

their call center.

A total of 20,000 calls came in during the month but 2,500 of them

dropped before they were answered (the caller hung up).

Results of the call center data set:

Samples = 20,000

Defects = 2,666

They hung up….



221


Attribute Capability Example (cont.)

If you want to know how that variation will affect the ability of your process to meet customerrequirements (CTQ's), you should use Cpk.

If you just want to know how much variation the process exhibits, a Ppk measurement is fine.

Remember Cpk represents the short-term capability of the process and Ppk represents the long-term capability of the process.

With the 1.5 shift, the above Ppk process capability will be worse than the Cpk short-term capability.

Follow these steps todetermine yourprocess capability.

Remember that,DPU is Defects perunit, the total number of possible errors ordefects that could becounted in a processor service. DPU iscalculated bydividing the totalnumber of defects bythe number of units

or products.

Process Capability

"Cpk” is an index (asimple number)which measures howclose a process isrunning to itsspecification limits,relative to the natural

variability of theprocess.

A Cpk of at least1.33 is desired andis about 4 sigma +with a yield of99.3790% .

The above Cpk of .87 is about 2.61

sigma or a 87%Yield.



223


Lean Six Sigma

Black Belt Training

The Measure Phase is now complete. Get ready to apply it. This module will help you create aplan to implement the Measure Phase for your project.

Measure PhaseWrap Up and Action Items



224



Measure Phase Overview - The Goal

Six Sigma Behaviors

!"# % &' ( &) *"# +#' ,-.# /"' ,# 0, *&1

! "#$%&#' #)*+,-# .&/ 0+.11%$2 345 6.-%.7+#1 81%&9 . 6.-%#:2 ,$ :,,+1; < "#:. %+#/ =-,0#11 >. **%&9

< ?%1@7,&# "%. 9-.A1

< 4BC "%. 9-.A1

< ?>DE

! "#A,&1:-.:# . F,-G%&9 G&,F+#/9# ,$ H.1%0 I:.:%1:%01 :, 81# .1 .

0,AA8&%0.:%,& :,,+ .&/ . 7.1%1 $,- %&$#-#&0#;

! =#-$,-A >#. 18-#A#&: J .*. 7%+%:2 1:8/%#1 ,& ,8:*8: 6.-%.7+#1;

! D6.+8.:# 1:.7%+%:2 ,$ *-,0#11 .&/ #1:%A.:# 1:.-:%&9 *,%&: 0. *. 7% +%:2;

• Being tenacious, courageous

• Being rigorous, disciplined

• Making data-based decisions

• Embracing change & continuous learning

• Sharing best practices

Each player

in the Six Sigma process must be A ROLE MODEL

for the Six Sigma culture

Walk

the

Walk



225


Measure Phase Deliverables

Measure Phase - The Roadblocks

You will run into roadblocks throughout your project. Listed here are some common ones thatBelts have to deal with in the Measure Phase.


Listed here are the Measure Deliverables that each candidateshould present in a Power Point presentation to their mentor andproject champion.

At this point you should understand what is necessary to provide thesedeliverables in your presentation.

– Team Members (Team Meeting Attendance)

– Primary Metric

– Secondary Metric(s)

– Process Map – detailed

– FMEA

– X-Y Matrix

– Basic Statistics on Y

–

MSA – Stability graphs

– Capability Analysis

– Project Plan

–

Issues and Barriers

Look for the potential roadblocks and plan to addressthem before they become problems:

–

Team members do not have the time to collect data.

– Data presented is the best guess by functional managers.

–

Process participants do not participate in the creation of the X-Y

Matrix, FMEA and Process Map.

It won

t all be

smooth sailing…



226


DMAIC Roadmap

Measure Phase

The DMAIC Phases Roadmap is a flow chart of what goals should be reached during each phase ofDMAIC. Please take a moment to review.




Identify and Prioritize All X’s

Prove/Disprove Impact X’s Have On Problem

Identify, Prioritize, Select Solutions Control or Eliminate X’s Causing Problems

Implement Solutions to Control or Eliminate X’s Causing Problems

Implement Control Plan to Ensure Problem Doesn’t Return



Estimate COPQ

Establish Team



Identify and Prioritize All X’s

Prove/Disprove Impact X’s Have On Problem

Identify, Prioritize, Select Solutions Control or Eliminate X’s Causing Problems

Implement Solutions to Control or Eliminate X’s Causing Problems

Implement Control Plan to Ensure Problem Doesn’t Return



Estimate COPQ

Establish Team

C h a m p i o n /

P r o c e s s O w n e r

D e f i n e

M e a s u r e

A n a l y z e

I m p r o v e

C o n t r o l

!"#$%&"' )*+,&"- .#$#"-"/# !"#"*-%/"'

011"11 2"$13*"-"/# .41#"-

5-6&"-"/# 7 8$/9"1 #+ 2$:" .41#"- 0;;"6#$,&"

!"#$%&"' )*+;"11 2$66%/9

5'"/#%<4 0&& )*+;"11 =>1 7 $31%/9 )*+,&"-1 ?@%18,+/"A )*+;"11 2$6B

."&";# #8" C%#$& @"D =>1 7 $31%/9 )*+,&"-1 ?=EF 2$#*%GA @2H0B

011"11 .#$,%&%#4 ?. #$#%1#%;$ & 7 +/#*+&B

011"11 7 $6$,%&%#4 ?)*+,&"- D%#8 7 "/#"*%/9I .6*"$'B

H1#%-$#" )*+;"11 .%9-$ J"K"&

L"$'4 <+* 0/$&4M"

L"6"$#$,&" N

L"6*+'3;%,&"OPP

FF

L"K%"D )*+9*"11 D%#8 7 8$-6%+/

This map of the Measure Phaserollout is more of a guideline thana rule. The way that you applythe Six Sigma problem-solvingmethods to a project depends onthe type of project your workingwith and the environment thatyou are working in.

For example in some cases it

may make sense to jump directlyinto Measurement System Analysis studies while you collectdata to characterize otheraspects of the process inparallel. In other cases it may benecessary to get a betterunderstanding of the processfirst. Let common sense anddata dictate your path.



227


Measure Phase Checklist

These are questions thatyou should be able toanswer in clear,understandable

language at the end ofthis phase.

Planning for Action


! " # $%& " ( %" $)*+,$

-.",)*/0 1&*)*1#2 3 4$ #,. 5+)",)*#2 /#*2%&" 6+."$

! "# %&' ()# *#+ ,-./'## 0)1 /-')%'23

! 4 -' %&' 2'/*#*.5 1.*5%# *2'5%*6*'23! 7 &'-' )-' %&' 2)%) /.88'/%*.5 1.*5%#3

! "# %&'-' )5 )5)89#*# .6 %&' :')#;-':'5% #9#%':3

! 7 &'-' 2*2 9.; <'% %&' 2)%)3

-.",)*/0 1&*)*1#2 3 4$ #,. 5+)",)*#2 /#*2%&" 6+."$

! "# %&'-' ) /.:18'%'2 =>? 0)%-*@3

! 7 &. 1)-%*/*1)%'2 *5 %&'#' )/%*A*%*'#3

! "# %&'-' ) /.:18'%'2 B0C4 3

! D)# %&' ,-.E8': F%)%':'5% /&)5<'23

! D) A' 9.; *2'5%*6*'2 :.-' G H ,I3

7)#8* 2 *)0 9$$"$$6 ",)

! *# %&' (J.*/' .6 %&' ,-./'##+ #%)E8'3

! "6 5.%K &)A' %&' #1'/*) 8 /);#'# E''5 )/L5.M8'2< '23

! G )5 %&' <..2 #*<5) 8# E' *5/.-1.-)%'2 *5%. %&' 1-./'##3

! G )5 %&' E)2 #*< 5)8# E' -':.A'2 6-.: %&' 1-./'##3! D.M #%)E8' /)5 9.; :)L' %&' 1-./'##3

: #5 #8 * 2* )0 9$ $ " $ $ 6 " ,)

! 7 &)% *# %&' #&.-%>%'-: )52 8.5<>%'-: /) 1) E*8*%9 .6 %&' 1-./'##3

! 7 &)% *# %&' 1-.E8':K .5' .6 /'5%'-*5<K #1-')2 .- #.:' /.:E*5)%*.53

; ","&# 2 ( %"$)*+,$

! 4 -' %&'-' )59 * ##;'# .- E)--*'-# %&)% 1-'A'5% 9.; 6-.: /.:18'%*5< %&*# 1&)#'3

! N. 9.; &)A' ) 2'O;)%' -'#.;-/'# %. /.:18'%' %&' 1-.P'/%3

Over the last decade of deploying Six Sigma it has been found that the parallel application of thetools and techniques in a real project yields the maximum success for the rapid transfer ofknowledge. For maximum benefit you should apply what has been learned in the Measure Phaseto a Six Sigma project. Use this checklist to assist.

!"#$%" '(" )* *+,*+$) '" "-"."%'/ ,# 0 )/'"

1 () ' ) +" 2 ,3+ 4"5,%6) +2 . "'+ $5/7

1 ()' $/ 2, 3+ 8+$.) +2 . "'+$57

1 () ' $/ 2, 3+ * +,9"5' #$%) %5$)- : ,) - ;')+ : "' < '$."= ',

+")5( $'7

>,0 $ / 2 ,3+ 6"#"5' . ") /3+"67

1 ("% 6 ,"/ 2 ,3+ 6" #"5' ,553+71 ()' $/ 2 ,3+ 6 "#"5'7

?()+' ) *-)% ', )55,.*-$/( '(" 6"/$+"6 /')'" ,# '("

53-'3+"

8+"6$5' '(" @$/A ,# /3/')$%) B$ - $'2

C 3)% '$#2 + $/A ,# .""'$%: 5+$'$5)- %""6 / ,# ?3/ ',."+D

E3/$%"// ) %6 8",*-"

F/')B- $/( *,'"%'$)- +"-)'$,%/($*/ B"'0 ""% G) +$)B-"/

E) -) %5" ) %6 H,53/ @ "/,3+5"/

I)- $6)'" H$%)%5$)- E"%"#$'/

!"#$%" ?() +)5'"+$/'$5/ ,# !) ')

H,53/ ,% '(" *+,B-". /,-G$%: *+,5"//

J6"%'$#2 '(" 5,.* -"K $'2 ,# '(" *+, 5"//

> L 11 > M N L O1 >M1 >FN1 > L1 >P O

!"#$%" '(" )* *+,*+$) '" "-"."%'/ ,# 0 )/'"

1 () ' ) +" 2 ,3+ 4"5,%6) +2 . "'+ $5/7

1 ()' $/ 2, 3+ 8+$.) +2 . "'+$57

1 () ' $/ 2, 3+ * +,9"5' #$%) %5$)- : ,) - ;')+ : "' < '$."= ',

+")5( $'7

>,0 $ / 2 ,3+ 6"#"5' . ") /3+"67

1 ("% 6 ,"/ 2 ,3+ 6" #"5' ,553+71 ()' $/ 2 ,3+ 6 "#"5'7

?()+' ) *-)% ', )55,.*-$/( '(" 6"/$+"6 /')'" ,# '("

53-'3+"

8+"6$5' '(" @$/A ,# /3/')$%) B$ - $'2

C 3)% '$#2 + $/A ,# .""'$%: 5+$'$5)- %""6 / ,# ?3/ ',."+D

E3/$%"// ) %6 8",*-"

F/')B- $/( *,'"%'$)- +"-)'$,%/($*/ B"'0 ""% G) +$)B-"/

E) -) %5" ) %6 H,53/ @ "/,3+5"/

I)- $6)'" H$%)%5$)- E"%"#$'/

!"#$%" ?() +)5'"+$/'$5/ ,# !) ')

H,53/ ,% '(" *+,B-". /,-G$%: *+,5"//

J6"%'$#2 '(" 5,.* -"K $'2 ,# '(" *+, 5"//

> L 11 > M N L O1 >M1 >FN1 > L1 >P O



229


Lean Six Sigma

Black Belt Training

Now that we have completed the Measure Phase we are going to jump into the Analyze Phase.

Welcome to Analyze will give you a brief look at the topics we are going to cover.

Analyze PhaseWelcome to Analyze



230


Welcome to Analyze

Overview

Analyze Phase Roadmap

These are thedeliverables for the Analyze Phase.

! " # $%&'( )( +'(%),- . . / 0 1! " # $%&'( )( +'(%),- . . / 0 1

! " #$ %&'( )( +'(% ),- . / 01! " #$ %&'( )( +'(% ),- . / 01

2,%3$ %$ ! " #$ %&'( )( +'(%),-2,%3$ %$ ! " #$ %&'( )( +'(% ),-

2,4'3' ,%)5 6 7%5 %)(%)8(2,4'3' ,%)5 6 7%5 %)(%)8(

9 : ; 7)4%),-9 : ; 7) 4%),-

< '68$= ' %$ > ,5 6"? '< '68$= ' %$ > ,5 6"? '

! " #$ %&'( )( +'(% ),- . / 0@! " #$ %&'( )( +'(% ),- . / 0@

< 35 # A# B > 8%)$, 2%'=(< 35 # A# B > 8%)$, 2%'=(

! " #$ %&' ()( +'(%),- . . / 0 @! " #$ %&' ()( +'(%),- . . / 0 @

! " # $%&'( )( +'(%),- . . / 0 1! " # $%&'( )( +'(%),- . . / 0 1

! " #$ %&'( )( +'(% ),- . / 01! " #$ %&'( )( +'(% ),- . / 01

2,%3$ %$ ! " #$ %&'( )( +'(%),-2,%3$ %$ ! " #$ %&'( )( +'(% ),-

2,4'3' ,%)5 6 7%5 %)(%)8(2,4'3' ,%)5 6 7%5 %)(%)8(

9 : ; 7)4%),-9 : ; 7) 4%),-

< '68$= ' %$ > ,5 6"? '< '68$= ' %$ > ,5 6"? '

! " #$ %&'( )( +'(% ),- . / 0@! " #$ %&'( )( +'(% ),- . / 0@

< 35 # A# B > 8%)$, 2%'=(< 35 # A# B > 8%)$, 2%'=(

! " #$ %&' ()( +'(%),- . . / 0 @! " #$ %&' ()( +'(%),- . . / 0 @

!"#$%&'( *+,-.#/ 0+#1

022#22 3%1-&.&%(4 5 161 -&.&%(4 1$" 7#1 28+#/#$% 3(2%#/2

!"#$%&'( 1$" *+&,+&%&9# 0.. :;2

*+,<#=>&26+,<# !/61?% :;2 @1<# A $ *+,-.#/

!"#$%&'(4 *+&,+&%&9#4 3#.#?% 3,.8%&,$2 5,$%+,. ,+ B.&/&$1%# :;2 51 82&$C *+,-.#/2

!/6.#/#$% 3,.8%&,$2 %, 5 ,$%+,. ,+ B.&/&$1%# :;2 5 182&$C *+,-.#/2

!/6.#/#$% 5 ,$%+,. *.1$ %, B$28+# *+,-.#/ >,#2$;% D#%8+$

E#+&'( F&$1$?&1. !/61?%

>#%#+/&$# 06 6+,6+&1 %# *+,G#?% F,?82

B2%&/1%# 5A *H

B2%1-.&2I J#1 /

!"#$%&'( *+,-.#/ 0+#1

022#22 3%1-&.&%(4 5 161 -&.&%(4 1$" 7#1 28+#/#$% 3(2%#/2

!"#$%&'( 1$" *+&,+&%&9# 0.. :;2

*+,<#=>&26+,<# !/61?% :;2 @1<# A $ *+,-.#/

!"#$%&'(4 *+&,+&%&9#4 3#.#?% 3,.8%&,$2 5,$%+,. ,+ B.&/&$1%# :;2 51 82&$C *+,-.#/2

!/6.#/#$% 3,.8%&,$2 %, 5 ,$%+,. ,+ B.&/&$1%# :;2 5 182&$C *+,-.#/2

!/6.#/#$% 5 ,$%+,. *.1$ %, B$28+# *+,-.#/ >,#2$;% D#%8+$

E#+&'( F&$1$?&1. !/61?%

>#%#+/&$# 06 6+,6+&1 %# *+,G#?% F,?82

B2%&/1%# 5A *H

B2%1-.&2I J#1 /

5 I 1 / 6 & , $ =

* + , ? # 2 2 A K $ # +

> # ' & $ #

7 # 1 2 8 + #

0 $ 1 . ( 9 #

! / 6 + , < #

5 , $ % + , .



231


Analyze Phase Process Map

This provides a process look at putting “ Analyze” to work. By the time we complete this phase youwill have a thorough understanding of the various Analyze Phase concepts.

We will build upon the foundational work of the Define and Measure Phases by introducingtechniques to find root causes, then using experimentation and Lean Principles to find solutions toprocess problems. Next you will learn techniques for sustaining and maintaining processperformance using control tools and finally placing your process knowledge into a high level processmanagement tool for controlling and monitoring process performance.


!"#$% '() *+, -.(/#"0"(.

1#$#( 23$4#"4$% 56(73"(, 70 !"#$% '() 8+, -9:$4# 7/ 237;%(9

53$/,%$#( 23$4#"4$% 56(73"(, "/#7 14"(/#"0"4 <=:7#6(,",

1(%(4# >/$ %=,", 577%, #7 237?(@ A",:37?( <=:7 #6(,",

B 7%%(4# A$#$

2(30739 1#$#",#"4$% 5(,#,

1#$#( 23$4#"4$% B 7/4%C,"7/

D:.$#( 'EF>

-.(/#"0= G77# B $C,(

G($.= 073 -9:37?( $/. B 7/#37%

HH

II

1#$#",#"4$%%=

1"J/"0"4$/#K

23$4#"4$%%=

1"J/"0"4$/#K

G77#

B$C,(

II

II

HH

HH



232


Lean Six Sigma

Black Belt Training

Now we will continue in the Analyze Phase with “X Sifting” – determining what the impact of theinputs to our process are.

Analyze PhaseX”

Sifting



235


Multi-Vari Example

Typically, we start witha data collection sheetthat makes sensebased on ourknowledge of theprocess. Then followthe steps.

If we only see minorvariation in thesample, it is time to goback and collectadditional data. Whenyour data collectionrepresents at least80% of the variationwithin the

Method

To put Multi-Vari studies in practice follow an example of an injection molding process.

You are probably asking yourself what is Injection Molding? Well basically an injection moldingmachine takes hard plastic pellets and melts them into a fluid. This fluid is then injected into amold or die, under pressure, to create products, such as piping and computer cases.

X” Sifting

process then you should have enough information to evaluate the graph.

Remember for a Multi-Vari Analysis to work the output must be continuous and the sourcesof variation discrete.

Sampling Plans steps:

1. Create Sampling Plan

2. Gather Passive Date

3. Graph Data

4. Check to see if Variation is Exposed

5. Interpret Results

Gather

Passive

Data

Graph

Data

Is

Variation

Exposed

Interpret

Results

Create

Sampling

Plan

No Yes



236


Sources of Variation

In this example there are 4 widgets created with each die cycle. Therefore, a unit is 4 widgets thatwere created at that unique time.

Machine Layout & Variables

An example of Within Unit Variation is measured by differences in the 4 widgets from a singledie cycle. For example, we could measure the wall thickness for each of the 4 widgets.

Between Unit Variation is measured by differences from sequential die cycles. An example ofBetween Unit Variation is, comparing the average of wall thickness from die cycle to die cycle.

Temporal Variation is measured over some meaningful time period. For example, we would

compare the average of all the data collected in a time period say the 8 o’clock hour to the 10o’clock hour.

X” Sifting

! "#$"% '%"# () !"#$% $"&'(

* ! "#$"% '"()( *+,"+ #"-% ,(.+#(/ #- #$( 0(-1(#,2 -3 #$( '+,#4

* 5+,"+#"-% +),-66 + 6"%0.( 7%"# )-%#+"%"%0 1+%2 "%/"*"/7+. '+,#6

67)$ +6 + 8+3(, )-%#+"%"%0 1+%2 )-1'7#(, ',-)(66-,64

* 9-)+ #"-% "% + :+#)$ ',-)(66 67)$ +6 '.+#"%04

+,#-,,% '%"# () )*+( $+'(

* 5+,"+#"-% +1-%0 )-%6()7#"*( '"()(64

* 5+,"+#"-% +1-%0 0,-7'6 -3 '"() (64

* 5+,"+#"-% +1-%0 )-%6()7#"*( :+#)$(64

,-./"0' ( () . /,) #"0, ;$"3#<#-<;$"3#

* =+2<#-<=+2

* ! ((><#-<! ((>

Within unit, betweenunit and temporalare the classiccauses of variation.

A unit can be asingle piece or agrouping of piecesdepending onwhether they werecreated at uniquetimes.

Multi-Vari Analysiscan be performed onother processes,

simply identify thecategorical sourcesof variation you areinterested in.

!" #

$#%#&'#

() * " # + ,

-#).

/+0#1,"2+ 45#''65#4#5 7&8",9

:&',#5 /+0#1,"2+

45#''65#

;%6"< =#8#%

> ? @ 9A #+

B C

B D

B E

B F

!"',&+1# ,2 ,&+G

!" #

-#).

!" #

$#%#&'#

() * " # + ,

-#).

/+0#1,"2+ 45#''65#4#5 7&8",9

:&',#5 /+0#1,"2+

45#''65#

;%6"< =#8#%

> ? @ 9A #+

B C

B D

B E

B F

!"',&+1# ,2 ,&+G

!" #

-#).



237


Sampling Plan

X” Sifting

! "#$%& ()

*$+

! &,-+

()

./01"& 2 +10+31"& 45$1"&

*$+

! &,-+

(6

*$+

! &,-+

(7

! "#$%& (6

! "#$%& (7

! "#$%& (8

*$+

! &,-+

()

*$+

! &,-+

(6

*$+

! &,-+

(7

*$+

! &,-+

()

*$+

! &,-+

(6

*$+

! &,-+

(7

To continue with thisexample, the Multi-Varisampling plan will be togather data for 3 die cycles

on 3 different days for 4widgets inside the mold.

If you find this initialsampling plan does notshow the variation ofinterest, it will be necessaryto continue sampling, ormake changes to thesampling plan.

Within-Unit Encoding

Between-Unit Encoding

Temporal Encoding

!"#

% &'(#

)*

+,-./& 0 #.-#1./& 23"./&

!"#

% &'(#

)4

!"#

% &'(#

)5

!"#

% &'(#

)*

!"#

% &'(#

)4

!"#

% &'(#

)5

!"#

% &'(#

)*

!"#

% &'(#

) 4

!"#

% &'(#

)5

% /6"7& )*

% /6"7& )4

% /6"7& )5

% /6"7& )8

Comparing individual datapoints within a die cycle isWithin Unit Variation.Examples of measurementcould be wall thickness,diameter or uniformity ofthickness to name a few

! "#$%& ()

*$+

! &,-+

()

./01"& 2 +10+31"& 45$1"&

*$+

! &,-+

( 6

*$+

! &,-+

( 7

! "#$%& (6

! "#$%& (7

! "#$%& (8

*$+

! &,-+

()

*$+

! &,-+

(6

*$+

! &,-+

( 7

*$+

! &,-+

( )

*$+

! &,-+

( 6

*$+

! &,-+

(7Comparing the averagesfrom each die cycle iscalled Between UnitVariation.

! "#$%& ()

*$+

! &,-+

()

./01"& 2 +10+31"& 45$1"&

*$+

! &,-+

(6

*$+

! &,-+

(7

! "#$%& (6

! "#$%& (7

! "#$%& (8

*$+

! &,-+

()

*$+

! &,-+

(6

*$+

! &,-+

(7

*$+

! &,-+

()

*$+

! &,-+

(6

*$+

! &,-+

(7Comparing the averageof all the data within aday and plot 3 timeperiods is known asTemporal Variation.



238


Using Multi-Vari to Narrow X s

Now let’s use the same information from the X-Y Diagram that was created in the Measure Phase. Thefollowing exercise will help you assign one of the variables to the family of variation. If you find yourselfwith a variable or (X) then assign percentages to split. Use your best judgment for the splits. Don’tassume that the true X’s causing variation has to come from one in the list.

X” Sifting

! "#$%& #$% ()*# +, -+#%.#)" ( /0* ".1 " **)2. #+ +.% +, #$% ,"3)()%* +,

4"&)"#)+.5

6 7$)* ).,+&3"#)+. 8" . 9% -:((%1 ,&+3 #$% /;< =)"2&"3 ,&+3 #$%

>%"*:&% ?$"*%5

@, ". / *-".* +.% +& 3+&% ,"3)()%*A "**)2. B0* #+ #$% *:--+*%1 *-()#5

!"#$ & ' ( )*$+ "+# ,* "* -)./ "+# $).0#11 23 456"2'7* )2 -.)/8

!"#$ 9 ' :,#3"2-; "+# 6*)<#1" -*/26; .- =*)2*"2.38

!"#$ > ' ?1"*@621+ 1"*"21"20*6 12<32-20*30# "+).5<+ "+# *$$).$)2*"#

1"*"21"20* 6 "#1"23< 8

!"#$ A ' B.051 -5)"+#) #--.)" .3 "+# CD1 *11.02*"#, E2"+ "+# -*/26; .-

6*)<#1" =*)2*"2.38

!"# "# $ "% '(" ) *+ , -. /* ' '* */,0

1-) 2 %" * 2 ' 3 ( + ' -' -. 4 $ 2 ' 3 ( + ' -' -. / * '5



239


Open the workbook“ Analyze Datasets.xls” andselect the worksheet“MVInjectionMold ” .

Now create the Multi-VariChart in SigmaXL®.

1.

SelectSigmaXL>GraphicalTools>Multi-Vari Options.Uncheck StandardDeviation Chart.2.

Click Finish. SigmaXLwill then open the Multi-VariCharts dialog box.

Data Worksheet

Run Multi-Vari

Here is the graph that should have been generated.

X” Sifting

3. If the Multi-Vari Options have been previously saved, select SigmaXL>Graphical Tools>Multi-Vari Charts.4. Select “Diameter ” as Numeric Response (Y), “Unit to Unit” as Group Category (X1), and“Temporal” as Group Category (X2). “Within Unit” should not be added as a group category.SigmaXL® will display the “Within Unit” variation automatically as a vertical bar.

After you create the graph as indicated, take a few minutes to create graphs using a different order. Always use the graph that shows the variation in the easiest manner to interpret.



240


Identify The Largest Family of Variation

To find an example ofwithin unit variation,look at Unit 1 in thesecond time period.

Notice the spread ofdata is 0.07.

Now let’s try and findbetween unit variation,compare the averagesof the units within atime period. All threetime periods appearsimilar so looking at thefirst time period it

Root Cause Analysis

After the analysis wenow know thelargest source ofvariation is occurringdie cycle to die cyclewe can focus oureffort on those X’sthat we suspecthave the greatest

impact. In this case,the pattern ofvariation is notconsistent within thesmall scope of datawe gave gathered. Additional data maybe required or thisprocess may beready forexperimentation.

X” Sifting

appears the spread of the data is 0.18 units. To determine temporal variation, compare theaverages between time periods. It appears time period 3 and 2 have a difference of 0.06.

To determine within unit variation, find the unit with the greatest variation like Unit 1 in the secondtime period. Notice the spread of data is 0.07. It appears the second unit in the third.

Notice that the shifting from unit to unit is not consistent, but it certainly jumps up and down. Thequestion at this point should be: Does this graph represent the problem I’m working on? Do I seeat least 80% of the variation? Read the units off the Y axis or look in the worksheet. Notice thespread of the data is 0.22 units. If the usual spread of the data is 0.25 units, then this data setrepresents 88% of the usual variation which tells us our sampling plan was sufficient to detect theproblem.



241


Call Center Example

Let’s try another example,open the worksheet“CallCenter ”. This

example is a transactionalapplication of the tool.

In this particular case, acompany with two callcenters wants to comparetwo methods of handlingcalls at each location atdifferent times of the day.One method involves ateam to resolve customerissues, and the other

method requires a singlesubject-matter expert tohandle the call alone.

What is the largest source of variation…!

Method?!

Location?

!

Time?

X” Sifting

Method



242


Call Center Example (cont.)

This example is not as easy to draw conclusions because of the source of the data. With the injectionmolding process we know we are making the same parts over and over. However, in this example ofa call center, there is no control over the nature of calls coming in, so a single outlier could affect your judgment.

It is not necessary to force fit any one tool to your project. For transactional projects Multi-Vari maybe difficult to interpret purely graphically. We will re-visit this data set later when working throughHypothesis Testing.

Is the largest source of variation more or less obvious? Notice the Multi-Vari graph plotted isdependent on the order in which the variable column names are entered into SigmaXL®.

X” Sifting

Location

Time



243


Multi-Vari Exercise

X” Sifting

Notes



244


MVA Solution

Normal, the distribution is quite wide. If you had a process where you were filling bottles wouldn’tyou expect the process to be Normal?

X” Sifting

Do you recall the reasonwhy Normality is an issue?Normality is required if youintend to use the

information as a predictivetool. Early in the SixSigma process there is noreason to assume thatyour data will be Normal.Remember, if it is notNormal it usually makesfinding potential causeseasier. Let’s work theproblem now.

First check the data forNormality. UseSigmaXL>ProcessCapability>CapabilityCombination Report

Having a graphicalsummary is quite

nice since itprovides a pictureof the data as wellas the summarystatistics.Histograms andDescriptiveStatistics is apowerful tool whichallows you to chickfor Normality.

Notice that the P-value in this windowis the same as theprevious.

Notice that eventhough the data are

(Individuals). Select Volume as Numeric Data Variable (Y), Set USL to 500. From the generatedreport we can see that the P-value is greater than 0.05, therefore the data is considered Normal.

Check for Normality !

Is that

normal



245


MVA Solution (cont.)

SigmaXL® has a template that will allow us to determine the Sigma Level for this process. “SelectProcess Capability>Basic Process Capability Templates>Process Sigma Level – Continuous” toopen the template. Using the data from the Process Capability Report, we can find the SigmaLevel.

Is this process is in trouble? The answer is yes, since the Z bench value is negative! That is very

bad. To correct this problem the process has to be set in such a manner that none of the bottles areever under filled, while trying to minimize the amount of overfill.

X” Sifting

Now it is time toperform theprocess capability.For subgroup size

is enter 12 sinceall 12 bottles arefilled at the sametime. Also, use500 milliliters asthe upper speclimit in order tosee how bad thecapability wasfrom amanufacturers

prospective.

To answerstep three ofthis exercise,it is acombinationof reducingvariation and

shifting theMean. TheMean cannotbe shiftedhowever, untilthe variationis reduceddramatically.



246


The order in which you enter the factors will produce different graphs.The “classical” method is to use Within, Between and over-time(Temporal) order. SigmaXL®’s Multi-Vari Charts do not require thelowest level “Within” category. This will appear automatically as

vertical bars.

So to fix this processyour game planshould be based on

the information in theExcel file and involveadditional informationyou have about theprocess.

This example wasbased on a realprocess where thenasty culprit wasactually the location

of the in-line scale.No one wanted tobelieve that a highprice scale could begenerating significantvariation.

The graph shows the variation within a unit (vertical bars) is fairly consistent across all the data.The variation between units (red lines connecting means) also looks consistent across all the data.What seems to stand out is the machine may be set up differently from first shift (top row) to second(bottom row). That should be easy to fix! What is the largest source of variation? Within UnitVariation is the largest, Temporal is the next largest (and probably easiest to fix) and Between UnitVariation comes in last.

X” Sifting

The in-line scale weighed the bottles and either sent them forward to ship or rejected them to betopped off. The wind generated by the positive pressure in the room blew across the scalemaking the weights recorded fluctuate unacceptably. The filling machine was actually quite good,there were a few adjustments made once the variation from the scale was fixed. Once thevariation in the data was reduced, they were able to shift the Mean closer to the specification of

500 ml.

MVA Solution (cont.)



247


Data Collection Sheet

The data sheet isnow balanced

meaning thatthere is an equalnumber of datapoints for eachcondition in thedata table andready for data tobe entered.

X” Sifting

The injectionmolding datacollection sheetwas created toinclude:

3 time periods4 widgets per

die cycle3 units per time

periodfor a total of 36rows of data. (3times 4 times 3)



248


Classes of Distributions

By now you areconvinced thatMulti-Vari is a toolthat helps screen

X’s by visualizing

three primarysources ofvariation. At thispoint we will reviewclasses and causesof distributions thatcan also help usscreen X’s toperform HypothesisTests.

The Normal (Z) Distribution

Please review the characteristics of the Gaussian curve shown here…

X” Sifting

!"#$% &'( )% %+ ( $,,# $-($ -.#/+ +0)..1 2 3+ 45 6 %+"( # %7 %18

$-).. /) %9( )5 +,")0.+ , : 6 ( ) %($%,1; <( $.) = . = % ##

/.):,)9 > 5 /, $-.+%+ ?.+$+ 4( +.@ , 1 ,") : %1@%18 + ;

! " "$%& '(%)" *+ *%,, -+.%+* /,0&&+& 0)1 /0 2&+& (3 1%&"-%42"%()& "$0"

/0) 0,&( $+,' 2& &/-++) 56& "( '+-3(-7 89'("$+&%& :+&"&;

< = (-70, >%&"-%42"%()

< = ()?)(-70,%"9 < @ A-%70-9 B ,0&&%3%/0"%()&

C; DE+*)+&&

F; G2,"%',+ G(1+&

H; I2-"(&%&

@ ; J -0)2,0-%"9

Characteristics of Normal Distribution (Gaussian curve) are:

– It is considered to be the most important distribution in statistics.

– The total area under the curve is equal to 1.

– The distribution is mounded and symmetric; it extends indefinitely in

both directions, approaching but never touching the horizontal axis.

– All processes will exhibit a normal curve shape if you have pure random

variation (white noise).

– The Z distribution has a Mean of 0 and a Standard Deviation of 1.

–

The Mean divides the area in half, 50%on one side and 50% on

the other side.

– The Mean, Median and

Mode are at the same

data point.

+6-1-3-4-5-6 -2 +4+3+2+1 +5



249


Copyright OpenSourceSixSigma.com

Normal Distribution

This Normal Curve isNOT a plot of ourobserved data!!!This theoretical

curve is estimatedbased on our data’sMean and StandardDeviation. ManyHypothesis Teststhat are availableassume a NormalDistribution. If theassumption is notsatisfied we cannotuse them to infer

anything about thefuture.

However, justbecause a

Non-Normal Distributions

distribution of sample data looks Normal does not mean that the variation cannot be reduced and anew Normal Distribution created.

X” Sifting

Data may follow Non-normal Distributions for a variety of reason, or there may be multiple sources ofvariation causing data that would otherwise be normal to appear not Normal.

1 Skewed 2 Kurtosis

3 Multi-Modal4 Granularity



250


Skewness Classification

When a distributionis not symmetrical,then it’s Skewed.Generally a Skewed

distribution longesttail points in thedirection of theSkew.

Mixed Distributions 1-3

What causes Mixed Distributions? Mixed Distributions occur when data comes from several sourcesthat are supposed to be the same but are not.

Note that both distributions that formed the combined Skewed Distribution started out as Normal

Distributions.

X” Sifting

!"#$%#&'( *' +,$, "- . / $0 %$,,

!"! # $%&'$( *+,+%-

!". / '%+0+1+$ ( *+,+%- 234'%+567

!"8 9+:%&';-

!"< # 45"*+5;$' =;($%+45->+?-

!"@ A5%;'$1%+45-

!"B # 45"=$5C4, D$%%;'5- /1'4-- E+,;

1&2 3# . / $04$-# . / $0

4 5 6 7 8 9 1 0 11

0

10

20

30

40

50

60

F r e q u e n c y

10 15 20

0

10

20

30

40

F r e q u e n c y

1&2 3# . / $04$-# . / $0

4 5 6 7 8 9 1 0 11

0

10

20

30

40

50

60

F r e q u e n c y

10 15 20

0

10

20

30

40

F r e q u e n c y

!"# $% '"()*"+, )"-.( !""#$ &'() *+,+ "!-(. /$!- -#0,120( .!#$"(.

,'+, +$( .#22!.(* ,! 3( ,'( .+-( 4(, +$( )!,5

! " # $ % & ( ! " # $ % & )

* + # , - . & /

0"12-.& (

3 $ & 4 " 5 + 4 (

6 " 7 # & . 5 0 & 52 + / (

8.5&49-&: &4 (

0"12-.& )

3 $ & 4 " 5 + 4 )

6 " 7 # & . 5 0 & 52 + / )

8.5&49-&: &4 )

6 7! " # $ % & (! " # $ % & ( ! " # $ % & )! " # $ % & )

* + # , - . & /

0"12-.& (

3 $ & 4 " 5 + 4 (

6 " 7 # & . 5 0 & 52 + / (

8.5&49-&: &4 (

0"12-.& )

3 $ & 4 " 5 + 4 )

6 " 7 # & . 5 0 & 52 + / )

8.5&49-&: &4 )

6 7



251


1-4 Non-Linear Relationships

Just becauseyour Input (X)is NormallyDistributed

about a Mean,the Output (Y)may not beNormallyDistributed.

1-5 Interactions

If you find that two inputs have a large impact on Y but would not effect Y by themselves, this iscalled a Interaction.

For instance, if you spray an aerosol can in the direction of a flame what would happen to room

temperature? What do you see regarding these distributions?

X” Sifting

! "# $%&#'( ) +' ,(-&"#./ &0. !""#$ & '() *'( + , )- . /",0(/

, $( - 122($()*3

4, $5 1), 0 6 1/*$ 17#*1!)

! 2 +

100500

10

5

0

X

Y

4 , $ 5 1 ) , 0 6 1 / * $ 1 7 # * 1 ! )

! 2 .

4, $5 1), 0 6 1/*$ 17#*1!)

! 2 +

100500

10

5

0

X

Y

4 , $ 5 1 ) , 0 6 1 / * $ 1 7 # * 1 ! )

! 2 .

!"#$%&'#()"* !""#$ &'() *&! +),#*- +)*($."* &+*' (."' !*'($ *!

'./( . 0.$1($ +2,."* !) 3 *'.) (+*'($ &!#04 56 *'(2-(0/(-7

With FireNo Fire

35

30

25

Interaction Plot for Process Output

R o o m T

e m p e r a t u r e

Spray

No Spray

Aerosol Hairspray

On

Off



252


1-6 Time Relationships / Patterns

Timerelationshipsoccur when the

distribution isdependent ontime, someexamples aretool wear,chemical bathdepletion, stockprices, etc.

Non-Normal Right (Positive) Skewed

To measure Skewness we use Descriptive Statistics. When looking at a symmetrical distribution,Skewness will be close to zero. If the distribution is skewed to the left it will have a negative number,

if skewed to the right, it should be positive.

X” Sifting

!"# %&'() &*+ (&,- &' % #. #-% #-( ,- (&/#0

1 2(#- '##- 3 "#- (,,4 &-5 )#6+ &)#' 7 3 8 )/ &-5 +. 9 : (,,4 3 #8 ):

;"#/ &;8 4 *8 (" % #.4#(&,-': 8 / *&#-( (#/ .#)8 (+)# #22#;( ,- (,,4 &-5 0

1 2(#- ' ##- 3 "#- (,,4 &-5 )#6+ &)#' 7 3 8 )/&-5 +. 9 : (,,4 3 #8 ):

;"#/ &;8 4 *8 (" % #.4#(&,-': 8 /* &#-( (#/ .#)8 (+)# #22#;( ,- (,,4 &-5 0

!&/#

10 20 30 40 50

20

25

30

< 8 ) 5 & - 8 4 = & ' ( ) & * + ( & , -

, 2 >

!&/#

10 20 30 40 50

20

25

30

< 8 ) 5 & - 8 4 = & ' ( ) & * + ( & , -

, 2 >

Open the

worksheet “Distrib1”, select PosSkew.



253


Kurtosis 2

Platykurtic areflat with short-tails.

Platykurtic

Open the worksheet “Distrib 1”, select Flat. Negative coefficient of Kurtosis indicates Platykurtic

distribution.

X” Sifting

! " # $% & ' & !"#"!$ &' &(" $ () *" '# &(" &)+ ,$-

! "#$%&'()%*+

! ,-.%/'()%*+0 1*22#)#3% +&56*3.%*&37 &2 8*7%)*6(%*&37 +. (7#7 %9# )#7(-%*3: &;#).--

79.$#7<

."* &'/ 0!&+1

2") / "3 4 +&( .'56 78) +,$

2,) &9 / 0!&+1

:,)& 4 +&( ;('!&78)+,$

Multiple Means shifting over time produces a plateauof the data as the shift exhibits this shift.

Causes:

2-1. Mixtures: (Combined

Data from Multiple

Processes)

Multiple Set-UpsMultiple Batches

Multiple Machines

Tool Wear (over time)

2-2 Sorting or Selecting:Scrapping product that falls

outside the spec limits

2-3 Trends or Patterns:

Lack of Independence inthe data (example: tool

wear, chemical bath)

2-4 Non LinearRelationships

Chemical Systems



255


Bimodal Distributions

This is an example of a Bi-Modal Distribution. Interestingly each peak is actually a NormalDistribution, but when the data is viewed as a group it is obviously not Normal.

Extreme Bi-Modal (Outliers)

If you see an extreme outlier, it usually has its on cause or own source of variation. It’s relatively

easy to isolate the cause by looking on the X Axis of the Histogram. Open the worksheet“Distrib1”, select Extreme BiModal.

X” Sifting

Open the

worksheet“Distrib 1”,select BiModal.



256


Bi-Modal – Multiple Outliers

Open theworksheet“Distrib 1”,select Multiple

Outliers.

Having multipleoutliers is moredifficult tocorrect. Thisaction typicallymeans multipleinputs.

Granular 4

Open the worksheet “Distrib 1”, select Granular and let’s take a moment and notice the P-value inthe Normal Probability Plot, it is definitely smaller than 0.05!

There simply is not enough resolution in the data.

X” Sifting



257


Normal Example

Conclusions Regarding Distributions

Here is what to conclude regarding distributions.

X” Sifting

Open the worksheet

“

Distrib 1”

, select

Normal Dotplot.

Hey Honey, I found the key….



258



You have now completed Analyze Phase – ”X” Sifting.

!

Perform a Multi-Vari Analysis

!

Interpret and a Multi-Vari Graph

! Identify when a Multi-Vari Analysis is applicable

! Interpret what Skewed Data looks like

! Explain how data distributions become Non-normal

when they are really Normal

X” Sifting

Notes



259


Lean Six Sigma

Black Belt Training

Now we will continue in the Analyze Phase with Inferential Statistics.

Analyze PhaseInferential Statistics



260


Inferential Statistics

Overview

Nature of Inference

One objective of Six Sigma is to move from only describing the nature of the data or descriptive

statistics to that of inferring what will happen in the future with our data or Inferential Statistics.

The corefundamentals of thisphase are InferentialStatistics, Nature of

Sampling andCentral LimitTheorem.


! "#$%& () * "+,-./0! "#$%& () * "+,-./0

1 &/#%"- 2.+.# 34&(%&+1 &/#%"- 2.+.# 34&(%&+

5/)&%&/#."- *#"#.6#.765/)&%&/#."- *#"#.6#.76

! " #$ %&'()( +'(%),- . . / 0 1! " #$ %&'()( +'(%),- . . / 0 1

! " #$ %&'()( +'(%),- . / 01! " #$ %&'()( +'(%),- . / 01

2,%3$ %$ ! " #$%&'()( +'(%),-2,%3$ %$ ! " #$%&'()( +'(%),-

2,4'3',%)5 6 7 %5 %)(%)8(2,4'3',%)5 6 7%5 %)(%)8(

9 : ; 7)4%),-9 : ; 7)4%),-

< ' 68$=' %$ >,5 6"?'< ' 68$=' %$ > ,5 6"?'

! " #$ %&'()( +'(%),- . / 0@! " #$ %&'()( +'(%),- . / 0@

< 35# A# B > 8%)$, 2%'= (< 35 # A # B >8%)$, 2%'=(

! " #$ %&'()( +'(%),- . . / 0 @! " #$ %&'()( +'(%),- . . / 0 @

!"#$%&#%"'% !!"" $%&' ()* +, -,+)'.. +/ 0',12134 5+41)(5 )+3)56.1+3.

/,+7 -,'71.'. 83+93 +, (..67'0 *+ :' *,6'; %&' ()* +/ ,'(.+3134/,+7 /()*6(5 83+95'04' +, '210'3)';< =

#" %&'(&)!*+,"')-

!"#$%&#%"'% !!"" $%&' ()* +, -,+)'.. +/ 0',12134 5+41)(5 )+3)56.1+3.

/,+7 -,'71.'. 83+93 +, (..67'0 *+ :' *,6'; %&' ()* +/ ,'(.+3134/,+7 /()*6(5 83+95'04' +, '210'3)';< =

#" %&'(&)!*+,"')-

(" $%& %" )!* + - )* )!.)!'. > %+ 0,(9 13/','3)'. (:+6* *&' -,+)'.. +,

-+-65(*1+3 :'134 .*601'0 :? 7+0'5134 -(**',3. +/ 0(*( 13 ( 9(? *&(*

())+63* /+, ,(30+73'.. (30 63)',*(13*? 13 *&' +:.',2(*1+3.; @

." /&0&123&*"')-

(" $%& %" )!* + - )* )!.)!'. > %+ 0,(9 13/','3)'. (:+6* *&' -,+)'.. +,

-+-65(*1+3 :'134 .*601'0 :? 7+0'5134 -(**',3. +/ 0(*( 13 ( 9(? *&(*

())+63* /+, ,(30+73'.. (30 63)',*(13*? 13 *&' +:.',2(*1+3.; @

." /&0&123&*"')-

/0))!"1 )2% 3!%'%. 4$

)2% 305 5 +%

)41%)2%&67

Putting the pieces

of the puzzle

together….



261


5 Step Approach to Inferential Statistics

Types of Error

As with most things you have learned associated with Six Sigma – there are defined steps to betaken.

Types of error contribute to uncertainty when trying to infer with data.

There are four types of error that are explained above.


! " $%&'

()*+,-"&+./0

1 / 2 3% , 4" ' ") 5 % &, ," 6 &" 5 0

7 / 2 3% , ,"" 8 5 - 88 9 -:* ' ") ,3% , -&;"<$ % ,-"&0

= / > " 5 ?" & ; -4 * & , % < * ' " ) " ; ' " ) < 4 % ,% + ) $ $ % < -* + 0

@ / > "5 5 - 88 ' ") ?"88*?, ,3* 4 % ,% 0

A / 2 3% , 6 -&4 " ; 4% ,% 4" *+ ,3% , ,""8 <*( )-<*0

! " #$$%$ '( )*+ ,- '(.

! "##$# &'( )$ &*++(#(,-(. /0$,1 ./023(. &#/ 4, /) #/,&$0 +#$0 )5(

2$2'3/)*$, 63'-7 $+ )5( &#/489

! :5*. *. )5( $,3; .$'#-( $+ (##$# )5/) .)/)*.)*-. -/ , /--$00$&/ )(9

/ " 0 '* ) '( ) * + , - '( .

! "##$# &'( )$ 3/-7 $+ *,&(2(,&(,-( /0$,1 #/,&$0 ./ 023(. $# &'( )$

.;.)(0/)*- ./023*,1 2#$-(&'#(. 65(*15) $+ 5$#.( <$-7(;. $,3;89

1 " #$ $ % $ '( + 2 * ) 3 $ 2 + 2 ( 4

! "##$# *, )5( 0(/.'#(0(,) $+ )5( ./023(. 6=>?@ A BCB8

5 " 6*7 8 % 9 + 2* )3$2+ 2(4 :* - '; ' 4<

! "##$# *, )5( 0(/.'#(0(,) &$(. ,$) /-)'/33; 0(/.'#( 45/ ) *) *,)(,&. )$

0(/.'#( 623/-*,1 / 2#$D( *, )5( 4#$,1 .3$) 0(/.'#*,1 )(02(#/)'#(

4*)5 / )5(#0$0()(# )5/) *. <'.) ,(E) )$ / +'#,/-(89

So many

questions.….



262


Population, Sample, Observation

Let’s just review a few definitions: A population is EVERY data point that has ever been or ever willbe generated from a given characteristic. A sample is a portion (or subset) of the population, eitherat one time or over time. An observation is an individual measurement.

Significance


! " # $ % & ' ( " )

! "#"$% '( )( *+,-) ).() .(/ 0102 300- +2 0102 4,55 30 60-02()0' 72+8 ( 6 ,10-

9.(2(9)02,/),9:

* & + # % ,

! ; *+2),+- <+2 /=3/0)> +7 ).0 *+*=5( ),+-? 0,).02 ( ) +-0 ),80 +2 +102 ),80:

- . / , 0 1 & '( " )

! ; - ,-',1,'=( 5 80(/=2080-):

X

X

X

X

X

X X

X

X

X

X

Practical difference and significance is:

– The amount of difference, change or improvement that will be ofpractical, economic or technical value to you.

– The amount of improvement required to pay for the cost of making theimprovement.

* RORI includes not only dollars and assets but the time and participation of your teams.

Six Sigma decisions will ultimately havea return on resource investment (RORI)*

element associated with them.

Significance –

Statistical difference and significance is:

The magnitude of difference or change required to distinguish betweena true difference, change or improvement and one that could haveoccurred by chance.



263


The Mission

A Distribution of Sample Means


Mean Shift VariationReduction

Both

Your mission, which you have chosen to accept , is to reduce cycle time, reduce the error rate,reduce costs, reduce investment, improve service level, improve throughput, reduce lead time,increase productivity… change the output metric of some process, etc…

In statistical terms, this translates to the need to move the process Mean and/or reduce the processStandard Deviation

You’ll be making decisions about how to adjust key process input variables based on sample data,not population data - that means you are taking some risks.

How will you know your key process output variable really changed, and is not just an unlikelysample? The Central Limit Theorem helps us understand the risk we are taking and is the basis forusing sampling to estimate population parameters.

The Central Limit Theorem says that as the sample size becomes large, this new distribution (the

sample Mean distribution) will form a Normal Distribution, no matter what the shape of thepopulation distribution of individuals.

Central Limit Theorem -

1. Individual values of a

population form some

distribution.

2.

A sample will yield a Mean.

3. Another sample will shift the

Mean.

4. At some point the distributionwill become Normal.



264


Sampling Distributions—The Foundation of Statistics

Constructing Sampling Distributions

To demonstrate how sampling distributions work we will create some random data for die rolls.

Create a sample of 1,000 individual rolls of a die that we will store in a variable named“Population”. From the population, we will draw five random samples.

Every statistic derives from a sampling distribution. For instance, if you were to keep takingsamples from the population over and over, a distribution could be formed for calculating Means,Medians, Mode, Standard Deviations, etc. As you will see the above sample distributions eachhave a different statistic. The goal here is to successfully make inferences regarding the statisticaldata.


!

"

#

$ #

$ %

$

&

$ #

"

&

$ #

$ '

!

&

$ $

($ %

$ %

$ #

!"#$%&' (")

$ ( #

$ # * !

( " &

+ $ ' $ $

* $ % $ %

* & + # %, . * & + # %, / * & + # %, 0

+ ,' ( ,# & ,'

! "#$%&'( *+,$ -.' %,%/&#-0,12 '#3. 40-. *05' ,6('+5#-0,1(7

! 81 -.0( '9# $%&'2 4' .#5' -#:'1 -.+'' (#$%&'( ,/- ,* -.'%,%/&#-0,12 '#3. 40-. *05' ,6('+5#-0,1( 01 0-; < ' 3,$%/-'= #

>'#1 *,+ '#3. (#$%&'; ? ,-' -.#- -.' >'#1( #+' 1,- -.' (#$'@

! < .A 1,-B

! < .#- 4,/&= .#%%'1 0* 4' :'%- -#:01C $,+' (#$%&'(B



265


Sampling Distributions

Select the “Die Example” worksheet. This sheet has been created using a sample size of 5, 10and 30 from the Population column.

Now compare the Mean and Standard Deviation of the samples of 5 observations to thepopulation. What do you see?


Sampling Error

Calculate the Mean and Standard Deviation for Population andSamples 1-5 and compare the sample statistics to the population.

Range in Mean 1.2 Range in Stdev 0.59

SigmaXL>Statistical Tools>Descriptive Statistics:Numeric Data Variables (Y): Population, Sample1, Sample 2, Sample 3, Sample 4, Sample 5

Select Column Format

for easer viewing

Let

s do something with the data -

Select the Die Example

worksheet.



266


Sampling Error - Reduced


Calculate the Mean and Standard Deviation for Samples 6-10 and compare the sample statisticsto the population.

Can you tell what is happening to the Mean and Standard Deviation? When the sample sizeincreases, the values of the Mean and Standard Deviation decrease.

What do you think would happen if the sample increased? Let’s try 30 for a sample size.

With 10 observations, the differencesbetween samples are now much smaller.

Range in Mean 0.9 Range in Stdev 0.667

Calculate the Mean and Standard Deviation for Samples 6-10 andcompare the sample statistics to the population.

SigmaXL>Statistical Tools>Descriptive Statistics:Numeric Data Variables (Y):, Sample 6, Sample 7, Sample 8, Sample 9, Sample 10



267


Sampling Error - Reduced

Now instead of looking at the effect of sample size on error, we will create a sampling distributionof averages. Follow along to generate your own random data. Rename the column headings to

Roll 1, Roll 2, …, Roll 10.


Do you noticeanythingdifferent?

Look how muchsmaller therange of theMean andStandarddeviations. Didthe samplingerror getreduced?


Feeling lucky…?



268



The commands shown above will create new columns that are now averages from the columns ofrandom population data. We have 1000 averages of sample size 5 and 1000 averages of samplesize 10.

In SigmaXL® follow the above commands. The Histogram being generated makes it easy to seewhat happened when the sample size was increased.




269


Different Distributions

Observations

Everything we have gonethrough with sampling errorand sampling distributionswas leading up to theCentral Limit Theorem.


Central Limit TheoremIf all possible random samples, each of size n, are taken from any

population with a Mean µ and Standard Deviation !, the distribution

of sample Means will:

have a Mean

have a Std Dev

and be Normally Distributed when the parent population is

Normally Distributed or will be approximately Normal for samples

of size 30 or more when the parent population is not Normally

Distributed.

This improves with samples of larger size.

Bigger is Better!

Good news: the Mean of the sample

Mean distribution is the Mean of thepopulation.

Better news: I can reduce my

uncertainty about the populationMean by increasing my sample size n.

The Mean of the sample Meandistribution:

The Standard Deviation of thesample Mean distribution, also

known as the Standard Error.

Answers -

1.

The Center remains the same.

2.

The variation decreases.

3.

The shape of the distribution changes - it tending to Normal.



270


So What?

What is the likelihood of getting a sample with a 2 second difference? This could be caused eitherby implementing changes or could be a result of random sampling variation, sampling error. The95% confidence interval exceeds the 2 second difference (delta) seen as a result. What is the deltacaused from? This could be a true difference in performance or random sampling error. This is why

you look further than only relying on point estimators.


A Practical Example

!"#$% %' ( ( )* + , +)-".# /% #) +"0 *." #1" %"#*, #/2 " 3) + '

4' +5 " .' %#/6 5 7

! "#$%& () # $#*+,% (- ./ $%01+$2 3(1 ,%#4) 05#0 3(14 6#$%,7)%

#8%4#9% 7$ :; *7)10%$2 <705 # =0#)&#4& >%87#07() (- ?/

*7)10%$@

! "%A#1$% 057$ 7$ B1$0 # $#*+,%2 05% :; *7)10% #8%4#9% 7$ B1$0 #)

%$07*#0% (- 05% 041% #8%4#9%@

! C$7)9 05% A%)04#, ,7*70 05%(4%*2 05%4% 7$ D;E +4(6#67,703 05#0

05% 041% #8%4#9% 7$ $(*%<5%4% 6%0<%%) :/@; #)& :D@;

*7)10%$@

! F5%4%-(4%2 &()G0 9 %0 0(( %HA70%& 7- 3(1 *#&% # +4(A%$$ A5# )9%

05#0 4%$1,0%& 7) # 4%&1A07() (- (),3 . *7)10%$@

Recall that 95% of Normally Distributed data is within ± 2 Standard Deviations from the Mean.Therefore, the probability is 95% that my sample Mean is within 2 standard errors of the truepopulation Mean.

So how does this theorem help meunderstand the risk I am taking when I usesample data, instead of population data?



271


Sample Size and the Mean

Standard Error of the Mean


! "#$ &' ( )$* ' + ' , - .# / # "' 0# 1$.2 #+ &), ' &#3 &"#

&45# 6#'$ !

# $ %% &' ()*& +, -./- -.' -01' 2'/) %+', ,*3'&.'0' &+-.+) -.'

-.'*0'-+4/% 5+,-0+61-+*) *7 ,/38%' 2'/), *0 -.' -95+,-0+61-+*) &.+4. /0'/)/%:; '5 1,+)< -9-',-,=

# >9-',-, 3'/,10' -.' ,+<)+7+4/)4' *7 5+77'0')4', 6'-&'') 2'/ ),=

7)+&4 )85&)1$ 19

)$3)0)35'.+ )$ &"#

-1-5.'& )1$

:"#14#&);' . 3)+&4 )85 &)1$ 1 9

+ ' , - . # 6 # ' $ + 9 1 4 $ < = >

:"#14#&);' . 3)+&4 )85&)1$ 19

+ ' , - . # 6# ' $ + 9 1 4 $ < ?

!"# !"#$% #& % ()* +#"+,$ %&' ("# )*+(' *,-(*&. &% /#0.+ *+

1 0 2 2#) ("# + (0 .) 0 ' ) #' ' & ' & % ("# /#0 . 0 .) * + )#% *.#) 0 + 3

! "#$% '()*+,- %#(.% /#-/ /#0 10- 2 $% *()0 %/-3,0 /#-2 - %$24 ,0

(3%0)5-/$(2 36 - '-7/() (' /#0 %8+-)0 )((/ (' /#0 %-*9,0 %$: 0;



272


Standard Error

When comparing standard error with sample size, the rate of change in the standard errorapproaches zero at about 30 samples. This is why a sample size of 30 comes up often indiscussions on sample size.

This is the point at which the t and the Z distributions become nearly equivalent. If you look at aZ table and a t table to compare Z=1.96 to t at 0.975 as sample approaches infinite degrees offreedom they are equal.


3 02 01 00

Sample Size

S t a n d a r d

E r r o r

5

Standard Error approaches zero at about 30 samples.



273



You have now completed Analyze Phase – Inferential Statistics.

! Explain the term “Inferential Statistics”

!

Explain the Central Limit Theorem

!

Describe what impact sample size has on your

estimates of population parameters

! Explain Standard Error


Notes



274


Lean Six Sigma

Black Belt Training

Now we will continue in the Analyze Phase with“Introduction to Hypothesis Testing

”.

Analyze PhaseIntroduction to Hypothesis Testing



275


Introduction to Hypothesis Testing

Overview

Six Sigma Goals and Hypothesis Testing

Our goal is to improve our Process Capability, this translates to the need to move the process Mean

(or proportion) and reduce the Standard Deviation.!

Because it is too expensive or too impractical (not to mention theoretically impossible) tocollect population data, we will make decisions based on sample data.!

Because we are dealing with sample data, there is some uncertainty about the truepopulation parameters.

Hypothesis Testing helps us make fact-based decisions about whether there are different populationparameters or that the differences are just due to expected sample variation.

The corefundamentals of thisphase areHypothesis Testing,

Tests for CentralTendency, Tests forVariance and ANOVA.


!"#$# &'( )"*$(+, !"*-"*./!"#$# &'( )"*$(+, !"*-"*./

!"#$# &'( 0 + ( 1+*."!"#$# &'( 0 +( 1+ *."

2 3 4 0 22 3 4 0 2

5/ 6'$7"# 1# !"#$1*8 9:(6 '#"5/ 6'$7"# 1# !"#$1*8 9:(6 '#"

5 /6 '$7"#1# !"#$1*8 3 3 ; 9 <5/ 6' $7"#1# !"#$1*8 3 3 ; 9<

5/ 6'$7"# 1# !"#$1*8 3 ; 9<5/ 6' $7"#1# !"#$1*8 3 ; 9 <

=*$(' $' 5 / 6' $7"#1# !"#$1*8=*$(' $' 5 /6 '$7"#1# !"#$1*8

=*&"("* $1+ , >$+$1#$1.#=*&"("*$1+, >$+$1#$1.#

? @ A > 1&$1*8? @ A > 1&$1*8

B ",.'C " $' 2 *+ ,/D "B ",.'C " $' 2* + ,/D"

5 /6 '$7"#1# !"#$1*8 3 ; 9E5 / 6'$7"#1# !"#$1*8 3 ; 9E

B (+ 6 F 6 G 2.$1'* =$"C#B (+ 6 F6 G 2 .$1'* =$"C #

5 /6 '$7"#1# !"#$1*8 3 3 ; 9 E5 / 6' $7"#1# !"#$1*8 3 3 ; 9E



276


Purpose of Hypothesis Testing

The Basic Concept for Hypothesis Tests

The purpose of appropriate Hypothesis Testing is to integrate the Voice of the Process with theVoice of the Business to make data-based decisions to resolve problems.

Hypothesis Testing can help avoid high costs of experimental efforts by using existing data. This

can be likened to:Local store costs versus mini bar expenses.There may be a need to eventually use experimentation, but careful data analysis canindicate a direction for experimentation if necessary.

The probability of occurrence is based on a pre-determined statistical confidence.

Because of not having the capability to test an entire population, having to use a sample is theclosest we can get to the population. Since we are using sample data and not the entirepopulation we need to have methods what will allow us to infer the sample if a fair representationof then population.

When we use a proper sample size, Hypothesis Testing gives us a way to detect the likelihoodthat a sample came from a particular distribution. Sometimes the questions can be: Did oursample come from a population with a mean of 100? Is our sample variance significantly different

than the variance of the population? Is it different from a target?


!

Decisions are based on:! Beliefs (past experience)!

Preferences (current needs)!

Evidence (statistical data)!

Risk (acceptable level of failure)

Recall from the discussion on classes and cause of distributions that a data set may seem Normal,yet still be made up of multiple distributions.

Hypothesis Testing can help establish a statistical difference between factors from differentdistributions.

3210-1-2-3

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0.0

x

f r e q

Did my sample come from this population? Or this? Or this?

Relax, it

s just a

hypothesis test



277


!"# "$%"$&% ( )*+ $,- # . -"/* ,* 0*1 2 "* ,- "-&" ,$ 3 3-)-4&-%5

! "# $%&'() %+, -. +/0'12( 2+33(4(/0() +/ )1&&'+(4)5 )-+3.) 64

(71+&%(/.8

! 9:6 .;&() 63 )+, /+3+0$/. 2+33(4(/0() 60014 $/2 %1). <( :(''

1/2(4).6625 ! "# $%&$ # ' $/2 ( %# %&(%&$# ' 8

! =$ +'14( .6 .+( .-()( .:6 2+33(4(/0() .6, (.-(4 +) 6/( 63 .-( %6).

06%%6/ (4464) +/ ).$.+).+0)8

6 7 8 9/- %: 2 $% 4 *" 3# 0 0$41 5

6 ; 8 9/- %: 2 $% 3# 0 0$41 5

Significant Difference

We will discuss the difference between practical and statistical throughout this session. We can

affect the outcome of a statistical test simply by changing the sample size.

Detecting Significance


!"# %&# %'( )*+%"*,-%*(.+ /+*0.*1*23.%456 )*11#"#.% 1"(7 #32&

(%&#"8 9(' +-"# 3"# '# (1 (-" )#2*+*(.8

9(' )( %&# .-7,#" (1 (,+#":3%*(.+ 311#2% (-" 2(.1*)#.2# *.

)#%#2%*.0 ;(;-43%*(. <#3.8

µ

µ

! " # $ %& (! " # $ %& )

Do you see a difference between Sample 1 and Sample 2? There may be a real differencebetween the samples shown; however, we may not be able to determine a statistical difference. Ourconfidence is established statistically which has an effect on the necessary sample size. Our abilityto detect a difference is directly linked to sample size and in turn whether we practically care aboutsuch a small difference.



278


Practical vs. Statistical

Detecting Significance

Lets take a moment to explore the concept of Practical Differences versus Statistical Differences.

small overlap of the distributions. The smaller the delta is, the larger the sample size has to be to beable to detect a statistical difference.


!"#$%&$#' )&**+"+,$+- !"# %&''#(#)*# +"&*" (#,-./, &) 0)

&12(34#1#)/ 3' 2(0*/&*0. 3( #*3)31&* 40.-# /3 /"# *3120)56

7 89012.#: 0) &12(34#1#)/ &) 5&#.% '(31 ; < /3 ;; 2#(*#)/6

.%#%&/%&$#' )&**+"+, $+- = %&''#(#)*# 3( *"0)># /3 /"# 2(3*#,, /"0/

2(3?0?.5 @+&/" ,31# %#'&)#% %#>(## 3' *3)'&%#)*#A %&% )3/ "022#)

?5 *"0)*#6

7 89012.#, 1&>"/ &)*.-%# %&''#(#)*#, &) ,-22.&#(,: 10(B#/, 3( ,#(4#(,6

! " $ % && '"" ()* ( %( %' + ,' '%-&" (, ."* &%/ " * '(* (%'(%0* & &1

'%2 3%4%0* 3( 5%44"."30" $ %(), 6( ."* &%/ %32 * +. * 0(%0* &&1'%2 3%4%0* 3( 5%44"."3 0"7

! "#$ & '( ) *

+#, (#* (- $

."/01*(-$

During the Measure Phase, it is important that the natureof the problem be well understood.

In understanding the problem, the practical difference tobe achieved must match the statistical difference.

The difference d can be either a change in the Mean or inthe variance.

Detection of a difference is then accomplished usingstatistical Hypothesis Testing.

An important concept to understand is the process ofdetecting a significant change. How much of a shift in the

Mean will offset the cost in making a change to theprocess?

This is not necessarily the full shift from the BusinessCase of your project. Realistically, how small or how largea delta is required? The larger the delta, the smaller thenecessary sample will be because there will be a very



279


Hypothesis Testing

DICE Example

You have rolled dice before haven’t you? You know dice that you would find in a board game or inLas Vegas. Well assume that we suspect a single die is “Fixed.” Meaning it has been altered insome form or fashion to make a certain number appear more often that it rightfully should.

Consider the example on how we would go about determining if in fact a die was loaded.

If we threw the die five times and got five one’s, what would you conclude? How sure can you be?

The probability of getting just a single one. The probability of getting five ones.

A Hypothesis Test is an a priori theory relating to differences between variables. That means webegin by saying either this will happen or that will happen. Then we proceed with a statistical test orHypothesis Test to prove or disprove on or the other.

A Hypothesis Test converts the practical problem into a statistical problem. Since relatively smallsample sizes are used to estimate population parameters, there is always a chance of collecting anon-representative sample. Therefore we use Inferential statistics to help us estimate theprobability of getting a non-representative sample.


! " $%&'( )*+%, -) . /&01"+ %2 )-0"3 ./( )+.$4 *%, 0./5 ".$* 2.$"

%$$&++"(6 ! -)* . 3)./(.+( (-"7 ," ,%&'( "89"$) ".$* 2.$" )% %$$ &+ :; < %+

:<6<=> %2 )*" )-0"6

?2 ," )*+", )*" (-" @ )-0"3 ./( A %) @ %/"B37 ,*.) ,%&'( 5%& $%/$'&("C D%,

3&+" $./ 5%& 1"C

E F+ G: %/"H I J 6: <<= F+ G@ %/"3H I GJ6: <<=H@ I J6JJJ:K

L*"+" .+" .99+%8-0.)"'5 :6K $*./$"3 %&) %2 :JJJ )*.) ," $%&'( *. M" A%))"/

@ %/"3 ,-)* . 3)./(.+( (-"6

L*"+"2%+"7 ," ,%&'( 3. 5 ," . +" ,-''-/A )% ).4" . J6: > $*./$" %2 1"-/A

,+%/A .1%&) %&+ *59%)*"3-3 )*.) )*" (-" ,.3 N'%.("(O 3-/$" )*" +"3&')3 (% /%)

$%0" $'%3" )% %&+ 9+"(-$)"( %&)$%0"6



280


Hypothesis Testing

When it comes to HypothesisTesting, you must look at threefocus points to help validateyour claim. These points are

Type I, Type II and SampleSize.

Statistical Hypotheses


! n

"

DECISIONS

A hypothesis is a predetermined theory about the nature of, or relationships between variables.Statistical tests can prove (with a certain degree of confidence) that a relationship exists. WithHypothesis Testing the primary assumption is that the null hypothesis is true. Therefore statisticallyyou can only reject or fail to reject the null hypothesis. The Null Hypothesis is always the “default” assumption.

If the null is rejected, this means that you have data that supports the alternative hypothesis.Shortly we’ll look at how P-values help us understand the relationships.

Two alternatives –

Making a decision does not FIX a problem,

taking action does.

P-value > 0.05 Ho = no difference or relationship

P-value < 0.05 Ha = is a difference or relationship

Ha the alternative hypothesis

Ho the null hypothesis



281


Steps to Statistical Hypothesis Testing

There are six steps to Hypothesis Testing:

1. State the Practical Problem.

2. State the Statistical Problem.

3. Select the appropriate statistical test and risk levels. –Your alpha may change depending on theproblem at hand. An alpha of .05 is common in most manufacturing. In transactional projects, analpha of 0.10 is common when dealing with human behavior. Being 90% confident that a change toa sale procedure will produce results is most likely a good approach. A not-so-common alpha is0.01. This is only used when it is necessary to make the null hypothesis very difficult to reject.

4. Establish the Sample Size required to detect the difference.

5. State the Statistical Solution.

6. State the Practical Solution.


Noooot THAT practical

solution



283


Hypothesis Testing Risk

Alpha Risk

The beta risk or Type 2 Error (also called the “Consumer ’s Risk”) is the probability that we couldbe wrong in saying that two or more things are the same when, in fact, they are different.

Another way to describe beta risk is failing to recognize an improvement. Chances are thesample size was inappropriate or the data was imprecise and/or inaccurate.

Reading the formula: Beta is equal to the probability of making a Type 2 error.

Or: Beta is equal to the probability of failing to reject the null hypothesis given that the nullhypothesis is false.


! "# $ % ' ( ) *+, + % )- - . #) -++-/ )-"% 0*1- 02 % )-3-)-45-

/*+0)*670*248

9*+0)*670*24+ *45"7/-:

! !"#$%!&$'(!$)*

! +"#$%!&$'(!$)*

! ; " # $%!&$'( !$)*

! ,"#$%!&$'(!$)*

<-= *24

23

9> ?@A

<-= *24

23

9> ?@A

. // 01 ! 2 % /3 2 * /0 # $4 40 &0* /0 %

<-= *24

23

9> ?@A

<-= *24

23

9> ?@A

<-= *24

23

9> ?@A

<-= *24

23

9> ?@A

. // 01 ! 2 % /3 2 * /0 # $4 40 &0* /0 %

A$- % B "-1-" *+ )-# )-+-40-/ 6C

0$- 5 "27/-/ % )-%+8

D% E# "- )-+7 "0+ *4 0$ * + %)-%

"-%/ 02 )-F-50*24 23 G H 8

A$- % B "-1-" *+ )-# )-+-40-/ 6C

0$- 5 "27/-/ % )-%+8

D% E# "- )-+7 "0+ *4 0$ * + %)-%

"-%/ 02 )-F-50*24 23 G H 8

!"#$ &'(()(

!"#$ **'(()(

+ )(($,-

.$,/0/)1

+ )(($,-.$,/0/)1

! "#$% & () *+ ,#,)*-

2 )- ./33$($1- ./33$($1-

2 )- ./33$($1-2 )- ./33$($1-

.#% #,-#,"%&

()*"&$-,)*-

45) /0 !(6$7 45) /0 89:0$7

489/: -) ;$<$,- 5)7

./33$($1-./33$($1-4;$<$,- 5)7

!"#$ &'(()(

!"#$ **'(()(

+ )(($,-

.$,/0/)1

+ )(($,-.$,/0/)1

! "#$% & () *+ ,#,)*-

2 )- ./33$($1- ./33$($1-

2 )- ./33$($1-2 )- ./33$($1-

.#% #,-#,"%&

()*"&$-,)*-

45) /0 !(6$7 45) /0 89:0$7

489/: -) ;$<$,- 5)7

./33$($1-./33$($1-4;$<$,- 5)7



284


Beta Risk

Distinguishing between Two Samples

Beta and samplesize are veryclosely related.When calculating

Sample size inSigmaXL®, wealways enter the“power ” of thetest which is oneminus beta. Indoing so, we areestablishing asample size thatwill allow theproper overlap of

distributions.


!"#$ &'() '( #*" +,-.$.'/'#0 -1 1$'/'23 #- ,"4"5# #*" 26// *0+-#*"('(

7*"2 $ 8'11","25" "9'(#(:

µ

!"#$%"&'$"() "+ , - "#

$%'.

!"#$#%&' )&'*+ ,-

$+.$ .$&$#.$#%

!" #$#%&' )&'*+ ,-

$+.$ .$&$#.$#%

/.0.1$ , 2

3 4% 5678 . 9 .% % ( %:

/.0.1$ , 2

3 4% 5678 . 9 .% % ( %:

;11.8$ , 2

3 4%567 8. < < .%%(%:

! ; < :<=

>< ?$/6"

!"#$%"&'$"() "+ , 2 "#$%'.

Theoretical Distribution

of Means

When n = 2

! = 5

S = 1

Theoretical Distribution

of Means

When n = 30

! = 5

S = 1

Recall from the Central Limit Theoremas the number of individual

observations increase the StandardError decreases.

In this example when n=2 we cannotdistinguish the difference between theMeans (> 5% overlap, P-value > 0.05).

When n=30, we can distinguishbetween the Means (< 5% overlap, P-value < 0.05) There is a significantdifference.



285


Delta Sigma—The Ratio between and S

All samples are estimates of the population. All statistics based on samples are estimates of theequivalent population parameters. All estimates could be wrong!

These are typical questions you will experience or hear during sampling. The most common answeris “It depends.”. Primarily because someone could say a sample of 30 is perfect where that mayactually be too many. Point is you don’t know what the right sample is without the test.


Large Delta

Large S

Delta (!) is the size of the difference betweentwo Means or one Mean and a target value.

Sigma (S) is the sample Standard Deviation of

the distribution of individuals of one or both ofthe samples under question.

When ! / & S is large, we don’t need statisticsbecause the differences are so large.

If the variance of the data is large, it is difficultto establish differences. We need largersample sizes to reduce uncertainty.

We want to be 95% confident in all of our estimates!

Typical Questions on Sampling

Answer: No, not if you took the correct number of samples in the

first place!

Question: Should we take some more samples just to be sure?

Answer: Well, that depends on the size of your delta andStandard Deviation

.

Question: Was the sample we took large enough?

Answer: Well, that depends on what you want to know .

Question: How should we conduct the sampling?

Answer: Well, that depends on the size of your delta and

Standard Deviation

.

Question: How many samples should we take?



287


Hypothesis Testing Roadmap – Continuous Data

Hypothesis Testing Roadmap – Attribute Data




288


Common Pitfalls to Avoid


Notes

While using Hypothesis Testing the following facts should be borne

in mind at the conclusion stage:

– The decision is about Ho and NOT Ha.

– The conclusion statement is whether the contention of Ha was upheld.

– The null hypothesis (Ho) is on trial.

– When a decision has been made:

• Nothing has been proved.

• It is just a decision.

•

All decisions can lead to errors (Types I and II).

– If the decision is to Reject Ho, then the conclusion should read

There is sufficient evidence at the ! level of significance to show thatstate the alternative hypothesis Ha.

– If the decision is to Fail to Reject Ho, then the conclusion should read

There isnt sufficient evidence at the ! level of significance to show

that state the alternative hypothesis.



289



You have now completed Analyze Phase – Introduction to Hypothesis Testing.

! Articulate the purpose of Hypothesis Testing

!

Explain the concepts of the Central Tendency!

Be familiar with the types of Hypothesis Tests


Notes



290


Lean Six Sigma

Black Belt Training

Now we will continue in the Analyze Phase with“Hypothesis Testing Normal Data Part 1

”.

Analyze Phase

Hypothesis Testing Normal Data Part 1



291



Overview

Test of Means (t-tests)

T-tests are used to compare a Mean against a target and to compare Means from two differentsamples and to compare paired data. When comparing multiple Means it is inappropriate to use a t-test. Analysis of variance or ANOVA is used when it is necessary to compare more than 2 Means.

The corefundamentals of thisphase areHypothesis Testing,

Tests for CentralTendency, Tests forVariance and ANOVA.


!"#$%&' )"*&#!"#$%&' )"*&#

+ & * ,- . %& ' / " # 0 ,$#+ & * ,- . %& ' / " # 0 ,$#

1 * 2 3 ," 1 % . "1 * 2 3 ," 1 % . "

4- 35$6"#%# !"#$%&' 7 7 8 9:4 - 35 $6"#%# !"#$%&' 7 7 8 9 :

4- 35$6"#%# !"#$%&' 7 8 9 :4- 35$6"#%# !"#$%&' 7 8 9 :

;&$<5 $5 4-35$6"#%# !"#$%&';&$<5 $5 4-35$6"#%# !"#$%&'

;&="<"&$%*, 1$*$%#$%>#;&="<" &$%* , 1$* $%#$%>#

? @ A 1%=$%&'? @ A 1%=$%&'

B " ,> 5 2 " $5 + & * , - ."B ",>52 " $5 +&* ,-. "

4- 35$6"#%# !"#$%&' 7 8 9 C4- 35$6"#%# !"#$%&' 7 8 9 C

B <*3 D3 E +>$ %5& ; $"2#B <*3 D3 E +>$ %5& ; $"2 #

4- 35$6"#%# !"#$%&' 7 7 8 9C4- 35$6"#%# !"#$%&' 7 7 8 9C

They don t look the

same to me



292


1 Sample t

1 Sample t-test Sample Size

Here we are looking for the region in which we can be 95% sure our true population Mean will lie.This is based on a calculated average, Standard Deviation, number of trials and a given alpha riskof .05.

spread of the distribution of averages from samples of 2 will create too much uncertainty and make itvery difficult to statistically say there is a difference.

If you remember from earlier, 95% of the area under the curve of a Normal Distribution falls withinplus or minus 2 Standard Deviations. Confidence intervals are based on your selected alpha level, soif you selected an alpha of 5%, then the confidence interval would be 95% which is roughly plus orminus 2 Standard Deviations. Using your eye to guesstimate you can see that the target value fallswithin plus or minus 2 Standard Deviations of the sampling distribution of sample size 2.

If you used a sample of 30, could you tell if the target was different? Just using your eye it appearsthat the target is outside the 95% confidence interval of the Mean. Luckily, SigmaXL® makes this very

easy…


In order for the Meanof the sample to beconsidered notsignificantly differentthan the target, thetarget must fall withinthe confidenceinterval of the sampleMean.

! " #

$%&'()* +%!

! " , -

.) ! ! %* *0( ( *10

2+33040!50

60*7 00! *10 8)9&(0

)! 2 *10 *)4: 0*;

.) ! *0( ( *10

2+33040!50

60*7 00! *10 8)9&(0

)! 2 *10 *)4: 0*;

<)4: 0*

n

SMeanSE =

X X

T

X

XXX X

X XXXXX

X

X

X

X

X

X

X

X X X

<)4: 0*

n

SMeanSE =

X X

T

X

XXX X

X XXXXX

X

X

X

X

X

X

X

X X X

One common pitfall instatistics is not understandingwhat the proper sample size

should be. If you look at thegraphic, the question is: Isthere a difference between myprocess Mean and the desiredtarget. If we had populationdata, it would be very easy –no they are not the same, butthey may be within anacceptable tolerance (orspecification window). If wetook a sample of 2 can we tell

a difference? No, because the



293


Sample Size

Notice that as the samplesize increases, there isnot as big an effect on thedifference. If it was onlynecessary to see adifference of 0.9, whybother taking any more

samples than 15? TheStandard Deviationentered has an effect onthe difference calculated.

Take a few moments andexplore different StandardDeviation sizes inSigmaXL® to see theireffect on difference.

do not have an estimate for the Standard Deviation of the process. For example, if you want todetect a shift of 1.5 Standard Deviations enter that in difference and enter 1 for Standard Deviation.If you knew the Standard Deviation and it was 0.8, then enter it for Standard Deviation and 1.2 forthe difference (which is a 1.5 Standard Deviation shift in terms of real values).

If you are unsure of the desired difference, or in many cases simply get stuck with a sample sizethat you didn’t have a lot of control over, SigmaXL® will tell you how much of a difference can bedetected. You as a practitioner must be careful when drawing Practical Conclusions because it is

possible to have statistical significance without practical significance. In other words - do a realitycheck. SigmaXL® has made it easy to see an assortment of sample sizes and differences.

Try the example shown.


Instead of goingthrough the dreadfulhand calculations ofsample size we willuse SigmaXL®. Twoof the main fields mustbe filled in and oneselected as the SolveFor. If you want toknow the sample size,you must enter thedifference, which isthe shift that must bedetected. It iscommon to state the

difference in terms of“generic” StandardDeviations when you



294


1-Sample t Example

Let’s now try a 1-sample t example.

Step 1: Take a moment and review the practical problemStep 2: The Statistical Problem is: The null hypothesis is the Mean of the new supplier is equal to5. The alternative hypothesis is the Mean of the new supplier is not equal to 5. This is considered a2-tailed test if you’ve heard that terminology before.Step 3: Our selected alpha level is 0.05 and beta is 0.10.


! " $%&'()'&* $%+ ,*-./

! " # %&# '()*+,#&+)- '.%)-+)- */001+#&* 2(& % 0%&3 3.%3 4# '/&&#)315

0/&'.%*# 2&(6 % */001+#& 3.%3 '.%&-#* /* % 0&#6+/6 2(& 3.# .%&,#)+)-

0&('#**7

! 8.# 0&(0(*#, )#4 */001+#& .%* 0&(9+,#, /* 4+3. % *%601# (2 3.#+&

0&(,/'37 8.#5 .%9# *3%3#, 3.%3 3.#5 '%) 6%+)3%+) % - +9#) '.%&%'3#&+*3+'

(2 : () 3.#+& 0&(,/'37

! " # 4%)3 3( 3#*3 3.# *%601#* %), ,#3#&6+)# +2 3.#+& '1%+6 +* %''/&%3#7

0 " 1(&()2()'&* $%+ ,*-. /

;(< µ=7 > 7 ? :

;%< µ=7 > 7 ! :

3 " !42& . 5*- (4 (-2( !"#" $%& '(#) +'&), & -, ./0 (&' (#) $)1 )#2 )3

4#5 "& -()6 '# '&- 6 /'78

" ? @7@: # ? @7A@



298


Manual Calculation of 1- Sample t


Confidence Intervals for Two-Sided t-test

Here is the formulafor the confidenceinterval. Notice weget the sameresults asSigmaXL®.

!"# %& '( )*+ %&' + ,- & ./ 01 #1 ,.,#/ , 0/2

4.9789to4.5989

.0824*2.306788.4SEtX

or

n

stXµ

n

stX

meancrit

1n!/2,1n!/2,

±=±

+!!"""

Ho4.5989 4.9789

4.7889

X

If the calculated t-value lies anywhere in the critical regions reject the null hypothesis.

degrees of

freedom

.600 .700 .800 .900 .950 .975 .990 .995

1 0.325 0.727 1.376 3.078 6.314 12.706 3 1.821 6 3.657

2 0.289 0.617 1.061 1.886 2.920 4.303 6.965 9.925

3 0.277 0.584 0.978 1.638 2.353 3.182 4.541 5.841

4 0.271 0.569 0.941 1.533 2.132 2.776 3.747 4.604

5 0.267 0.559 0.920 1.476 2.015 2.571 3.365 4.032

6 0.265 0.553 0.906 1.440 1.943 2.447 3.143 3.707

7 0.263 0.549 0.896 1.415 1.895 2.365 2.998 3.499

8 0.262 0.546 0.889 1.397 1.860 2.306 2.896 3.355

9 0.261 0.543 0.883 1.383 1.833 2.262 2.821 3.250

10 0.260 0.542 0.879 1.372 1.812 2.228 2.764 3.169

T - Distribution

! /2 =.025! /2=.025

0

-2.306 2.306

Critical Regions

-2.56

The data here supports the alternative

hypothesis that the estimate for the

Mean of the population is not 5.0.



299


1-Sample t Exercise


Notes



300


1-Sample t Exercise: Solution

Since we do not know thepopulation StandardDeviation, we will use the1 sample t-test to

determine if we are attarget.


Depending on the test you are running you may need to change Ha (Not Equal To, Less Than, orGreater Than). Also ensure your desired Confidence Level is set.

Select the “RM Suppliers” Worksheet.



301


1-Sample t Exercise: Solution (cont.)


Because the null hypothesis value is within the confidence level, we “fail to reject” the nullhypothesis and accept the equipment is running at the target of 32.0. Also, as you can see, the P-value is 0.201. Because it is above 0.05, we “fail to reject” the null hypothesis so we accept theequipment is giving product at a target of 32.0 ppm VOC.

32.0 37.25130.832

Reject or Accept?



302


2 Sample t-test

Hypothesis Testing Roadmap


Notice thedifference in thehypothesis fortwo-tailed vs.one-tailed test.This terminologyis only used toknow whichcolumn to lookdown in the t-table.



303


Sample Size


As you can see we used the samecommand here just as in the 1-sample t.

Do you think the results are different?

Correct, the results are different.

Instead of going through the dreadful hand calculations of sample size we will use SigmaXL®.Three fields must be filled in and one left blank in the sample size window. SigmaXL® will solve forthe third. If you want to know the sample size, you must enter the difference, which is the shift thatmust be detected. It is common to state the difference in terms of “generic” Standard Deviations

when you do not have an estimate for the Standard Deviation of the process. For example, if youwant to detect a shift of 1.5 Standard Deviations enter that in difference and enter 1 for StandardDeviation. If you knew the Standard Deviation and it was 0.8, then enter it for Standard Deviationand 1.2 for the difference (which is a 1.5 Standard Deviation shift in terms of real values).

If you are unsure of the desired difference, or in many cases simply get stuck with a sample sizethat you didn’t have a lot of control over, SigmaXL® will tell you how much of a difference can bedetected. You as a practitioner must be careful when drawing Practical Conclusions because it ispossible to have statistical significance without practical significance. In other words - do a realitycheck. SigmaXL® has made it easy to see an assortment of sample sizes and differences. Try theexample shown.



304


2-Sample t Example


Now in Step 4. Open the worksheet: “Furnace”

How is the data coded?

Over the next severallesson pages we willexplore an examplefor a 2-Sample t-test.

Step 1. ReadPractical Problem

Step 2. The nullhypothesis is theMean of BTU.In fordamper 1 is equal tothe Mean of BTU.Infor damper 2.The alternativehypothesis is the

Means are not equal.

Step 3. We will usethe 2-Sample t-testsince the populationStandard Deviationsare unknown.

No, not that kind of damper



305


2-Sample t Example


Notice the “unstacked” data for each damper. WE NOW HAVE TWO COLUMNS.

We will unstack the data in BTU.In by Damper.



306


2-Sample t Example


Now let us perform a 2 Sample t Example. In SigmaXL® select “Statistical Tools>Power & Sample

Size Calculators> 2 Sample t-Test Calculator ” .

For the field “Sample Sizes:” enter ‘40’. You may then use SigmaXL®’s Recall Last Dialog

function to repeat the last calculation. Now enter a Sample Size of 50, because our data set hasunequal sample sizes which is not uncommon. The smallest difference that can be detected isbased on the smallest sample size, so in this case it is: 0.734.

Example: Follow the Roadmap…



307


Normality Test – Is the Data Normal?


The data is considered Normal since the P-value is greater than 0.05.

This is the Normality Plot for damper 2. Is the data Normal? It is Normal, continuing down theroadmap…

Is that normal

Or that



308


Test of Equal Variance (Bartlett

s Test)


In SigmaXL® select “Statistical Tools>2 Sample Comparison Tests” .

The F-test P-value of 0.5578 indicates that there is no statistically significant difference in variance.

For this example we will only focus on the Test for Equal Variances portion of the 2 Sample

Comparison Test Results.



309


2 Sample t-test Equal Variance


Let’s first view this data graphically with a Box Plot.

The Box Plots do not show much of a difference between the dampers.

Box Plot



310


SigmaXL® Results


Take a moment and review the SigmaXL® results.

3 Sample t-Test

Let’s continue along theroadmap… Perform the 2-Sample t-test; be sure to checkthe box “ Assume equal

variances”.



311


2 Sample t-Test: Solution


To unstack the data follow the steps here. This will generate two new columns of data shown on thenext page…



312




By unstacking the data wehow have the Clor.Lev dataseparated by the distributor it

came from. Now let’s moveon to trying to determine

correct sample size.

Select “SigmaXL>Statistical Tools>Power & Sample Size Calculators>2 Sample t-Test Calculator ”

.



313




We want to determine what is thesmallest difference that can bedetected based on our data.

Fill in the Power (1-Beta) and SampleSize (N) select Difference (Mean1-Mean2) to be solved for. SigmaXL® will tell us the differences we need.

The smallest difference that can be calculated is based on the smallest sample size.

In this case:.7339 rounded to.734



314




Check Normality for Clor.Lev_Post_1

The results shows us a P-value of 0.304 so our data is also Normal.

Check Normality for Clor.Lev_Post_2

The results shows us a P-value of 0.941 so our data is also Normal.



315




Test for Equal Variances

Before calculating a 2 samplet-Test we must test for Equal

Variances.

SigmaXL® Path:“Statistical Tools > 2

Sample Comparison Tests”

For the “Numeric Data Variable (Y)” we select our stacked column ‘Clor.Lev_Post’

For our “Group Category (X)” we select our stacked column ‘Distributor ’



316




Look at the P-value of 0.113.

This tells us that there is no statistically significant difference in the variance in these two data sets.

What does this mean….We can finally run a 2 sample t–test with Equal Variances?

Follow the command prompt shown here and enter the data as shown. Remember you must click

on graphs and check the Box Plot data option. This way SigmaXL®

will create a Box Plot. Equalvariances can be assumed based on the test for equal variances on the previous page.



317




Look at the Box Plot and Session Window. There is NO significant difference between theDistributors.

The Box Plots show VERY little difference between the Distributors, also not the P-value in theSession Window– there is no difference between the two Distributors.


Look at the Box Plot and 2 Sample t-Test Results.

There is NO significant difference between the distributors.

Hmm, we

re a

lot alike



318


Unequal Variance Example


Open the worksheet named “2 SAMPLE UNEQUAL VARIANCE DATA”.

Normality Test

Don

t just sit there….

open it



319


Test for Equal Variance


This is the output from a SigmaXL® Multi-Vari Chart. This can be created through “SigmaXL >

Graphical Tools > Multi-Vari Chart ” . The F-Test Statistics were obtained using SigmaXL®'s 2Sample Comparison Test. This can be selected through “SigmaXL>Statistical Tools> 2 Sample

Comparison Tests”

2-Sample t-Test Unequal Variance

The Box Plot shows no difference between the Means. The overall box is smaller for sample on the

left, which is an indication for the difference in variance.



320


2-Sample t-Test Unequal Variance


By looking at the histogram of Sample 3, you can notice a big spread or variance of the data.



321


2-Sample t-test Unequal Variance


What does the P-value of 0.996mean? Afterconducting a 2-

sample t-test there isno significantdifference betweenthe Means.




323


Example (cont.)


Paired t-test Example

Now let’s openEXH_STAT Deltaworksheet for

analysis. Usecolumns labeledMat-A and Mat-B.

In SigmaXL® open “Statistical Tools>Power & Sample Size Calculators> 1 Sample t-Test

Calculator ” ”. Enter in the appropriate Sample Size, Power Value and Standard Deviation.

Given the sample size of 10 we will be able to detect a difference of 1.15. If this was your processyou would need to decide if this was good enough. In this case, is a difference of 1.15 enough to

practically want to change the material used for the soles of the children’s shoes.

Now that

s

a tee test



324





For the next test we must first calculate the difference between the two columns. We will useExcel’s native functions to perform this calculation. Select Cell E2, enter: “=C2-B2”. We cannow copy this formula for the remaining cells to show the difference between Mat-A and Mat-B.We placed Mat-B first in the equation shown because it was generally higher than the values for

Mat-A.

We are going to use the difference column in a One Sample t-Test however, SigmaXL® also has aPaired t-Test where the difference column is created automatically.



325


1-Sample t


Box Plot

From the results we see that the Null Hypothesis falls outside the confidence interval, so we reject theNull Hypothesis. The P-value is also less than 0.05. Given this we are 95% confident that there is adifference in the wear between the two materials used for the soles of children’s shoes.

The marker for our Hypothesized Mean has been added to illustrate our point.



326


Paired T-Test

Distinguishing between Two Samples

As you will see the conclusions are the same, but just presented differently.




327


Paired T-Test

If you analyze this as a 2-sample t–test it simply compares the means of Material A to Material B.The power of the paired test is that it increases the sensitivity of the test without having to look at aseries of other factors.

Paired T-Test Exercise




328


Paired t-test Exercise: Solution

We must confirm thedifferences (now in anew calculated column)are from a NormalDistribution. This wasconfirmed with the Anderson-DarlingNormality Test by doinga graphical summaryunder Basic Statistics.

Because the two labsensured to exactly reportmeasurement results forthe same parts and the

results were put in thecorrect corresponding row,we are able to do a pairedt-test.

The first thing we must dois create a new columnwith the differencebetween the two testresults.




329


Paired t-test Exercise: Solution




330


Continuous Data Roadmap


Notes



331



You have now completed Analyze Phase – Hypothesis Testing Normal Data Part 1.

! Determine appropriate sample sizes for testing Means

!

Conduct various Hypothesis Tests for Means!

Properly Analyze Results


Notes



333



Overview

Tests of Variance

We are nowmoving intoHypothesisTesting Normal

Data Part 2 wherewe will addressCalculatingSample Size,Variance Testingand AnalyzingResults.

We will examinethe meaning ofeach of these andshow you how to

apply them.

!"#$"%&' )'*+ $%,!"#$"%&' )'*+ $%,

- %" ./0' 1'*2. +*- %" ./0' 1'*2. +*

3 " .&2 ."+' 4"5 6.' 4 $0'3 ".&2 ."+' 4" 56.' 4 $0'

7/ 68+9'*$* )'*+$%, : : ; <=7/ 68+9'*$* )'*+$%, : : ; < =

7/ 68+9'*$* )'*+$%, : ; <=7/ 68+9'*$* )'*+$%, : ; <=

>%+#8 +8 7/68+9'*$* )'*+$%,>%+#8 +8 7/68+9'*$* )'*+$%,

>%?'#'% +$" . 4 +" +$*+$&*>%?'#'% +$" . 4 +" +$*+$&*

@ A B 4$?+$%,@A B 4$?+$%,

C '.&85' +8 - %" ./ 0'C '.&85' +8 - %" ./0 '

7/ 68+9'*$* )'*+$%, : ; <D7/ 68+9'*$* )'*+$%, : ; < D

C #" 6 E 6 F -&+ $8% > +'5 *C #" 6 E 6 F -&+ $8% > +'5*

7/ 68+9'*$* )'*+$%, : : ; <D7/ 68+9'*$* )'*+$%, : : ; < D

Normal Data

–

1 Sample to a target

–

2 Samples – F-Test

–

3 or More Samples Bartletts Test

Non-Normal Data

– 2 or more samples Levenes Test

The null hypothesis states there is no difference between theStandard Deviations or variances.

–

Ho: !1 = !2 = !3 " –

Ha = at least on is different

Now that s non-normal!



334


1-Sample Variance

1 Sample t-test Sample Size

The Statistical Problem can be stated two ways:The null hypothesis: The variance is equal to 0.10 and the alternative hypothesis: The variance isnot equal to 0.10ORThe null hypothesis: The Standard Deviation is equal to 0.31 and the alternative hypothesis: The

Standard Deviation is not equal to 0.31


! # $%& ' ()* +& , -& ./* 0*%0 -% 1%*2 03 /3' (& ,* & . *4 (*/0*2

(3 (1 )&0-3. +& ,-&. /* 03 & 0& ,5 *06

78 09* 0& ,5 *0 + & ,-& ./* ) -*% -.%-2 * 09* /3 .8-2*. /* -.0*,+ & ): 8& - )

03 ,*;*/0 09* .1)) 9<(309*%-%6

! = 3> !?@& '( )* A !?

B& ,5 *0

! = & > !?@& '()* " !?

B& ,5 *0

C%* 09* %& ' ()* % - D* /& )/1 )& 0-3.% 83, & # %& ' ()* 0$ 0*%0 % -./*

09*< & ,* ,&,* )< ( *,83,' *2 E -09310 (*,83,' -.5 & # %& ' ()* 0$

0*% 0 & % E *))6

Stat > Basic Statistics > Graphical Summary

!" #$%&' (&%) #$+,)-. !

! " # % &# '()*+,#& +)- '.% )- +)- */0 01 +#* 2(& % 0% &3 3.% 3 4 #

'/&&#)315 0/&'.% *# 2 &(6 % */0 01 +#& 3.% 3 '.%&- #* %0&#6 +/6 2(& 3.# .% &,#)+)- 0&('#** % ), .% * % 1% &- #

7%& +%)'# +) 3.#+& 0&('#**8

! 9.# 0&(0( *#, )#4 */0 01 +#& .%* 0&(7 +,#, /* 4 +3. %*% 6 01# (2 3.# +& 0&(, /'38 9.#5 .% 7# *3% 3#, 3.#5 '% )

6 % +) 3% +) % 7 % & +% ) ' # ( 2 : 8 ; : 8

/ " 0 '%' (1'(&% ) # $+, )-.2

< (! != > : 8; : ( & < (! ! > : 8? ;

< % ! !=

" : 8; : < % ! ! " : 8 ? ;

3 " ! 4 1 % . 5 ) - 6 % $ (% 7 & - 2

# > : 8 : @ $ > : 8; :



335


1-Sample Variance

Take time to notice the Standard Deviation of 0.31 falls within 95% confidence interval. Based offthis data the Statistical Solution is “fail to reject the null”. What does this mean from a practicalstand point? They can maintain a variance of 0.10 that is valid.

Typically, shifting a Mean is easier to accomplish in a process than reducing variance. The newsupplier would be worth continuing the relationship to see if they can increase the Mean slightlywhile maintaining the reduced variance.




336


Test of Variance Example

The Statistical problem is:The null hypothesis: The Standard Deviation of the first method is equal to the Standard Deviationof the second method.The alternative hypothesis: The Standard Deviation of the first method is not equal to the StandardDeviation of the second method.

These hypotheses can also be stated in terms of variance.


! " #$ %&'(&% ) #$ +, )- . /

! " $%&' '( )"'"*+,&" '-" ".."/' (. '$( ),.."*"&' 0'(*%1" +"'-()0 (&

'-" *('',&1 (. 2('%'("03 4(5 0'5)6 /(&),',(&0 /(&)5/,7" '( 2('%'( *('86 ,&9"/',&1 2('%'("0 $,'- 8%/'"*,% '-%' /%50" *('',&1 %&) 0589"/',&1

'-"+ '( ),.."*"&' '"+2"*%'5*" %&) (:61 "& *"1 ,+"03 ! " /%& '"0' '-"

)% '% '( )"'"*+,&" ,. '-"*" ,0 % ),.."*"&/" ,& '-" ;'%&)%*) <"7,% ',(& (.

'-" *(' ',+" 8"'$""& '-" '$( ),.."*"&' +"'-()03

0 " 1'%'(2'(&%) # $+, )-. /

=(> !? @ !A

=%

> !?

" !A

3 " 456 %) 7% $ (%8 &- '- 2' BCD'"0' 0,&/" '-"*" %*" (&E6 A .%/'(*03F

Now open theworksheet“EXH_AOV ”.Follow along inSigmaXL®.

Note: Thesample size is

for each level.



337


Normality Test – Follow the Roadmap

According to the graph we have Normal data.

Check for Normality.




339


Test for Equal Variance (Normal Data)

Normality Test




340


Continuous Data - Normal

Test of Equal Variance


An alternative tousing the 2SampleComparison Testis the 2 SampleF-Test Calculatorwhich requiresmanual entry ofsummarystatistics asshown.

This calculator

can be foundunder StatisticalTools>BasicStatisticalTemplates>2Sample F-Test(Compare 2StDevs)

You can see thereis no statisticaldifference forvariance in Rotbased ontemperature as afactor. Since thedata is NormallyDistributed and wehave 2 samples,use F-Teststatistic.

Note: The Box Plotwas not generated

using the 2SampleComparison Test.It has been addedas a graphicalillustration.

This calculation confirms the P-value previously calculated.



341


Test For Equal Variances

Continuous Data - Normal

SigmaXL®’s tests for equal variances only allow one factor, so the Temp and Oxygen arecombined using Excel’s Concatenate Function to create a single factor Temp/Oxygen column.


This time wehave Rot as theresponse and

Temp/Oxygen asthe factor.

From the Hypothesis TestingRoadmap, we will now useBartlett’s Test for unequalvariances since there are morethan 2 levels (groups) in thetemp/oxygen factor.



342


Test For Equal Variances Statistical Analysis


Note that Bartlett’s Test for Equal Variance should only be used if the data is normal in each group.Since the P-Values for all Anderson Darling Tests are >0.05, we will assume Normality for each

group. If we had Non-normal data, then Levene’s Test for Equal Variance would be used.



343


Tests for Variance Exercise: Solution

Tests for Variance Exercise


First we want to do a graphical summary of the two samples from the two suppliers.



344


Tests for Variance Exercise: Solution

In “Numeric Data Variables (Y)” enter ‘ppm VOC’

In “Group Category (X1)” enter ‘RM Supplier ’

We want to see if the two samples are from Normal populations.


The P-value is greaterthan 0.05 for both Anderson-Darling

Normality Tests so weconclude the samples arefrom Normally Distributedpopulations because we“failed to reject” the nullhypothesis that the datasets are from NormalDistributions.



345


Tests for Variance Exercise: Solution (cont.)


Because the 2

populations wereconsidered to beNormally Distributed,the F-test is used toevaluate whether thevariances (StandardDeviation squared) areequal.

The P-value of the F-test was greater than

0.05 so we“fail toreject” the null

hypothesis.

So once again inEnglish: The variancesare equal between theresults from the twosuppliers on ourproduct’s ppm VOClevel.

Continue todetermine ifthey are of

Equal Variance.



346






347


Purpose of ANOVA


Is the between group variation large enough to be distinguished from the within group variation?

What do we want to know?

µ1 µ2

delta

(!)

!"#$% ##& ( )*+, -. )/.$/*&0

1 /$2/& ( )*+ , -. )/. $/*&

!3#4#3 *5 6+,,3/#) 70

8*$. 3 !9 4#). 330 - . )/.$/*&

X

X

X

XX

X X

X

X

Analysis of Variance extends the two sample t-test for testing

the equality of two population Means to a more general null

hypothesis of comparing the equality of more than two Means,

versus them not all being equal.

–

The classification variable, or factor, usually has three or

more levels (If there are only two levels, a t-test can be

used).

–

Allows you to examine differences among means using

multiple comparisons.

–

The ANOVA test statistic is:

withinS betweenS

withinSSAvg betweenSSAvg 2

2

=

There s a Nova again



348


Calculating ANOVA


The reason we don’t use a t-test to evaluate series of Means is because the alpha risk increasesas the number of Means increases. If we had 7 pairs of Means and an alpha of 0.05 our actualalpha risk could be as high as 30%. Notice we did not say it was 30%, only that it could be as high

as 30% which is quite unacceptable.

Take a moment to review the formulas for an ANOVA.

!!= =

"g

1 j

nj

1i

2

ij )X(X

VariationTotal

!=

"g

1 j

2

nj )X(Xj

VariationGroupBetween

!!= =

"g

1 j

nj

1i

2

ij )X(X

VariationGroupWithin

! "#$#%

& ( )"# *+, -#$ . / 0 $.+1 2 3 4#5#42 6* )"# 2)+78 9

:6; < )"# 6*765 67+= 4 6* )"# ;)" 0 $.+1

* ; < )"# *+, -#$ ./ 6*765 67+= 42 6* )"# ;)" 0 $.+1 .$ 4#5#4

< )" # 0 $ = * 7 > # = *

? ; < )"# >#=* ./ )"# ; )" 0 $.+1 .$ 4#5#4

X

!"#$%

&!'

3@#)A ##* & $.+1 B= $ 6=) 6.*9

! 6)"6* & $.+1 B= $6=)6.*

C.)=4 3D 5#$=449 B=$6=)6.*

!"#$%

&!'

3@#)A ##* & $.+1 B= $ 6=) 6.*9

! 6)"6* & $.+1 B= $6=)6.*

C.)=4 3D 5#$=449 B=$6=)6.*

Calculating ANOVA

!"# % &'"% ( )* + ),- (# % * # * % * ."# ,/0 1# ( 23 4# % ,*

),-(#% *#* 5 )." % ' % )(65 )*# .6.#*. *-"#0 #7 !"# 32(0 /&% 32(

.#*.),8 0 2(# ."% , 2,# ' % )( 23 4#% ,* /* ),8 % .6.#*. )* 9

( )

( )risk alpha30%or

30.00.05-1-1

:0.05!anandmeansof pairs7forso,

meansof pairsof numberk where

!11

7

k

=

=

=

!!



349


Three Samples


We have three potential suppliers that claim to have equal levels of quality. Supplier B provides aconsiderably lower purchase price than either of the other two vendors. We would like to choose thelowest cost supplier but we must ensure that we do not effect the quality of our raw material.

Follow the Roadmap…Test for Normality

Compare P-values.



350


Test for Equal Variance…


There doesn’t seem to be a huge difference here.

This Box Plot was not generated using Bartlett’s Test, we are using it to graphically display thedata.

According toBartlett’s Test thereis no significantdifference in thevariance of the 3suppliers.

ANOVA



351


ANOVA


Looking at the P-value the conclusion is we fail to reject the null hypothesis. According to thedata there is no significant difference between the Means of the 3 suppliers.

Note that the Mean/CI graph shows the 95% confidence intervals on the mean for each supplierusing a pooled standard deviation. The fact that the confidence intervals overlap indicates that

there is no statistical evidence of a difference in Supplier Means.

Follow along inSigmaXL®.

Note thatSigmaXL®’s One-Way ANOVA uses aconfidence level of95.0%.



352


ANOVA


Let’s check on how much difference we can see with a sample of 5.

Before looking up the F-Critical value you must first know what the degrees of freedom is. Thepurpose of the ANOVA’s test statistic uses variance between the Means divided by variance within thegroups. Therefore, the degrees of freedom would be three suppliers minus 1 for 2 degrees of freedom.The denominator would be 5 samples minus 1 (for each supplier) multiplied by 3 suppliers, or 12

degrees of freedom. As you can see the F-Critical value is 3.89 and since the F-Calc is 1.40 and notclose to the critical value, we fail to reject the Null Hypothesis.

Sample Size

Will having a sample of5 show a difference? After crunching thenumbers, a sample of 5can only detect adifference of 2.56Standard Deviations.Which means that theMean would have to beat least 2.56 StandardDeviations until wecould see a difference.To help elevate thisproblem a largersample should be used.If there is a largersample you would beable to have a moresensitive reading for theMeans and the

variance.



353


ANOVA Assumptions


SigmaXL® V6 does not include Residuals in One-Way ANOVA, so we will now manuallycalculate the Residuals. The Residuals are the individual data points subtracted by the Mean of

the group. This slide uses Descriptive Statistics to calculate the Mean. This may also be doneusing Excel’s AVERAGE function. These group Residuals are then stacked in the column“Stacked Residuals”.

Residual Plots

! " # $%&'() *+,-% ) '& ) /&01) *&23 /&%4' +$&/ $3 *5& 6 ,/&2 "

7 " 8 '','% ) '& -,'6 ) 223 ) -/ +-/&9&-/ &-*23 / +% *' +$1*&/"

: " ;,6 ,< &-&+*3 , = () ' +) -4& ) 6 ,-< =)4*,' 2&(&2% "

>- ,-&?@ ) 3 AB # C AD 6 ,/&2 ) /&01) 43 4) - $ & 45&4E &/$ 3 &+*5& ' ,= *5& =,22,@ +-< F

! " G5&4E *5& /) *) =,' B ,'6 ) 2 +*3 ) * &) 45 2&(& 2 ) -/ =,'5,6 ,< &-&+*3 ,= () ' +) -4& ) 4',%% ) 2 2 2&(&2% "

7 " 8H ) 6 +-& *5& '&% +/1) 2% I) '&% +/1) 2 +% *5& /+==&'&-4& +-@ 5) * *5& 6 ,/ &2 9'&/ +4*% ) -/ *5& *'1& , $%&'( ) *+,-J"

! " B ,'6 ) 2 92,* ,= *5& '&%+/1) 2%

7 " K &% +/1) 2% (&' %1% =+ *%

: " K & % +/ 1 ) 2% ( & '% 1 % , '/ & '

>= *5& 6 ,/ &2 +% ) /& 01 ) *&D *5& '& %+/1) 2 92,*% @ + 22 $& %*'14*1'&2& %%"

Note thatResiduals areavailable inTwo-Way ANOVA andRegression Analysis which

will be coveredat a later point.



354


Histogram of Residuals


The Normality plot of the Residuals should follow a straight line on the probability plot. (Does apencil cover all the dots?)

Normal Probability Plot of Residuals

The Histogram of Residualsshould show a bell shapedcurve.



355


Residuals versus Fitted Values


ANOVA Exercise

This chart wascreated using aScatter Plot of“Stacked Residuals” Vs “Supplier Mean”.



356


ANOVA Exercise: Solution


First let’s look at the Histogram and Descriptive Statistics for the 3 shifts.

We want to see if the 3 samples are from Normal populations.

In “Numeric Data Variables (Y)” enter ‘ppm VOC’

In “Group Category (X1)” enter ‘Shift’

Worksheet: RM Suppliers



357




Following the Hypothesis Testing Roadmap, we will use Bartlett’s Test for Equal Variance, sincethere are 3 groups and each group is assumed to have Normal data.



358




If the variances are unequalthen use Welch’s ANOVAinstead of One-Way ANOVA.



359




The steps to create these Residual plots are as follows:

1. Select SigmaXL>Statistical Tools>Regression>Multiple Regression.2.

Select “ppm VOC” for Numeric Response (Y).3.

Select “Shift” for Categorical Predictors (X).

4.

Ensure “Display Residual Plots” is checked.5. Click OK, the residuals can be found in the Mult Reg Residuals worksheet.

A visual display of our Residuals indicates that the data is Normal. Since our Residuals look NormallyDistributed and randomly patterned, we will assume our analysis is correct.

This graphical

display wasgenerated usingMultiple Regressionwhich we will coverin detail later.

We accept

the alternate hypothesis that the Mean product quality is different from at least one shift.

Don

t miss

that shift

Since the confidence intervalsof the Means do not overlap

between Shift 1 and Shift 3, wesee one of the shifts isdelivering a product quality with

a higher level of ppm VOC.



360



You have now completed Analyze Phase – Hypothesis Testing Normal Data Part 2.

! Be able to conduct Hypothesis Testing of Variances

!

Understand how to Analyze Hypothesis Testing Results


Notes



361


Lean Six Sigma

Black Belt Training

Now we will continue in the Analyze Phase with“Hypothesis Testing Non-Normal Data Part 1

”.

Analyze Phase

Hypothesis Testing Non-Normal Data

Part 1



362


Hypothesis Testing Non-Normal Data Part 1

Overview

Non-Normal Hypothesis Tests

At this point we have covered the tests for determining significance for Normal Data. We willcontinue to follow the roadmap to complete the test for Non-Normal Data with Continuous Data.

Later in the module we will use another roadmap that was designed for Discrete data.

Recall that Discrete data does not follow a Normal Distribution, but because it is notContinuous Data, there are a separate set of tests to properly analyze the data.

The corefundamentals of thisphase are EqualVariance Tests and

Tests for Medians.


!"#$# &'( )"*+,-#!"#$# &'( )"*+,-#

./0,1 2 ,(+, -3" !"#$#./0,1 2,(+, -3" !"#$#

! " #$ %&'()( +'(%),- . . / 01! " #$ %&' ()( +'(%),- . . / 0 1

!" #$%&'()( +'(%),- . / 01!" #$ %&'()( +'(% ),- . / 01

2,%3$ %$ ! " #$%&'()( +'(% ),-2,%3$ %$ ! " #$ %&'()( +'(% ),-

2,4'3' ,%)56 7%5 %)(%)8(2,4'3' ,%)56 7%5 %)(%)8(

9 : ; 7)4%),-9 : ; 7)4%),-

< '68$= ' %$ >,5 6"? '< '68$= ' %$ >,5 6"? '

! " #$%&'()( +'(%),- . / 0@!" #$ %&'()( +'(% ),- . / 0@

< 35 # A # B >8% )$, 2%'=(< 35# A # B >8% )$, 2 %'=(

! " #$ %&'()( +'(%),- . . / 0@! " #$ %&' ()( +'(%),- . . / 0 @

We can test for anything

Normal

Non-Normal

Continuous

Discrete



363


1 Sample t

Why do we care if a data set is Normally Distributed?

Skewness is a natural state for much data. Any data that has natural or artificial limits typicallyexhibits a Skewed Distribution when it is operating near the limit. The other 3 causes for Non-normality are usually a symptom of a problem and should be identified, separated and corrected.

We will focus on Skewness for the remaining tests for Continuous Data. A common reaction to Non-normal Data is to simply transform it. Please see your Master Black Belt to determine if a transform isappropriate. Often data is beaten into submission only to find out that there was an underlying cause

for Non-normality that was ignored. Remember, we want you to predict whether the data should beNormal or not. If you believe your data should be Normal but it is not, there is most likely anunderlying cause that can be removed which will then allow the data to show it’s true nature and beNormal.


! When it is necessary to make inferences about the true nature of thepopulation based on random samples drawn from the population.!

When the two indices of interest (X-Bar and s) depend on the databeing Normally Distributed.!

For problem solving purposes, because we don’t want to make a baddecision – having Normal Data is so critical that with EVERY statisticaltest, the first thing we do is check for Normality of the data.

Recall the four primary causes for Non-normal data:

!

Skewness – Natural and Artificial Limits! Mixed Distributions - Multiple Modes!

Kurtosis!

Granularity

We will focus on skewness for the remaining tests for Continuous Data.


Now we willcontinue downthe Non-Normal side ofthe roadmap.Notice thisslide isprimarily fortests ofMedians.



364


Sample Size

You have already seen this command in the last module, this is simply the application for Non-normal Data. The question is: Are any of the Standard Deviations or variances statisticallydifferent?


Follow the Roadmap…

!"#"$"%& ("&( )* "+,-. #-/0-$1"2 ,&"3 () 1)45-/" (6" "&(04-("3

5)5,.-(0)$ 7(-$3-/3 8"#0-(0)$& */)4 (9) )/ 4)/" &-45."&

90(6 : )$;: )/4-. 30&(/0<,(0)$&=

> ?)@ !A B !C B !D E

> ?-@ F ( ."-&( )$" 0& 30**"/"$(=

Open theworksheet“EXH_AOV ”.Select“SigmaXL>Graphic

al Tools > Normal

Probability Plots”. As you can clearlysee from the chart,this is not a normalprocess.

Next we will seethat the AndersonDarling P-valuesare much less than0.05.



365


Test of Equal Variance Non-Normal Distribution

Next we test for Equal Variance. From the Hypothesis Testing Roadmap, we see that since“Factors2” has 2 levels we will use the Levene’s Test in the 2 Sample Comparison Tests. If wehad more than two levels we would use “SigmaXL>Statistical Tools>Equal Variance Tests>Levene”

Select: “SigmaXL>Statistical Tools > 2 Sample Comparison Tests”. Since the data is Non-normal,

the test highlighted by SigmaXL®

is the Levene’s test and not the F-test.


Test of Equal Variance Non-Normal Distribution



366


Hypothesis Test Exercise

Test for Equal Variance Example: Solution

First test to see if the data is Normal or Non-Normal.




367



Since there are twovariables we need toperform a Normality Teston CallsperWk1 andCallsperWk2.

First select the variable‘CallsperWk1’ andPress “OK”.

Follow the same stepsfor ‘CallsperWk2’.

From the Descriptive Statistics and the Normal Probability Plots we can see that the data for bothgroups is Non-normal.




368



As you can see the data illustrates a P-value of 0.247 which is more than 0.05. As a result, there isno variance between CallperWk1 and CallperWk2. Therefore with a 95% confidence level we rejectthe null hypothesis.


And here

s our answer !!



369


Mean and Median

Nonparametric Tests

A non-parametric test makes no assumptions about Normality.

For a Skewed Distribution:- The appropriate statistic to describe the central tendency is the Median, rather than

the Mean.- If just one distribution is not Normal, a non-parametric should be used.

Non-parametric Hypothesis Testing works the same way as parametric testing. Evaluate the P-value in the same manner.


!

Target2

X~

1X~

X~

In general, nonparametric tests do the following: rank order the data, sum the data by ranks, sign

the data above or below the target, and calculate, compare and test the Median. Comparisonsand tests about the Median make nonparametric tests useful with very Non-normal Data.

Note: SigmaXL® V6 does not report confidence intervals on the Median in Descriptive Statistics. However,Confidence Intervals on the Median are available in the Kruskal-Wallis and Mood’s Median Tests to becovered later.



370


SigmaXL®

s Nonparametrics


1-Sample Sign: performs a one-sample sign test of the Median and calculates the correspondingpoint estimate and confidence interval. Use this test as an alternative to one-sample Z and one-sample t-tests. 1-Sample Wilcoxon: performs a one-sample Wilcoxon signed rank test of the Median andcalculates the corresponding point estimate and confidence interval (more discriminating or efficientthan the sign test). Use this test as a nonparametric alternative to one-sample Z and one-sample t-tests.Mann-Whitney: performs a Hypothesis Test of the equality of two population Medians andcalculates the corresponding point estimate and confidence interval. Use this test as anonparametric alternative to the two-sample t-test.Kruskal-Wallis: performs a Hypothesis Test of the equality of population Medians for a one-waydesign. This test is more powerful than Mood’s Median (the confidence interval is narrower, onaverage) for analyzing data from many populations, but is less robust to outliers. Use this test asan alternative to the one-way ANOVA.Mood

s Median Test: performs a Hypothesis Test of the equality of population Medians in a one-

way design. Test is similar to the Kruskal-Wallis Test. Also referred to as the Median test or signscores test. Use as an alternative to the one-way ANOVA.

There are 5 basic nonparametric tests thatSigmaXL® calculates. Each one has acounterpart in normal Hypothesis Testing.



371


1-Sample Example

1-Sample Sign Test

depending on the distribution selected for the alternative.


Here is a little trick! Dividingthe sample size from a t-testestimate by 0.864 shouldgive you a large enoughsample regardless of theunderlying distribution…mostof the time.

For instance, having asample size of 23 using the t-test method, the sample sizewould increase by 3. If thereis a Normal Distribution(assuming) this numberwould increase by 1.

Truthfully, it is really possibleto decrease the sample size

The Statistical Problem is: The Null Hypothesis is that the Median is equal to 63 and the alternativehypothesis is the Median is not equal to 63.

Open the SigmaXL® Data File: “DISTRIB1.MTW ”. Next you have a choice of either performing a 1-Sample Sign Test or 1-Sample Wilcoxon Test because both will test the Median against a target.For this example we will perform a 1-Sample Sign Test.



372


1-Sample Example

As you can see the P-value is less than 0.05, so we must reject the null hypothesis which meanswe have data that supports the alternative hypothesis that the Median is different than 63. Theactual Median of 65.70 is shown in the Session Window. Since the Median is greater than thetarget value, it seems the new process is not as good as we may have hoped.


Perform the same steps as the 1-Sample Sign to use the 1-sample Wilcoxon.

=For a two tailed test,

choose the not equal

for

the alternative hypothesis.

Statistical Tools >Nonparametric Tests > 1 Sample Wilcoxon



373


1 Sample Example: Solution

Hypothesis Test Exercise


According to the Hypothesis the Mine Manager feels he is achieving his target of 2.1 tons/day.

H0: M = 2.1 tons/day

Ha: M ! 2.1 tons/day

Since we are using one sample, we have a choice of choosing either a 1 Sample-Sign or 1Sample Wilcoxon. For this example we will use a 1 Sample-Sign.



374


Mann-Whitney Example

1 Sample Example: Solution


We disagree



375


Mann-Whitney Example


Perform the Mann-Whitney test.

The Practical Conclusion is that there is a difference between the Medians of the two machines.

When looking at theProbability Plot,Match A yields a lessthan .05 P-value.Now look at GraphB? Ok now you haveone graph that isNon-normal Data andthe other that isNormal. The goodnews is whenperforming aNonparametric Testof 2 Samples, onlyone has to be

Normal. With thatsaid, now let’sperform a Mann-Whitney.



376


Exercise


Mann-Whitney Example: Solution

Exercise objective: To practice solving problem presentedusing the appropriate Hypothesis Test.

A credit card company now understands there is no variabilitydifference in customer calls/week for the two different credit cardtypes. This means no difference in strategy of deploying theworkforces. However, the credit card company wants to see if thereis a difference in call volume between the two different card types.The company expects no difference since the total sales among thetwo credit card types are similar. The Black Belt was selected andtold to evaluate with 95% confidence if the averages were the same.The Black Belt reminded the credit card company the calls/day werenot Normal distributions so he would have to compare usingMedians since Medians are used to describe the central tendency ofNon-normal Populations.

1.

Analyze the problem using the Hypothesis Testing roadmap.2. Use the columns named CallsperWk1 and CallsperWk2.3. Is there a difference in call volume between the 2 different card

types?

Worksheet: Hypothesis Test Study



377


Mann-Whitney Example: Solution


The final 2 tests are the Mood’s Median and the Kruskal Wallis.

Mood

s Median Test

!" # $ &'()*$() +,)-&$. /&$012 0, +,)-&31 041 ,-13&0*,$ ,5 *06

04311 5&+*'*0*16 /,3'2/*21" 741. /&$0 0, 611 *5 04131 *6 & 2*55131$+1

*$ 041 31+,813*16 &),$9 041 04311 ',+& 0*,$6" # :'&+; :1'0 /&6

&6;12 0, 41'- )&$&91)1$0 18&'(&01 041 31+,813*16 &0 041 ',+&0*,$6

/*04 <=> +,$5*21$+1"

?" @,A B! C B? C BD

@&A &0 '1&60 ,$1 *6 2*55131$0

D" E61 041 B,,2F6 )12*&$ 0160"G " :&612 ,$ 041 6)&''160 6&)-'1 ,5 !DH 041 0160 /*'' I1 & I'1 0, 2101+0

& 2*55131$+1 +',61 0, !"="

= " J0&0*60*+& ' K ,$+'(6*,$6A E61 +,'()$6 $&)12 L1+,813. &$2

M,+&0*,$ 5,3 &$&'.6*6"

= = ?



378


Follow the Roadmap…Normality


Notice evidence ofOutliers in at least 2of the 3 populations.You could do a BoxPlot to get a cleareridea about Outliers.

Instead of using the Anderson-Darling test for Normality, this time we used the graphical summarymethod. It gives a P-value for Normality and allows a view of the data that the Normality test doesnot.



379


Follow the Roadmap…Equal Variance


Mood

s Median Test

Check for Equal Variance using Levene’s Test. We conclude that the Variances are equal.



380


Kruskal-Wallis Test


The Kruskal-Wallis Test is more powerful than the Mood’s Median Test, but the Mood’s Median Testis more robust to Outliers.

Using the same data set, analyze using the Kruskal-Wallis test.

Exercise



381


Pagers Defect Rate Example: Solution


The P-value is over 0.05…therefore, we fail to reject the Null Hypothesis.

Let’s follow theRoadmap and checkto see if the data isNormal.

Take a moment tocompare the 3variables. Since our 3variables are less than0.05 the data is Non-normal.

SigmaXL>Graphical

Tools>Histograms

and Descriptive

Statistics…



382



Unequal Variance

! "#$# &' (') *' +, -"# $'.&/.0 +1 -"# 2.$+.,3# +4 ,'- #5).67

8 9,#5).6 2.$+. ,3#4 .$# )4).66( -"# $#4)6- '1 &+11#$#,3#4 +,

-"# 4".0# '1 -"# &+4-$+:)-+',;< =>-$#/# -.+64

< ? )-6+#$4

< @)6-+06# /'&#4

A"#4# 3',&+-+',4 4"')6& :# #>06'$#& -"$')*" &.-.

&#/'*$.0"+34;

B'$ CD#E#& F+4-$+:)-+',4 E+-" 3'/0.$.:6# @#&+.,4 +- +4

),)4).6 1'$ -"# 2.$+.,3#4 -' :# &+11#$#,- E+-"')- 4'/#

.44+*,.:6# 3.)4# +/0.3-+,* -"# 0$'3#44;

Example

This is an example of comparable products. To view these graphs open the worksheet “Var_Comp”.

As you can see, Model A is Normal but Model B is Non-normal.



383



Now let’s check thevariance.

Does Model B have a

larger variance thanModel A? The Medianfor Model B is muchlower. How can wecapitalize on ourknowledge of theprocess? Let’s lookat data demographicto help us explain thedifferences betweenthe two processes.

Example (cont.)

Data Demographics

What clues can explain the difference in variances? This example illustrates how Non-normal Data

can have significant informational content as revealed through data demographics. Sometimes thisis all that is needed to draw conclusions.



384



Black Belt Aptitude Exercise

Black Belt Aptitude Exercise: Solution

Which of these graphs has Normal Data and which one doesn’t? As you can see data forEngineering, Liberal Arts and Business is Normal Data. However, the data for Science is Non-normal.



385



Now let’s look at information given by SigmaXL®. As you can see the P-value is greater than 0.05.The data illustrates that there is not a difference in Variance.

Black Belt Aptitude Exercise: Solution (cont.)

Since the P-value is > .05, we fail to reject the null hypothesis, i.e., there is no difference betweena potential Black Belt’s degree and performance.



386



You have now completed Analyze Phase – Hypothesis Testing Non-Normal Data Part 1.

! Conduct Hypothesis Testing for Equal Variance

!

Conduct Hypothesis Testing for Medians

!

Analyze and interpret the results


Notes



387


Lean Six Sigma

Black Belt Training

Now we will continue in the Analyze Phase with“Hypothesis Testing Non-Normal Data Part 2

”.

Analyze Phase

Hypothesis Testing Non-Normal Data

Part 2



389


Sample Size and Types of Data

Proportion versus a Target

Sample size is dependent on the type of data.


This formula is an approximation for ease of manual calculation.

!"#$ &'$& #$ ($') &* )'&'+,#-' #. &"' /+*0'$$ /+*/*+&#*- 1/2'3(45$ $*,' )'$ # +') 64 5('7 / 8 9

!"' " : /*&"'$'$ ;

! < 8 ; / = / 8

! < 4 ; / > / 8

!"' *? $'+6 ') &'$& $&4 &#$&#0 #$ 04 50(54 &') 4 $ .*5 5*@ $;

1-*+, 4 5 4 // +*A #,4 &#*-2

!"#$ #$ 0*,/ 4 +') &* B 0+#& = B 4 C D

)( ) np1p

ppZ

00

0

obs

!

!=

ˆ



390



Now let’s try an example:


Take note of the how quickly the sample size increases as the alternative proportion goes up. Itwould require 1402 samples to tell a difference between 98% and 99% accuracy. Our sample of

500 will do because the alternative hypothesis is 96% according to the proportion formula.

Yes sir,they

re all

good



391


!" #$%&'# )* +#%,&-# . !" $%&'()'* +",-)./ (0* $%"1,*2

$%*+*.(*3 4+)./ (0* &$$%"$%)&(* 56$"(0*+)+ !*+(7

8"4 &%* (0* +0)$$)./ 2&.&/*% &.3 &%* ). '0&%/* "9

)2$%"-)./ +0)$$)./ &''4%&'67 8"4% &..4&, 1".4+

3*$*.3+ ". 6"4% &1),)(6 (" $%"-* (0&( +0)$$)./

&''4%&'6 )+ 1*((*% (0&. (0* (&%/*( "9 :;<7

=7 5"> 2&.6 +&2$,*+ 3" 6"4 .**3 (" (&?* )9 (0*

&.()')$&(*3 +&2$,* $%"$"%()". )+ :@<A

@7 B 4( "9 @;;; +0)$2*.(+ ".,6 =C :; >*%* &''4%&(*7

D E" 6"4 /*( 6"4% &..4&, 1".4+A

D F &+ (0* +&2$,* +)G* /""3 *."4/0A


After you analyze the data you will see the Statistical Conclusion is to reject the Null Hypothesis.

What is the Practical Conclusion…the process is not performing to the desired accuracy of 99%.


Sample Size Exercise

Select the Confidence Interval for One Proportion as shown above. Now for the “Number ofelements:” enter how many items were shipped and for the “Size of Sample” field enter the numberof accurate items shipped. SigmaXL® reports the Upper and Lower CI Limits.



392


Proportion vs Target Example: Solution

Power (1-Beta) should be .9 and the Alternative Proportion 1(P1) should be 0.82. TheHypothesized Proportion should be 0.80. Keep the default Alpha of .05.

As you can see the Sample Size should be at least 4073 to prove our hypothesis.


Do you get your bonus?

Yes, you get your bonus since .80 is not within the confidence interval. Because the improvement

was 84%, the sample size was sufficient.

Answer: Use alternative proportion of .82, hypothesized proportion of .80. n=4073. Either you’dbetter ship a lot of stuff or you’d better improve the process more than just 2%!

! "# %&' () *+ %*(%+ '& ,- # &

.&*&,/& "(. 0" 1()2

3 (' "- '4& 5 6 6 6

)4,78&1 ') 9 : ; < 6 # &.&

+ **(.+ '&= > + ) '4&

)+ 8 7%& ) ,? & )( --,*,&1'@ 0.842000

1680

n

X p ===

!



393


Comparing Two Proportions

SigmaXL® gives you achoice of using thenormal approximationor the exact method.We will use the exactmethod. The formula isan approximation forease of manualcalculation.

Sample Size and Two Proportions Practice


!"#$ &'$& #$ ( $') &* ) '&'+,#-' #. &"' / +*0'$$ )'.'0& +1 &' 2*+/+*/ *+&#*-3 /4 *. *-' $1 ,/ 5' )# ..'+$ 67 1 0'+&1 #- 1, *(-& 8.+*, &"1& *. 1 -*&"'+ $1 ,/ 5' 2'9: 9 3 6'.*+' 1 -) 1 .&'+ 7 *(+

#,/+*; ','- & 1 0&#*-$4

!"' "7 /*&"'$'$<

= > < / ? @ / A B 8

= 1 < / ? @ / A C 8

!"' &'$& $&1&#$&#0 #$ 0150(51&') 1$ .*55*D $<

!"#$ #$ 0*,/ 1 +') &* E 0+#&#015 B E 1 F A

( ) ( ) 222111

21obs

n p1 pn p1 p

D p pZ

!+!

!!

=

G1&0" $*,' E H$I

Answers:

34,24732,9864,3015,1425,8315,831

Catch some Z’s



394



In SigmaXL® click Statistic Tools > Power &Sample Size Calculators>2 Proportion Test Calculator . For the field“Proportion 1 (P1):” type .85 and for the field “Power (1-Beta):” type .90; The last field “Proportion2 (P2):” enter .95 then click OK.

A sample of at least 188 is necessary for each group to be able to detect a 10% difference. If youhave reason to believe your improved process is has only improved to 90% and you would like to

be able to prove that improvement is occurring the sample size of 188 is not appropriate.Recalculate using .90 for proportion 2 and leave proportion 1 at .85. It would require a samplesize of 918 for each sample!



!"# %&''&( )*+ , - .- ( #/# .- 0 #* 1

2-'34'-.# 5/&5&/. )&*61

7 # %& / # 89 5 / & : # 9 # * .1 ; < < 6 - 9 5 ' # 6 = > ? < - 3 34 / - .#

@ % .# / 8 9 5 / & : # 9 # * .1 A < < 6 - 9 5 ' # 6 = A A < - 3 34 / - .#

A ? AA A >@ % .# / 895 / &:# 9 # *.

> ? <; < <7# % &/ # 8 95/ &:# 9# *.

@334/-.#!&.- ' B- 95 '# 6

A ? AA A >@ % .# / 895 / &:# 9 # *.

> ? <; < <7# % &/ # 8 95/ &:# 9# *.

@334/-.#!&.- ' B- 95 '# 6

0.942225

212

n

X p

0.85600

510

n

X p

2

22

1

11

===

===

The datashown wasgathered fortwoprocesses.



395


Boris and Igor Exercise


To compare two proportions in SigmaXL® select Statistical Tools>Basic Statistical Templates>2

Proportion Test & Fisher ’s Exact.


Note: Fisher’s exact P-values should be used for any real world problem. The approximate P-valuesbased on the Normal Distribution are provided for instructional purposes, e.g., comparing to handcalculations.

The normal approximation uses a pooled estimate of proportion for the test.



396


As you can see we Fail to reject the null hypothesis with the data given. One conclusion is thesample size is not large enough. It would take a minimum sample of 1673 to distinguish thesample proportions for Boris and Igor.

2 Proportion vs Target Example: Solution


!"#$% ' ( ) ((* %+ ,- .,/.- %(

+/# ($%"0- %(* 1 2 - ) * 1 3 4+#

5+#"$ - )* 67 +#8

0.173571

99

n

X p

0.132356

47

n

X p

2

22

1

11

===

===!"#$%

&'"#

Results:

Poised for the

competition



397


2 Proportion vs Target Example: Solution


The Fisher ’s exact P-value (2-sided, Ha:P1!P2) is .096 so we fail to reject the Null Hypothesis.



398


Contingency Tables


!" #$%#& '#() +,- .'/ !"# %&#' () & *+%,(!-#)%& ,. /)+0!"#

+ )"# (1! - (2 ) & ! + 0,# 0 ")0 )"(*)-& 2 * (1 # ! /1 )(1#"3

4( *& /! , ,#' ! 5) -(*-6 #-/. 7! 8,# 8 #/! %& # 2 # ! "# (#&(*-6

2 1#(1#" (1# 0 ")0 )"(*)- *& /)-(*-6 #-( %0 )- 9 )" ' #0 #-' #-(

%0) - (1# :! /()" % &#' () &%86 ")%0 (1# ' ! (! 3

71*& (#&( 6 #-# "! , ,. 2 )"; & (1# 8 #&( 2 *(1 < )" + )"#

)8&#"= ! (*)-& *- #! /1 /# ,,3 > 8&#"= ! (*)-& /! - 8# 0) ),#' 8.

/)+8*-*-6 /#, ,&3

?) + # #@ ! + 0,#& :)" %&# *-/,%'#A ! B#(%"- 0 ")0 )"(*)- 8. 0") '% /( , *-#

! 5 ,! *+ 0 ")0)"(*)- 8. /%&()+ #"

! C #:#/( 0") 0) "(*)- 8. + ! -%:! /(%" *-6 , *-#

!"# %&' ' "( )* +"#,-, -, +". + +"# )* )& '. +-*% )/* )* /+-*%, *0

# . 1" 2 / * & ) . / # +" # , . 3 # 4

! 5 6 7 ) 8 9 ) : 9 ) ; 9 < 9 ) %

! 5 . 7 . + '#. ,+ *%# ) -, = - 0 0#/#%+

> +. +-,+-1-. %, " . ? # ," *@ % +". + +"# 0* ''*@ -%2 ,+. +-,+-1 0*/3 ,

. 1"-A,B&. /# = -,+/ -C& +-*% @ "#% 5 6 -, +/&#7

D "#/# E *C,#/? #=F -, +"# ,. 3 )'# 0 /#B&#%1( G E #H )#1+#=F-, +"# 1.'1&'.+#= 0/#B&#%1( C.,#= *% +"# %&' ' "()*+"#,-, G

. %= +"# ,& 3 3 . +-*% -, *? #/ . ' ' 1#'', -% +"# +. C'#4

( )!

"expected

expectedobserved 2

That? ..oh, that

s my

contingency table



399


Test Statistic Calculations

Wow!!! Can you believe this is the math in a Contingency Table. Thank goodness for SigmaXL®.Now let’s do an example.


Note the data gathered in the table. Curley isn’t looking too good right now (as if he ever did).

! " # $%& ' ( ) * ,* %-

! "#$# %

& ( )"# *+,#$-#. - / 01#

23$*4 ,/ 45 0# ./ )/ 6

7 ( )"# #8 5#9)#. -/ 01#

$ ( :14 +#$ *3 $*; ,

9 ( : 1 4 + # $ * 3 9* 0 1 4: ,

< $* ; ( )*)/0 3$#=1#:9> 3*$ )"/)

$* ;

<9* 0 ( )*)/0 3$#=1#:9> 3*$ )"/)

9*014:

< )*)/0 ( )*)/0 3$#=1#:9> 3*$ )"# )/+0#

: ( .#? $##, *3 3$##. *4 @2$AB629AB 6C

!!==

"=

c

1 j ij

2

ijijr

1i

2

oE

)E(O!

2

"#,

2

critical ! ! =

!"#$ &'( ) '*+,-./"( 0/12(

total

colrowij

F

)F*(FE =

Contingency Table Example

Can

t you clowns get

the entries correct?



400




The sample dataare the “observed” frequencies. Tocalculate the“expected” frequencies, firstadd the rows andcolumns. Thencalculate the overallproportion for eachrow.

The sample data are the observed

frequencies. To calculate

the expected

frequencies, first add the rows and columns:

Then calculate the overall proportion for each row:

Moe Larry Curley Total

Defective 5 8 20 33

OK 20 30 25 75

Total 25 38 45 108


Defective 5 8 20 33 0.306

OK 20 30 25 75 0.694

Total 25 38 45 108

33/108 = 0.306

75/108 = 0.694


Defective 5 8 20 33 0.306

OK 20 30 25 75 0.694

Total 25 38 45 108

0.306*45 = 13.80.694 * 38 = 26.4

Defective Proportion = 0.306

OK Proportion = 0.694

Now use these proportions to calculate the expected frequencies in each cell.



401


The final step is to create a summary table including the observed chi-squared.



! "# $ &' (&)(' $" $*" + ,'()" -./ "'&* &"( ( 01 $*" $'2("3

4 01' ((5 6 ' 77 $*"8" 1 )9 2"/8 $. : "$ $*" .2 8"/,"7 &* 0 ;8<)' /"3

( )2

expectedexpected-observed

7.02!

1.2500.4940.401

841.2123.1912.0!

2

obs

2

obs

=

++

+++=

Moe Larry Curley

Defective 0.912 1.123 2.841

OK 0.401 0.494 1.250

( )841.2

8.13

8.13202

=

"

! # $ % % & ' ( ) * +, - +& . /- 0

Moe Larry Curley

Observed 5 8 20

Expected 7.6 11.6 13.8

!20.912 1.123 2.841

Observed 20 30 25

Expected 17.4 26.4 31.3

!20.401 0.494 1.250

7.02! 2obs=

1-*-2+34-

5 6



402




! " # $ % &'# ( *+ , , # " - .

*&/'0 1%0 2 34 0"5 06 '%&748+# "0 09 '0064 1%0 '" &1&'# ( '%&7

48 +# "0: ; 0 "0 <0'1 1%0 /+(( %- $2 1%04 &4 1%# 1 1%0 60 =0'1

"# 10 &4 &/6 0$0 /6 0/1 2= ; %&'% $0"42 / 0/ 10"4 1%0 2 "6 0"4>

876543210

0.5

0.4

0.3

0.2

0.1

0.0

chi-square

f ! ""#$% &#'#"%

99.52crit= !

02.72

obs= !

( )*+,-./0# $023/3*4*%5 6#7,*%5 8.7"%*27 820 7 9 :



403


Contingency Table Example (cont.)


As you can see the data confirms: to reject the null hypothesis and the Practical Conclusion is: Thedefect rate for one of these stooges is different. In other words, defect rate is contingent upon thestooge.

For the Chi Square for Two-Way (contingency) tables ifyour data is in stackedcolumn format use the “ChiSquare Test.”

This data can be found inthe “Stooges” worksheet.



404


!" #$%&'# )* +#%,&-# . !" $%&'()'* +",-)./ (0* $%"1,*2

$%*+*.(*3 4+)./ (0* &$$%"$%)&(* 56$"(0*+)+ !*+(7

8 9"4 &%* (0* :4"(&()".+ 2&.&/*% &.3 6"4% (*&2 (0).;+ (0&( (0*

%*&+". 6"4 3".<( /*( & '".(%&'( 3*$*.3+ ". )(+ '"2$,*=)(67

8 9"4 3*(*%2).* & >&6 (" 2*&+4%* '"2$,*=)(6 &.3 ',&++)?6 ,"+(

'".(%&'(+ &+ ?",,">+@

A7 B %)(* (0* .4,, &.3 &,(*%.&()-* 06$"(0*+)+7

C7 D"*+ '"2$,*=)(6 0&-* &. *??*'(E

Low Med High

Price 8 10 12

Lead Time 10 11 9

Technology 5 9 16

Quotations Exercise


Contingency Table Example: Solution



405


Contingency Table Example: Solution (cont.)


Overview

After analyzing the data we can see the P-value is 0.426 which is larger than 0.05. Therefore, weaccept the null hypothesis.

Instructor notes:

1. Ho: plow = pmed = phighHa: at least one is different2. Obs Chi square = 3.856 Crit Chisquare = 9.488 df = (3-1)(3-1)

Fail to reject. There is no basis that theydon’t get contracts because of their

complexity.

Contingency Tables are another form of Hypothesis Testing.

They are used to test for association (or dependency) between two

classifications.

The null hypothesis is that the classifications are independent.

A Chi-square Test is used for frequency (count) type data.

If the data is converted to a rate (over time) then a continuous type

test would be possible. However, determining the period of time that

the rate is based on can be controversial. We do not want to justpick a convenient interval; there needs to be some rational behind

the decision. Many times we see rates based on a day because that

is the easiest way to collect data. However, a more appropriate way

would be to look at the rate distribution per hour.

Per hour Per day Per month



406



You have now completed Analyze Phase – Hypothesis Testing Non-Normal Data Part 2.

! Calculate and explain test for proportions

!

Calculate and explain contingency tests


Notes



407


Lean Six Sigma

Black Belt Training

Now we will conclude the Analyze Phase with“Wrap Up and Action Items.

Analyze Phase




408



Analyze Phase Wrap Up Overview

Six Sigma Behaviors

A Six Sigma Black Belt has a tendency to take on many roles, therefore these behaviors helpthroughout the journey.

! "#$%&'()* ',&)*-

! . /)0()1/12 3-&%)()*

! 4-()* 0-)&'(/12 &)5 '/1%&*-/12

! 6&7- 5&0&8$&2-5 5-'(2(/)2

! 4-()* %(*/%/12

! 9,()7()* /102(5- /: 0,- $/;

!" #$ & ' ( " ) *+ , -. /$ * 0 - 1 0 - 2 3 " ' + 4 #*5 5 3 6 5 / 7 *

8 9 : ;! <: =!;

>4 + /$ * 0 -1 0 -2 3 " #6 (/6 +* ?

!"#$!"#$ & & ' (" ) * + ' (" ) *+ , , -. /$* 0 -1 0 -23 " '+4 #*55 3 65/ 7*-. /$* 0 -1 0 -23 " '+4 #*55 3 65/ 7*

8 9 : ;! <: =!; 8 9 : ;! <: =!;

>4 + /$ * 0 -1 0 -2 3 " #6 (/6 +* ? >4 + /$ * 0 -1 0 -2 3 " #6 (/6 +* ?



409


Analyze Deliverables

Analyze Phase - The Roadblocks

Sample size is dependent on the type of data.

Each phase will have roadblocks. Many will be similar throughout your project.

! "#$%&' )&*+, -.& %/& 0 1-*23 & 4/-$& '&*#5&.-)*&$ %/-% &-6/ 6-1'#'-%&

,#** 7.&$&1% #1 - 4+,&. 4+#1% 7.&$&1%-%#+1 -% %/& )&8#11#18 +9 %/&: +1%.+* 4/-$& %.-#1#18;

! 0 % %/#$ 7+#1% 2+< $/+<*' -** <1'&.$%-1' ,/-% #$ 1&6&$$-.2 %+ 7.+5#'&

%/&$& '&*#5&.-)*&$ #1 2+<. 7.&$&1%-%#+1;

= >&-? @&?)&.$ A>&-? @&&%#18 0 %%&1'- 16&B

= 4.#?-.2 @&%.#6

= C&6+1'- .2 @&%.#6A$B

= D- %- D&?+8.-7/#6$

= E27+%/&$#$ >&$%#18 A-77*#6- )*& %++*$B

= @+'&*#18 A-77*#6- )*& %++*$B

= C%.-%&8 2 %+ .&'<6& FG$

= 4.+H&6% 4*-1

= I$$<&$ - 1' J- ..#&.$ !"#$ & '() $*'+,


It s your show

Look for the potential roadblocks and plan to addressthem before they become problems:

–

Lack of data

–

Data presented is the best guess by functional

managers

–

Team members do not have the time to collect data

–

Process participants do not participate in the analysis

planning

–

Lack of access to the process



410


DMAIC Roadmap

Now you should be able to prove/disprove the impact “X’s” have on a problem.

Analyze Phase

!"#$%&'( *+,-.#/ 0+#1

022#22 3%1-&.&%(4 51 61-&.&%(4 1$" 7#128+#/#$%3 (2%#/2

!"#$%&'( 1$" *+&,+&%&9# 0 .. :;2

*+,<#=>&26+,<# !/61?% :;2 @1 <# A $ *+,-.#/

!"#$%&'(4 *+&,+&%&9#4 3#.#?% 3,.8%&,$2 5 ,$%+,. ,+ B.&/&$1%# :;2 5 182&$C *+,-.#/2

!/6.#/#$%3 ,.8%&,$2 %, 5, $%+,. ,+ B.&/&$1%# :;2 51 82&$C *+,-.#/2

!/6.#/#$%5 ,$%+,. *.1$ %, B$28+# *+,-.#/ >,#2$; % D#%8+$

E#+&'( F&$1$?&1. !/61?%

>#%#+/&$# 066+,6+&1%# *+,G#?% F,?82

B2%&/1%# 5A *H

B2%1-.&2I J#1/

5 I 1 / 6

& , $ =

* + , ? # 2 2 A K $ # +

> # ' & $ #

7 # 1 2 8 + #

0 $ 1 . ( 9 #

! / 6 + , < #

5 , $ % + , .

!"#$%&'( *+,-.#/ 0+#1

022#22 3%1-&.&%(4 51 61-&.&%(4 1$" 7#128+#/#$%3 (2%#/2

!"#$%&'( 1$" *+&,+&%&9# 0 .. :;2

*+,<#=>&26+,<# !/61?% :;2 @1 <# A $ *+,-.#/

!"#$%&'(4 *+&,+&%&9#4 3#.#?% 3,.8%&,$2 5 ,$%+,. ,+ B.&/&$1%# :;2 5 182&$C *+,-.#/2

!/6.#/#$%3 ,.8%&,$2 %, 5, $%+,. ,+ B.&/&$1%# :;2 51 82&$C *+,-.#/2

!/6.#/#$%5 ,$%+,. *.1$ %, B$28+# *+,-.#/ >,#2$; % D#%8+$

E#+&'( F&$1$?&1. !/61?%

>#%#+/&$# 066+,6+&1%# *+,G#?% F,?82

B2%&/1%# 5A *H

B2%1-.&2I J#1/

5 I 1 / 6

& , $ =

* + , ? # 2 2 A K $ # +

> # ' & $ #

7 # 1 2 8 + #

0 $ 1 . ( 9 #

! / 6 + , < #

5 , $ % + , .

Over 80% of projects willrealize their solutions in the Analyze Phase – then wemust move to the ControlPhase to assure we cansustain our improvements.

!"#$% '() *+, -.(/#"0"(.

1#$#( 23$4#"4$% 56(73"(, 70 !"#$% '() *+, -89$4# 7/ 237:%(8

53$/,%$#( 23$4#"4$% 56(73"(, "/#7 14 "(/#"0"4 ; <97#6(,",

1(%(4# =/$%<,", 577%, #7 237>(?@",937>( ; <97#6(,",

A 7%%(4# @$#$

2(30738 1#$#",#"4$% 5(,#,

1#$#( 23$4#"4$% A 7/4%B,"7/

C9.$#( 'DE=

-.(/#"0< F77# A $B,(

F($.< 073 -8937>( $/. A 7/#37%

G

H

1#$#",#"4$%%<1"I/"0"4$/#J

23$4#"4$%%<

1"I/"0"4$/#J

F77#

A$B,(

H

H

G

G

!"#$% '() *+, -.(/#"0"(.

1#$#( 23$4#"4$% 56(73"(, 70 !"#$% '() *+, -89$4# 7/ 237:%(8

53$/,%$#( 23$4#"4$% 56(73"(, "/#7 14 "(/#"0"4 ; <97#6(,",

1(%(4# =/$%<,", 577%, #7 237>(?@",937>( ; <97#6(,",

A 7%%(4# @$#$

2(30738 1#$#",#"4$% 5(,#,

1#$#( 23$4#"4$% A 7/4%B,"7/

C9.$#( 'DE=

-.(/#"0< F77# A $B,(

F($.< 073 -8937>( $/. A 7/#37%

GG

HH

1#$#",#"4$%%<1"I/"0"4$/#J

23$4#"4$%%<

1"I/"0"4$/#J

F77#

A$B,(

HH

HH

GG

GG




411


Analyze Phase Checklist

This is a template that should be used with each project to assure you take the proper steps –remember, Six Sigma is very much about taking steps. Lots of them and in the correct order.

Planning for Action

! "#$% # '(# ) %* # ++* ,'(-." /0.-$0/ .%# %0 *1 +2(%2$0

3 2#)%-14 $-.5 *1 ,00%-)6 )00/ . *1 +2.%*,0$7 82.-)0.. #)/ '0*'(0

9$0/-+% $-.5 *1 .2.%#-)#8-(-%4

:#(-/#%0 ;-)#)+-#( <0)01-%.

=+"-0>-)6 8$0#5%"$*26" -) ? @-%" ,-)-,2, 011*$%.

A*/0(-)6 ! *)%-)2*2. *$ B *) ! *)%-)2*2. C 2%'2%

A-)-,-D0 $-.5 *1 '$*+0.. 1#-(2$0

=..0.. ."-1% -) '$*+0.. (*+#%-*)

E).2$0 +*,'(-#)+0 %* '$*8(0, .*(>-)6 .%$#%064

3 2#)%-%#%->0 .+$00)-)6 *1 >-%#( 1$*, +*)%$*((#8(0 %$->-#( F .

3 2#(-%#%->0 .+$00)-)6 1*$ *%"0$ 1#+%*$.

3 2#(-%#%->0 .+$00)-)6 *1 >-%#( 1$*, +*)%$*((#8(0 %$->-#( F.

! " ## ! $ & " '# ! $# ! ( &# ! "# ! ) '

! "#$% # '(# ) %* # ++* ,'(-." /0.-$0/ .%# %0 *1 +2(%2$0

3 2#)%-14 $-.5 *1 ,00%-)6 )00/ . *1 +2.%*,0$7 82.-)0.. #)/ '0*'(0

9$0/-+% $-.5 *1 .2.%#-)#8-(-%4

:#(-/#%0 ;-)#)+-#( <0)01-%.

=+"-0>-)6 8$0#5%"$*26" -) ? @-%" ,-)-,2, 011*$%.

A*/0(-)6 ! *)%-)2*2. *$ B *) ! *)%-)2*2. C 2%'2%

A-)-,-D0 $-.5 *1 '$*+0.. 1#-(2$0

=..0.. ."-1% -) '$*+0.. (*+#%-*)

E).2$0 +*,'(-#)+0 %* '$*8(0, .*(>-)6 .%$#%064

3 2#)%-%#%->0 .+$00)-)6 *1 >-%#( 1$*, +*)%$*((#8(0 %$->-#( F .

3 2#(-%#%->0 .+$00)-)6 1*$ *%"0$ 1#+%*$.

3 2#(-%#%->0 .+$00)-)6 *1 >-%#( 1$*, +*)%$*((#8(0 %$->-#( F.

! " ## ! $ & " '# ! $# ! ( &# ! "# ! ) '


Analyze Questions

Define Performance Objectives Graphical Analysis • Is existing data laid out graphically?• Are there newly identified secondary metrics?

• Is the response discrete or continuous?

• Is it a Mean or a variance problem or both?

Document Potential X

s Root Cause Exploration• Are there a reduced number of potential Xs?

• Who participated in these activities?

• Are the number of likely Xs reduced to a practical number for analysis?

•

What is the statement of Statistical Problem?

•

Does the process owner buy into these Root Causes?

Analyze Sources of Variability Statistical Tests

•

Are there completed Hypothesis Tests?

•

Is there an updated FMEA?

General Questions

•

Are there any issues or barriers that prevent you from completing this phase?

•

Do you have adequate resources to complete the project?



412


At this point, you should:

You have now completed the Analyze Phase. Congratulations!

! Have started to develop a project plan to meet the deliverables

!

Have identified ways to deal with potential roadblocks

!

Be ready to apply the Six Sigma method through your project


Notes

You

re on your way



413


Lean Six Sigma

Black Belt Training

Now that we have completed the Analyze Phase we are going to jump into the Improve Phase.Welcome to Improve will give you a brief look at the topics we are going to cover.

Improve PhaseWelcome to Improve



414


Welcome to Improve

Overview

DMAIC Roadmap

We are currently in the Improve Phase and by now you may be quite sick of Six Sigma, really! In thismodule we are going to look at additional approaches to process modeling. Its actually quite fun in a

weird sort of way!

Well, now that the Analyze Phase is over,on to a more difficultphase. The good news

is….you’ll hardly everuse this stuff, so payclose attention!


!"## !% &'()*% # +, -. )*/. 0'1

+, -.)*/. 0'% # 2.'3(4 1

5.1 *6 0*0 6 +, -. )*/ .0 '1

74 8% 0 &.4 9)(&.11 2(4 .# *0 6 :

2;<

9)( &.11 2(4 .#*06 : <. 6 ).11 *(0

= .#&(/ . '( >/-)( 8.

!)%&'*(0%# !%&'()*%# +, -.)*/.0'1

= )% - ?- @ 7 &'*(0 >'./ 1

!"## !% &'()*% # +, -. )*/. 0'1

+, -.)*/. 0'% # 2.'3(4 1

5.1 *6 0*0 6 +, -. )*/ .0 '1

74 8% 0 &.4 9)(&.11 2(4 .# *0 6 :

2;<

9)( &.11 2(4 .#*06 : <. 6 ).11 *(0

= .#&(/ . '( >/-)( 8.

!)%&'*(0%# !%&'()*%# +, -.)*/.0'1

= )% - ?- @ 7 &'*(0 >'./ 1

!"#$%&'( *+,-.#/ 0+#1

022#22 3%1-&.&%(4 51 61-&.&%(4 1$" 7#128+#/#$% 3(2%#/2

!"#$%&'( 1$" *+&,+&%&9# 0.. :;2

*+,<#= >&26+,<# !/61?% :;2 @1 <# A $ *+,-.#/

!"#$%&'(4 *+&,+&%&9#4 3#.#? % 3,.8%&,$2 5,$%+,. ,+ B.&/&$1%# :;2 5 182&$C *+,-.#/2

!/6.#/#$% 3,.8%&,$2 %, 5,$%+,. ,+ B.&/&$1%# :2 5 182&$C *+,-.#/2

!/6.#/#$% 5 ,$%+,. *.1$ %, B$28+# *+,-.#/ >,#2$;% D#%8+$

E#+&'( F&$1$?&1. !/61?%

>#%#+/&$# 066+,6+&1%# *+,G#?% F,?82

B2%&/1%# 5A *H

B2%1-.&2I J#1/

5 I 1 / 6 & , $ =

* + , ? # 2 2 A K $ # +

> # ' & $ #

7 # 1 2 8 + #

0 $ 1 . ( 9 #

! / 6 + , < #

5 , $ % + , .

!"#$%&'( *+,-.#/ 0+#1

022#22 3%1-&.&%(4 51 61-&.&%(4 1$" 7#128+#/#$% 3(2%#/2

!"#$%&'( 1$" *+&,+&%&9# 0.. :;2

*+,<#= >&26+,<# !/61?% :;2 @1 <# A $ *+,-.#/

!"#$%&'(4 *+&,+&%&9#4 3#.#? % 3,.8%&,$2 5,$%+,. ,+ B.&/&$1%# :;2 5 182&$C *+,-.#/2

!/6.#/#$% 3,.8%&,$2 %, 5,$%+,. ,+ B.&/&$1%# :2 5 182&$C *+,-.#/2

!/6.#/#$% 5 ,$%+,. *.1$ %, B$28+# *+,-.#/ >,#2$;% D#%8+$

E#+&'( F&$1$?&1. !/61?%

>#%#+/&$# 066+,6+&1%# *+,G#?% F,?82

B2%&/1%# 5A *H

B2%1-.&2I J#1/

!"#$%&'( *+,-.#/ 0+#1

022#22 3%1-&.&%(4 51 61-&.&%(4 1$" 7#128+#/#$% 3(2%#/2

!"#$%&'( 1$" *+&,+&%&9# 0.. :;2

*+,<#= >&26+,<# !/61?% :;2 @1 <# A $ *+,-.#/

!"#$%&'(4 *+&,+&%&9#4 3#.#? % 3,.8%&,$2 5,$%+,. ,+ B.&/&$1%# :;2 5 182&$C *+,-.#/2

!/6.#/#$% 3,.8%&,$2 %, 5,$%+,. ,+ B.&/&$1%# :2 5 182&$C *+,-.#/2

!/6.#/#$% 5 ,$%+,. *.1$ %, B$28+# *+,-.#/ >,#2$;% D#%8+$

E#+&'( F&$1$?&1. !/61?%

>#%#+/&$# 066+,6+&1%# *+,G#?% F,?82

B2%&/1%# 5A *H

B2%1-.&2I J#1/

5 I 1 / 6 & , $ =

* + , ? # 2 2 A K $ # +

> # ' & $ #

7 # 1 2 8 + #

0 $ 1 . ( 9 #

! / 6 + , < #

5 , $ % + , .



415


Improve Phase

Welcome to Improve

!"# $%&'& ) *+,$-.-

/0-".'1% 2-3 4'.#$ 56&

78,-9'+-". .* : ,.'+'; - 4# $<- *1 56 &

='+<$#.- .>- ? -3 @9*A-&&

4#$'0#.- ? -3 @9*A-&&

/+,$-+-". ?-3 @9*A-&&

B-#0% 1*9 ) *".9*$

After completing the Improve Phase you will be able to put to use the steps as depicted here.



416


Lean Six Sigma

Black Belt Training

Now we will continue in the Improve Phase with “Process Modeling: Regression”.

Improve PhaseProcess Modeling Regression



417


Process Modeling Regression

Overview

In this module of Process Modeling we will study Correlation, Introduction to Regression and SimpleLinear Regression. These are some powerful tools in our data analysis tool box.

We will examine the meaning of each of these and show you how to apply them.

!"# # !% &'()*% # +, -.)*/ .0'1!"# # !% &'()*% # +, -.)*/ .0'1

+, -.)*/ .0'% # 2.'3(4 1+, -.)*/ .0'% # 2.'3(4 1

5.1 *6 0*0 6 +, -. )*/ .0'15.1 *6 0*06 +, - .)*/ .0 '1

74 8% 0&.4 9)( &.11 2(4 .# *06 :

2 ;<

74 8% 0&.4 9)( &.11 2(4 .# *06 :

2;<

9)(&.1 1 2(4 .# *06 : <. 6 ).11 *(09)(&.1 1 2(4 .# *06 : <. 6 ).11 *(0

= .#&(/ . '( >/-)(8 .= .#&(/ . '( >/-)(8 .

!)%&'*(0%# !%&'()*%#

+, -.)*/ .0'1

!)%&'*(0%# !%&'()*%#

+, -. )*/.0 '1

= )% - ?- @ 7 &'*(0 > './ 1= )% - ?- @ 7&'*(0 > './ 1

! "##$%&'(")! "##$%&'(")

*)'#"+,-'(") '" /$0#$11(")*)'#"+,-'(") '" /$0#$11(")

2(34%$ 5()$&# /$0#$11(")2(34%$ 5()$&# /$0#$11(")

!"# # !% &'()*% # +, -.)*/ .0'1!"# # !% &'()*% # +, -.)*/ .0'1

+, -.)*/ .0'% # 2.'3(4 1+, -.)*/ .0'% # 2.'3(4 1

5.1 *6 0*0 6 +, -. )*/ .0'15.1 *6 0*06 +, - .)*/ .0 '1

74 8% 0&.4 9)( &.11 2(4 .# *06 :

2 ;<

74 8% 0&.4 9)( &.11 2(4 .# *06 :

2;<

9)(&.1 1 2(4 .# *06 : <. 6 ).11 *(09)(&.1 1 2(4 .# *06 : <. 6 ).11 *(0

= .#&(/ . '( >/-)(8 .= .#&(/ . '( >/-)(8 .

!)%&'*(0%# !%&'()*%#

+, -.)*/ .0'1

!)%&'*(0%# !%&'()*%#

+, -. )*/.0 '1

= )% - ?- @ 7 &'*(0 > './ 1= )% - ?- @ 7&'*(0 > './ 1

! "##$%&'(")! "##$%&'(")

*)'#"+,-'(") '" /$0#$11(")*)'#"+,-'(") '" /$0#$11(")

2(34%$ 5()$&# /$0#$11(")2(34%$ 5()$&# /$0#$11(")

Correlation



418


Ho: No Correlation

Ha: There is Correlation

The Correlation Coefficient (always) assumes a value between –1 and +1.

The Correlation Coefficient of the population, R, is estimated by the sample

Correlation Coefficient, r:

Ho ho ho…

Ha ha ha…

Correlation Coefficient

The graphics shown here are labeled as the type and magnitude of their correlation: Strong,

Moderate or Weak correlation.

Types and Magnitude of Correlation

The null hypothesis for correlation is: there is no correlation, the alternative is there is correlation.The correlation coefficient (always) assumes a value between –1 and +1.

The correlation coefficient of the population, large R, is estimated by the sample correlationcoefficient, small r and is calculated as shown.




419


Limitations of Correlation

Correlation Example

To properlyunderstandregression youmust first

understandcorrelation.Once arelationship isdescribed, thena regression canbe performed.

A strong positiveor negativecorrelation

between X andY does notindicatecausality.Correlationprovides an

We will use some data from a National Football League player, Walter Payton formerly of the

Chicago Bears. Open the worksheet “RB Stats Correlation” as shown here.


! " $%&'() *'$+%+,- '& (-). %+,- /'&&-0.%+'( 1-%2--( 3 .(4 5 4'-$ ('% +(4+/. %-

/.6$.0+%78

! 9 '&&-0.%+'( *&',+4-$ .( +(4+/.%+'( ': %;- $%&-()%; 16% 4'-$ ('% *&',+4- 6$

2+%; . ( -<. /% (6=-&+/. 0 &-0.%+'($;+* >+8-8 5? :><@@8! A;- =.) (+%64- ': %;- /'&&-0.%+'( /'-::+/+-(% +$ $'=-2;. % &-0.%+,- .(4 $;'604

1- 6$-4 2+%; /.6%+'(8

! B6$% 0+C- .(7 '%;-& $%.%+$%+/D 7'6 (--4 %' .$$-$$ 2;-%;-& %;- /'&&-0.%+'(

/'-::+/+-(% +$ $%.%+$%+/. 007 $+) (+:+/. (%D .$ 2-00 . $ *&. /%+/. 007 $+)(+:+/. (%8

! "$ 6$6.0D $%.%+$%+/. 0 $+) (+:+/.(/- +$ E64) -4 17 /'=*.&+() . * F,.06- 2+%; %;-

/;'$-( 4-)&-- ': .0*;. &+$C8

! G 6+4-0+(-$ :'& *&./%+/.0 $+)(+:+/.(/- .&- .$ :'00'2$H

I J: K & K L M 8N MD &-0.%+'($;+* +$ *&. /%+/. 007 $+) (+:+/.(%

I J: K & K O M 8P MD &-0.%+'($;+* +$ ('% *&./%+/. 007 $+) (+:+/.(%

!" # $ % " # $$

&'() +, -(. ) /01(

2 0-() ' 3+''(2) /0+-

&'() +, -(. ) /01(

2 0-() ' 3+''(2)/0+-

&'() +, 4+5 0/ 01(

2 0-()' 3+''(2)/0+-6 + 20-() ' 3+''(2) /0+-

!$ #7 !$ #8 $ #8 $ #7

indication of the strength but does not provide us with an exact numerical relationship. Regressionhowever provides us with that data more specifically a y equals f of x equation. Just like any otherstatistic, be sure to assess the correlation coefficient is both statistically significant and practicallysignificant.



420


Correlation Analysis

Correlation Example

To generate a graph with the correlation data and a Trendline follow the sequence shown with ourdata set.

SigmaXL® V6 does notinclude LowessSmoothing. If a trendline is selected, it caneasily be modified usingExcel’s Chart tools.

In this example itappears that there isstrong correlation in thedata.


Get outta my way



421


Correlation Example (cont.)

Regression Analysis

Now we will generatethe CorrelationCoefficient using

SigmaXL®

. Follow theSigmaXL® commandpath shown here andselect the variables“payton carries” and“payton yards” asshown above. TheCorrelation Coefficientis high whichcorresponds to thegraph on the previousslide that showspositive correlation.

The P-value is low at .000 so we reject the

Correlation ONLY tells us the strength of a relationship while Regression gives the mathematical

relationship or the prediction model. The last step to proper analysis of Continuous Data is todetermine the Regression Equation. The Regression Equation can mathematically predict Y for anygiven X. The Regression Equation from SigmaXL is the BEST FIT for the plotted data.


null hypothesis by saying that there is significant correlation between Payton’s carries and thenumber of yards.

Prediction Equations:

Y = a + bx (Linear or 1st order model)

Y = a + bx + cx2 (Quadratic or 2nd order model)

Y = a + bx + cx2 + dx3 (Cubic or 3rd order model)

Y = a (bx) (Exponential)

Looking for the best fit



422


Simple vs. Multiple Regression

In SimpleRegression there is

only one Xcommonly referredto as a predictor orregressor. MultipleRegression allowsmany Y’s. Recallwe are onlypresenting SimpleRegression in thisphase and willpresent Multiple

Regression in detailin the next phase.

Regression Analysis Graphical Output

There are two ways to perform a Simple Regression. One is the Scatter Plot as shown. TheRegression Equation can be found in the top right corner. A Simple Regression can also beperformed in SigmaXL® using the Multiple Regression tool, which will be covered in the next slide.

Follow the SigmaXL® command prompt shown here, select “payton yards” for Response (Y) and“payton carries” for the Predictor (X1).




423


Regression Analysis Statistical Output

Regression (Prediction) Equation

The difference between R squared and adjusted R squared is not terribly important in SimpleRegression. In Multiple Regression where there are many X’s it becomes more important.We’ll look at that in the next module.

The Regression Analysisgenerates aprediction modelbased on the bestfit line through thedata representedby the equationshown here.

To predict thenumber of yardsthat Payton wouldrun if he had 250carries you simplyfill in that value inthe equation andsolve.


!" $%&'()* +", -./0 0.%'1 2.0*"/ ,"34' %3/ (5 +& +.' 678 ).%%(&1 31& *+&

$%&'()*("/ &93.*("/ .:";&<

! " # $ " % % &' ( * ( + ,- % & % . / + - 0 ' ( - + $ 1 % 2 " $ % 3 % / + - 0 ' ( 4 + $ $ &" %

!+& %&=%&11("/ &93.*("/ (1

2.0*"/ 0.%'1 > ?@AB<CDE F C<D@A66 2.0*"/ ).%%(&1

5 ' ( % 0 + ( 0

5'"66 &4 &"(0

7"2", '6 8

( ) 6.065,12504.91622163.497-yardsPayton =+=

Now we will performthe Simple LinearRegression usingSigmaXL®'s MultipleRegression Tool toget a more detailedstatistical analysis.SelectSigmaXL>StatisticalTools>Regression>MultipleRegression. Select“payton yards” forNumeric Response(Y) and “payton

carries” forContinuousPredictors (X).



424


Regression Graphical Output

Regression (Prediction) Equation (cont.)

Using Excel’s native functions we are able to modify the fitted line plot to both Quadratic and Cubicmodels.


You couldmake a roughestimate byusing aScatter Plot.To get anexact estimateuseSigmaXL®’sPredictedResponseCalculatorlocated in the“MultipleRegression”

worksheet.



425


Regression Graphical Output (cont.)

Use the best fitting equation by looking at the R-Sq value. If it improves significantly, or if theassumptions of the residuals are better met as a result of utilizing the quadratic or cubic equationyou should use it.

Here there is no big difference so we will stick with the linear model.

Residuals


Regression Analysis relies on assumptions about the residuals; differences between predictedand actual Y values. Then we analyze the residuals to look for evidence of an outlier, whichcould mean a typo or some assignable cause, or nonlinearity.

As in ANOVA, the residuals should:

– Be Normally Distributed (normal plot of residuals)

– Be independent of each other

• no patterns (random)

•

datamust

be time ordered (residuals vs. order graph) – Have a constant variance (visual, see residuals versus fits chart,

should be (approximately) the same number of residuals above

and below the line, equally spread.)



426


Residuals (cont.)

These graphs are found on the “Mult Reg Residuals” sheet.




427


Residual Analysis

Standardizedresidualsgreater than 2

and less than-2 are usuallyconsideredlarge. We willdiscuss themeaning ofthis a bit later.

The ResidualsTable can befound on the“Mult Reg

Residuals” worksheet.

Normal Probability Plot of Residuals

This NormalProbability Plot ofStandardizedResiduals can befound in the “MultReg Residuals” worksheet next to theMultiple Regressionresults. This chart isdisplayed starting incell R1.


As you can see the Normal probability plot of residuals evaluates the Normally Distributed responseassumption. The residuals should lay near the straight line to within a fat pencil. Looking at aNormal probability plot to determine normality takes a little practice. Technically speaking however,it is inappropriate to generate an Anderson-Darling or any other Normality test that generates a p-value to determine normality. The reason is that residuals are not independent and do not meet abasic assumption for using the Normality tests. Dr. Douglas Montgomery of Arizona State University

coined the phrase “fat pencil test” much to the chagrin of many of his colleagues.



428


Residuals vs Fitted Values

Residuals versusFitted Valuesevaluates theEqual Variance

assumption. Hereyou want to have arandom scatteringof points.

You DO NOT wantto see a “funneleffect” where theresiduals getsbigger and biggeras the Fitted Value

gets bigger orsmaller. Note: Thehorizontal line at 0was manuallyadded as areference.

Residuals vs Order of Data


Residuals versus the order of data is used to evaluate the independence assumption. It should notshow trends either up or down and should have approximately the same number of points aboveand below the zero line. The horizontal line at 0 was manually added as a reference.



429


Modeling Y=f(x) Exercise


Modeling Y=f(x) Exercise: Question 1 Solution



431


Modeling Y=f(x) Exercise: Question 2 Solution (cont.)




432




If Dorsett carries the football 325 times the predicted value would be determined that Dorsettwould carry the football for 1462.63 yards – approximately!


All three assumptions have been satisfied.



433



You have now completed Improve Phase – Process Modeling Regression.

! Perform the steps in a Correlation and a Regression Analysis

!

Explain when Correlation and Regression is appropriate


Notes



434


Lean Six Sigma

Black Belt Training

Now we will continue with the Improve Phase “ Advanced Process Modeling MLR”.

Improve PhaseAdvanced Process Modeling



435


Advanced Process Modeling

Overview

Correlation and Linear Regression Review

Recall the Simple Linear Regression and Correlation covered in a previous module. The essentialtools presented here describe the relationship between two variables. A independent or input factorand typically an output response. Causation is NOT always proved; however, the tools do present a

guaranteed relationship.

The core fundamentals of this phase are as shown.


!"#$"% ' ())*+ !",)"--$(.!"#$"% ' ())*+ !",)"--$(.

/ (.01$."2) !",)"--$(./ (.01$."2) !",)"--$(.

3)2.-4()5$., 6)(7"-- 82923)2.-4()5$., 6)(7"-- 8292

:;<9$=<" !",)"--$(.:;<9$=<" !",)"--$(.

!"## !%&'()*%# +, -.)*/.0'1!"## !%&'()*%# +, -.)*/.0'1

+, -.)*/ .0'%# 2 .'3(4 1+, -.)*/ .0'%# 2 .'3(4 1

5.1 *6 0*06 +, -. )*/ .0'15.1 *6 0*06 +, -. )*/ .0'1

74 8% 0&.4 9)(&.11 2 (4.# *06 :

2;<

74 8% 0&.4 9)( &.11 2(4.# *06 :

2;<

9)(&.11 2(4 .# *06 : < .6 ).11*(09)(&.11 2(4 .# *06 : <.6 ).11*(0

= .#&(/ . '( >/ -)(8 .= .#&(/ . '( >/- )(8 .

!)%&'*(0%# !%&'()*%#+, -. )*/ .0'1

!)%&'*(0%# !%&'()*%#+, -. )*/ .0'1

= )% - ? - @ 7 &'*(0 >'./ 1= )% - ? - @ 7 &'*(0 >'./ 1



436


Correlation Review

The PearsonCorrelationCoefficient,represented here

as “r ”, shows thestrength of arelationship incorrelation. Thecoefficient can varyONLY between -1and +1 while a zerovalue describes NOrelationship,meaning nocorrelation.

The P-value provesthe statisticalconfidences of ourconclusionrepresenting the

Linear Regression Review

Possibility that a relationship exists. Simultaneously; the Pearson Correlation Coefficient showsthe “strength” of the relationship. For example, P-value standardized at .05, then 95%confidence in a relationship is exceeded by the two factors tested.


Presented hereStirrate is directlyrelated to impurity ofthe process; therelationship betweenthe two, is one unitStir Rate causes .4566 Impurityincrease. Stir Ratelocked at 30 andImpurity calculated

by 30 times .4566,subtracting .289gives us a 13.4Impurity. Granted;that we have an errorin our model, the redpoints do not lie onthe blue line.

The dependent response variable is Impurity and the Stirrate is the independent predictor, asboth variables in this example are perpetual.



437


Correlation Review

Numericalrelationship is leftout when speakingof Correlation.

Correlation showspotency of linearrelationship,mathematicalrelationship isshown by andthrough thePrediction Equationof Regression. Asshown, theseCorrelations or

Regressions are notproven casualrelationships. Weare attempting to

Simple vs. Multiple Regression Review

PROVE statistical commonality. Exponential, quadratic, simple linear relationships or evenpredictable outputs (Y) concern REGRESSION equations. More complex relationships areapproaching.


Simply Regressionshave one X and arereferenced as theregressors orpredictors; multipleX’s give reason tooutput or responsevariable, this isMultiple Regressionaccounts.

Strength of theregression knownquantity by Rsquared and dictatesoverall variation inoutput (Y),independent variablesubjected to theregression equation.



438


Regression Step Review

How to run a Regressionis directed here. Using aScatter Plot, andunderstanding the

variation between the X’s

and Y’s, then activate aCorrelation analysisallowing a potential linearrelationship indication.Third step is to findexisting linearmathematicalrelationships which callsfor a Prediction Equationthen fourth to find the

potency or strength of thelinear relationship if oneexists. Linear Regressionaccompanied by the

Simple Regression Example

variation of the input gives a variety of output results and a completion of the fifth step denoted,the amount percentage a given output has. It also includes the answer to strength of statisticalconfidence within our Linear Regression.

To conclude a Linear Regression exists; majority has that a 95% statistical confidence or abovehas to be obtained. If unsatisfied conclusions are drawn, as a point of contingency, step 6 isessential. At present, in step 6, we contemplate the potential Non-linear Regression. However,this is only necessary if we can not find a Regression Equation (statistical and practical) variation

of output by way of scoping the input or by analyzing the model error for correctness. Step 7,depicted subsequently, validates residuals are a necessity for a valid model.


Recalling toolslearned in the Analyze Phase,presented here is aSimple Regressionexample examining a

piece of equipmentpertaining to a miningcompany. Thisdiagram plots outputto input, following theRegression steps.Notice how theequipment is agitatedby output of PGMconcentrate.

Opening the worksheet “Concentrator ” will show how output is always applied to the Y axis

(dependent) as input is always applied to the X axis (independent).

The basic steps to follow in Regression are as follows:

1. Create Scatter Plot with Trendline (Graphical Tools>Scatterplot )

2. Determine Correlation (Statistical Tools>Correlation Matrix – P-value less

than 0.05)

3. Run Regression ( Statistical Tools>Regression>Multiple Regression)(Unusual Observations?)

4. Evaluate R2, adjusted R2 and P-values

5. Consider quadratic or cubic Trendline. Add Non-linear terms toregression model if necessary

1. Add quadratic terms

2. Add cubic terms

6. Analyze residuals to validate assumptions

1. Normally distributed

2. Equal variance

3. Independence

4. Confirm one or two points do not overly influence model.

One step

at a time…



439


Example Correlation

Identifying theexisting LinearRegression is thesecond step.

Having thePearsonCorrelationCoefficient at .847and a P-value lessthan .05, we seewith a very strongstatisticalconfidence in aLinear Regression.If no Correlationexisted thecoefficient wouldbe closer to zero,remember?

Example Regression Line


Now finding the Prediction Equation of the linear relationship, two factors; output response andinput variable. Grams per ton of the PGM concentrate is the output and the RPM of the agitator isthe input. Knowing that a positive slope exists, by a greater than zero Correlation Coefficientindicates the agitators RPM increases in correlation with the PGM concentrate. The slope of

Linear Regression equals 1.333. Did you recall that the Pearson correlation coefficient exceededzero?



440


Example Linear Regression

Select SigmaXL>Statistical Tools>Regression>Multiple Regression. Select “PGM concentrate (g/ton)” as Numeric Response (Y) and “ Agitator RPM” as Continuous Predictor (X). Ensure that“Display Residuals” is checked and “Standardized Residuals” are selected.


Shown here is the Multiple Regression output (Single X, Simple Linear Regression) explaining 70%of the process variation. Highlighted above we see a potentially large residual. This was addedmanually for illustration purposes. SigmaXL® highlights standardized residual values greater than 3or less than -3 to minimize false alarms. R squared, and R squared adjusted pertain to our fullRegression analysis. With these concerns the addition of Non-linear Regression terms might be inconsideration.



441



Notice how the new line is a more appropriate demonstration of our data since the curvature betterfits the plotted points. This is the essence of choosing quadratic Regression. This model optioncan be used in Excel as follows:

1.

Select the Trendline2.

Right Click and select “Format Trendline” 3.

In the Trendline Options tab, select Polynomial Trend/Regression Type. Order 2 for quadratic,Order 3 for cubic.

Example Regression Line



442



Linear and Non-Linear Regression Example

We have hereboth Regression

models. In termsof R squaredbeing higher inpercentage rateon the Non-linearmodel asapposed to thatof the Linear wesee more processvariation. Inaddition, S

presentsestimatedStandardDeviation oferrors, Non-linearmodel has alower decimal.

Let us now consider the model error. You need not be perplexed, model error has many variables.Output dependency on the impact of other input variables and measurement system errors ofoutput and inputs can be causes.

Ensure “Display Residual Plots” is checked and standardized residuals are selected.

Residual Analysis Example

In order to create aquadratic modelusing SigmaXL®’sMultiple Regression

tool, you will need tosquare the databeing used as yourContinuousPredictor. Thenselect SigmaXL >Statistical Tools>Regression>Multiple Regression.Select both youroriginal and squared

columns ascontinuouspredictors.

Non- Linear Model:

Linear Model More variation is explained using

the Non-linear model since the R-Squared is higher and the S

statistic is lower which is the

estimated Standard Deviation of

the error in the model.



443



By clicking the Residualsworksheet, we now see allanalyses presented andmust keep in mind our

assumptions to consider thepossibilities of a validRegression. Residuals donot have a pattern acrossthe data collected, however,they do have a similarvariation across the board ofFitted Values. Moreover, in avalid Regression of allresiduals will be distributed.

Similarities between the

residuals across the FittedValues in the upper rightgraph show no monumentaldifferences as to variation.


When identifying Non-linear Relationships, looking at the graphical variation of output to input onany given Scatter Plot the Non-linear relationship is self evident. Using step four of the Regression Analysis methodology, unusual observation will ask us to focus deeper at Fitted Line Plots to seewhat is the solution for the historical data. To detect Non-linearity carefully look at the Residualsvs. Fitted Values graph of a Linear Regression. Finding clustering and/or trends of data one couldconclude a Non-linear Regression. Relying on a team or expert who has prior knowledge can availmuch information, also.

Random placement of the residuals are proven by the bottom right graph; no pattern is in essence.Looking for Normality the bottom left graph (the Histogram) indicates we have a bell curve, as doesthe upper right graph proving residuals placed near the straight line. Now, have we met thenecessary requirements of the criteria? With these randomly dispersed residual data points findingthe impact of just a single one is the confirmation.

Non-Linear Relationships Summary

!"#$%& ' #% ) *+& , %+ - .*+"/ 0 1" ./#*%+'$*2'3

! 45/##"0 6.%# *+&*5/#*+7 5809/#80":

! ;+8'8/ . %<'"09/ #*%+' *+ = *+"/ 0 1"7 0"'' *%+ >% &". :

! ?0"+& ' %) #$" 1 "'*&8/ . 9"0'8' #$" @*##"& A / .8"' 6 .%# *+

'*>2 ." = *+"/ 0 1 "7 0"''*%+:

! 48 <B"5# >/ ##"0 "C 2 "0# D +% E ."&7 " %0 #"/ > "C 2 "0*"+5":



444


Types of Non-Linear Relationships

The simpleLinear model,the quadraticmodel, the

logarithm modeland the inversemodel define themoreconventionalrelationshipsbetween outputsand inputs.


Open the worksheet “Mailing Response vs. Discount ”. This shows transactions by a retail storechain giving the relationship between discount percentages and the customer response. With theinput variable displayed in C1 and output displayed in C2, Belts need to establish which discountrate will yield a 10% response from customers.

Mailing Response Example

!"# %"&'" ()*+,-. /) ,0123h, which formula to use?

Clip ‘em



445


Mailing Response Scatter Plot

The output vs. theinput isgraphically plottedwith the output

plotted on the Y-axis. Notice wehave somecurvature in thecustomerresponse.


Now we are testingfor a Linearrelationship by

running aCorrelation. Theresults of theanalysis are astrong confidencelevel since the P-value is less than .05.

Do you notice thePearson

CorrelationCoefficient isalmost 1.0? Thatindicates a strongcorrelation.

Mailing Response Correlation

From SigmaXL®’s User Guide:

Pearson Correlation Coefficient (r) R-Squared (%) Degree of association0.9 <= |r| <=1 > 80 % Strong0.7 <= |r| < 0.9 50 % to 80 % Moderate|r| < 0.7 < 50 % Weak

Pearson Probability, p > 0.05 None



446


Mailing Response Fitted Line Plot

This model showsa very high R-squared at94.51%. Havingnoticed earlier theapparentcurvature of thedata, the nextstep is to considera Non-linearRegression Analysis. TheScatter Plot hasbeen recreatedwith Trendline

checked.

Mailing Response Non-Linear Fitted Line Plot


We are satisfied! The application of a Non-linear Regression Model shows an increased R-

squared.



447



In order to create a quadratic model using SigmaXL®’s Multiple Regression tool, you will need tosquare the data being used as your Continuous Predictor. Then select SigmaXL > StatisticalTools> Regression> Multiple Regression. Select both your original and squared columns ascontinuous predictors.


Confidence and Prediction Intervals

Keeping in mindthe originalquestion, the storewants 10% of thecoupons redeemedby their customersso what discountrate will generatethis response?

We will use thePredictedResponseCalculator toanswer thisquestion. Thiscalculator islocated to the rightof the regressionreport.

Here we must use the Multiple Regression Tool rather than the Scatter Plot because SigmaXL®’s

Scatter Plots provide prediction and confidence intervals only for a Linear (1 st Order) Trendline.

Select SigmaXL > Statistical Tools> Regression> Multiple Regression.

I found some

Residuals



448



Considering the question of yielding 10% or more, finding the Regression Equation is of menialimportance compared to estimating where the data ought to predict the relationship. ThePrediction Interval will provide a degree of confidence in how the customers will respond. Thisestimate is of great importance.

Our analysis tells us that to get at least a 10% response from customers, we must offer a 19%discount with our coupons.

This can be obtained through trial and error entry of “% discount” and calculated “Discount –

Sq” (Enter

“=K12^2

” in cell K13).

Having less data available to predict the Regression Equation usually causes the Confidence Intervalto flare out at the extreme ends. If a prediction equation exists, it would be found within the red linesindicating the Confidence Interval at the 95% confidence level.

Confidence and Prediction Intervals (cont.)



449



Now does the present data for the response fit the equation as predicted?

Residual Analysis

Confirming the validity, taking into consideration our residuals and completing step six is next.Having a variation of outputs is due to a high level in R-squared, but from that information we cannot draw the conclusion it’s a sufficient model. We can have confidence in our model because allthree assumptions are satisfied; outputs are Normally and Randomly Distributed across the

observation order and have similar variance across the Fitted Values. The store should give adiscount of 19% expecting at least a 10% response from customers.



451


Effect of Transformation

Using a mathematical function we have transformed this data. This example shows how taking asquare root of this data yields a Normal distribution. The challenge then is to find the appropriatetransform function.

Transforming Data Using SigmaXL®


Select worksheet: Transform

In finding an appropriate transform SigmaXL® performs a function to aid the Belt, this is known as

Box Cox Transformation.



452


Box Cox Transform

The transformed data is stored in the worksheet: “Box-Cox” column “Transformed Data(Y**0.500000)”.

This tool can also be found under “Process Capability > Nonnormal> Box-Cox Transformation” and“Control Charts> Nonnormal> Box-Cox Transformation>”.

Box-Cox is also included with automated distribution fitting (Process Capability >Nonnormal>Distribution Fitting)


Selecting a transform, in the upper graph SigmaXL® presents a lambda of .5, the lambda is amathematical function applied to the data. In taking a square root, you can notice two probabilitiesof plots in the graphs below. The right plot obviously shows a new data set after having beentransformed by the square root and the left showing Non-normal distribution with red dots away

from the blue line symbolized by a P-value of under .05.



454


Multiple Linear Regression

In a quick review, we only do Regression on historical data and Regression is not applied toexperimental data. Furthermore, we covered performing Regression involving one input and oneoutput. Now taking into account Multiple Linear Regressions and when they are applicable, allowsus to identify Linear Regression including one output and more than one input at the same time.

If you haven’t identified enough of the output variation, recall briefly R-squared measures theamount of variation for the output in Correlation with the input you selected. In looking at theequations here we can assume that in Multiple Linear Regressions each input are independent of

one another, no Correlation exists. Having the inputs independent of one another gives each ofthem their own slope. Also we see the epsilon at the end of the equation representing the fact thatevery Regression has model error.


!"# $"%% &'(% * $" $+( ' ( , &%-'$ &.*/ 0$'."%% 1* -* 2 3 - & % 4 5 6 * 7'$ 8 '7

"9 0"$&8"(-*-&'(2

:+/-&0/" ;&("* $ !"# $"%% &'( &(< "%-&# * -"% 8 +/-&0/" &(0+ - <* $&*= /"% > "77".- '(

*( '+-0+- % &8+/-*("'+%/? 2

! 37 ! @ & % ('- * % , &# , * % 1 "% &$"1 &( -," A &8 0/" ; &("*$ !"# $"%% &'(2

! B$'."%% C ('D /"1# " &8 0/ &"% 8 '$" -,* ( ' (" &(0 +- *7 7".-% -," '+ -0+-2

6," *% %+8 0-&'(% 7'$ $"% &1+* /% D & -, A &80/" !"# $"%% &'(% * $" %- &/ / ("."%%* $?

7'$ :+/-&0/" ;&("* $ !"# $"%% &'(%2

E ( * 11 &-&'(* / * %%+8 0-&'( 7'$ :;! &% -," &(1"0"(1 "(." '7 0 $"1&.-' $% FG >% H 2

! :34 36EI 6: .* ( -"%- 7'$ 8 +/-&.'/ /&("* $&-? F.'$$"/* -&'( = "-D ""( -,"

0$"1 &.-'$% ' $ G >%H2

:'1"/ "$$'$ F$"% &1+*/%H & % &80*.-"1 =? -," *11&- &'( '7 8"*%+$"8"(- "$$'$

7'$ * / / -," &(0+- <* $ &*=/"% 2



455


Definitions of MLR Equation Elements

Simple linear equations and multiple linear equations are very similar, however each in MultipleLinear Regression there is partial regression coefficient and beta one and beta zero apply toSimple Linear Regressions. Earlier we did Regressions in this module, do you recall theresiduals we had? Residuals are defined as the observed value minus the predicted value.

MLR Step Review

With many different input variables on hand and only one output it can be so tedious to find ifvariations come from one particular input, using a Matrix Plot can greatly speed up the process andit will show which is impacting the output the most. After narrowing the field of variables use thebest given command to complete the Multiple Linear Regression, we identify the correct commandby examining R-squared, R-squared adjustable, #’s of predictors, S variable and Mallows Cp;following this we must iteratively confirm inputs are statistically significantly. We have then onlyconfirmation of this valid model and we MUST especially in consideration for Multiple LinearRegressions process and witness the presently performing Regression.


!"# %# &'(')'*(+ &*, )"# # -#.# ()+ *& )"# / 0-)'1-# 2'(#3 , 4#5 ,#++' *(.* %#- 3 ,# 3 + &*- -*6 +7

8 9 !"# ,#+1*(+# :%#1#(% #(); <3 , '3 =-#>

? @ A ? B A ? C 7 !"# 1 ,#% 'D)*, : '(%#1 #(% #(); '(10 )+> !"# 1,# %'D)*,<3 ,'3=-#+ 0+#% )* #E 1-3 '( )"# <3 ,'3)'*( '( )"# *= +#,<#% ,#+1* (+#< 3 , '3 = - # A 8 >

!F 7 !"# < 3 -0# *& 8 6 "#( 3 - - )"# #E 1-3( 3 )*,G <3 ,'3= -#+ :)"# ? +; 3,##H03 - )* I#,*>

!@ A !B A !C :J3 ,)'3- 4#5 ,#++'*( K*# &&'D'#();7 !"# 3. *0 () =G 6 "'D")"# ,# +1 *(+ # < 3 ,'3= -# :8 ; D"3 (5 #+ 6 "#( )"# D* ,,#+1 *(% '(5 ? 'D"3( 5 #+ = G *(# 0(') 6 ')" )"# *)"#, '(10) <3 ,'3=-#+ ,#.3 '('(5D*(+)3()>

" :L,,*, *, 4#+'%03 -;7 !"# *= +#,<#% 8 .'(0+ )"# 1,#%'D)#% < 3 -0# *&8 &,*. )"# 4#5 ,#++ '*(>

Y =0+

1X

1+

2X

2+

3X

3+

!"# % & '() '*#+' *, -,. .,/ (0 12 .*(+.# . (0#& 3 3#4 3#''(,0 & 3#5

6 7 83#& *# 1& *3 (9 +.,* !"#$%&'($)#*+ - ./)0

:7 ;20 <#'* =2%'#*' ;#4 3#'' (,0 !1 )$)'23 4#3 55 */6' 73 5) 1 89 53 )50

> 7 ?@ & . 2& * # ; : A &BC2'*#B ; : A D& ..,/ 'E 8 +A 021 %#3 ,- + 3#B()*,3'

& 0 B = 7

F 7 G*#3& *(@#.H B#*#31(0# &+ +3,+ 3(&*# ;#4 3#''(,0 1,B #.7

!1 )$)'23 4#3 55 */6' 23 4#3 55 */6 ': %) */650

I 7 J 0 & . H K # 3 #' (B 2 & . ' !1 )$ )' 2 3 4 # 3 5 5 * / 6 ' 2 3 4 # 3 5 5 * / 6 ' " # $ % & 5 0

67 L ,31& . .H B ('*3 (%2*#B

: 7 ?M 2 & . @ & 3 (& 0 ) #

> 7 G 0 B #+ # 0 B # 0 )#

F 7 8,0-(31 ,0 # ,3 */ , +,(0*' B, 0,* ,@ #3 .H (0- .2#0)# 1, B#.7

N 7 O#3 ( -H H ,23 1 ,B#. %H 3200(04 + 3#'#0* +3,)#'' B&*& *, ),0-( 31

H ,2 3 1,B#. #3 3,37



456


Multiple Linear Regression Model Selection

Flight Regression Example

It’s in our best interest to use the least confusing Multiple Linear Regression model, usingthese particular guidelines.

Select the “Flight Regression MLR ” worksheet to see historical data being analyzed by an airplanemanufacturer. Output is listed as flight speeds and the other columns contain input variables. Withthese we will build a Scatter Plot Matrix and witness the possibility of relationships among thevariables come to fruition.




457


Flight Regression Example Model Selection

Flight Regression Example Matrix Plot

Select “Statistical Tools > Regression > Multiple Regression”. Select “Flight Speed” as NumericResponse (Y), and Select all inputs as Continuous Predictors (X).

SigmaXL® V6 currently includes Multiple Regression but does not include Best Subsets or StepwiseRegression. However, you can easily add or remove terms from the model using Recall SigmaXL

Dialog.


Now we are given afairly confusing graphof outputs and inputs tointerpret. Do not be

discouraged, this is justa plethora ofsporadically plotted,outputs and inputs,flight speeds vs.altitudes. Seeing atleast two inputs havingCorrelation shows theneed to continue with aMultiple LinearRegression. The lower

half has identical dataas the upper half of theoutputs just the axis arenot reversed.



458


Flight Regression Example Model Selection (cont.)

Use “Recall SigmaXL Dialog” and remove the “Temp” variable. Note that “ Altitude” now has aP-Value > 0.05. Again use “Recall SigmaXL Dialog” and remove “ Altitude”.

Do you notice any similarities here? A foreign column has appeared, labeled VIF, this indicates if ahigh Correlation among inputs exists. Temp has a high VIF, so we will remove it.


Variance Inflation Factor (VIF) detects Correlation among predictors.

• VIF = 1 indicates no relation among predictors

•

VIF > 1 indicates predictors are correlated to some degree

• VIF between 5 and 10 indicates Regression Coefficients are poorly

estimated and are unacceptable.

The VIF for temp indicates it should

be removed from the model.

Remove Altitude, re-run model.

The VIF values are NOW acceptable.

Evaluate the P-values:

• If p > 0.05, the term(s) should be removed

from the Regression.



459


Flight Regression Example Model Selection (cont.)

After removing “ Altitude” from the model we now see that “Turbine Angle” is not statisticallysignificant.

Shown here is the entire Regression output for a complete discussion of the final Multiple LinearRegression model. We have 2 predictor variables and all are statistically significant.

Also shown above is a portion of the residuals report showing a high leverage observation and

large standardized residual. If possible these data points should be examined.


Re-run the

Regression

The P-value for Turbine Angle

is P > 0.05 which indicates it

should be removed and re-run.



460


Flight Regression Example Residual Analysis

Now having a final model, it is VITAL to confirm the residuals are correct and the model is valid.

Select the “Mult Reg Residuals” worksheet. It appears our model is valid and the Residuals are

satisfactory!

How do we do this? Graph it and use the appropriate commands to analyze.




462


Lean Six Sigma

Black Belt Training

Now we are going to continue with the Improve Phase “Designing Experiments”.

Improve PhaseDesigning Experiments



463


Designing Experiments

Overview

Project Status Review

Within thismodule wewill provide anintroduction to

Design ofExperiments,explain whatthey are, howthey work andwhen to usethem.

! "#$%&'#( * +#(,-&-! "#$%&'#( * +#(,-&-

./ 0 123%454(46,./ 0 123%454(46,

72#-4+- 84" 09$2"&:2+3-72#-4+- 84" 09$2"&:2+3-

!"## !% &'()*% # +, -. )*/.0 '1!"## !% &'()*% # +, -. )*/.0 '1

+, -.)*/.0'%# 2.'3(41+, -.)*/.0'%# 2.'3(41

5. 1*6 0*0 6 +, -. )*/ .0'15. 1*6 0*0 6 +, -. )*/ .0'1

7 4 8 % 0 & .4 9 ) (& .11 2(4 .# *0 6 :

2;<

7 4 8 % 0 & .4 9 ) (& .11 2(4 .# *0 6 :

2;<

9)(&.1 1 2(4 .#*06 : <.6 ).11 *(09)(&.1 1 2(4 .#*06 : <.6 ).11 *(0

= .#&(/ . '( >/-)(8 .= .#&(/ . '( >/-)(8 .

!)%&'*(0%# !%&'()*%#

+, -. )*/.0 '1

!)%&'*(0%# !%&'()*%#

+, -. )*/.0 '1

= )%- ?- @ 7 &'*(0 > './ 1= )%- ?- @ 7 &'*(0 > './ 1

! !"#$%& '( "# *+ % ,%*-.$/ ( "# 0 '1 & 0/, ( 2' *" '3$ -+& 0"$& & 4

5!"#$%" 6! 7&'( -. 0&3$# 8 0%/ *- 9$2'0:$&;< *( .& 8*% 0/, %*: $/ $"'4 5!"#$%"6

! = +( "'08 0$# *+ % *+ ', +' 23( %( 2'$%0&'024 5!"#$%" 6

! >( . 0#( '$# '3$ / $( &+%$/ $"' &? &'$/ 8*% *+% *+ ',+ '

23(%(2'$%0&'024 &'"()*+",

! @#$"'080$# '3$ , %*2$&& 0",+' :( % 0( -.$& 0" *+% ,%* 2$&& 4

&'"()*+",

! A ( %%*B $# *+ % 0", +' :( %0( -.$& '* '3$ , *'$"'0( . C D 1&E '3%* +< 3

F'('0&'02( . G "( .?& 0& 4 &-%( ./0" ,

! F$ .$2'$# '3$ :0'( . 8$B D 1& '* *, '0/0H $ '3$ * +',+' %$&, *" &$5&64

& 123+45",

! = +( "'080$# '3$ %$.( '0*" &3 0, *8 '3$ I 1& '* '3$ D 1& B 0'3 I J 85K 64

& 123+45",

Keep an eye on where you

ve been



464


Six Sigma Strategy

Designs of Experiments help the Belt to understand the cause and effect between the processoutput or outputs of interest and the vital few inputs. Some of these causes and effects may

include the impact of interactions often referred to synergistic or cancelling effects.

Reasons for Experiments

This is reoccurring awareness. By using tools we filter the variables of defects. When talking ofthe Improve Phase in the Six Sigma methodology we are confronted by many DesignedExperiments; transactional, manufacturing, research.


!" # % & ' ()* # +" ' ,# & ' --. / #0 0 . / & 1" # 2' & ) 3& 4 5 1, 1. ' 6 -3 13 6' (

7#/ 8 &. / 31 3, &# 6#,,' -) 1. 0 #1#-23&# 1"# 4 -.4 #- , #113&9 , 7.- 1" #

:31' ( 7#/ 3&45 1, ;#6'5 ,#<

! !"# :31' ( 7#/ 4. 1#&13' ( () "' :# 3&1#-'613.&,=

! !"# :31' ( 7#/ / 3 ( ( "' :# 4 -#7#--#0 -' &9 #, 1. '6" 3#:# . 4132' ( -#,5 (1,=

! >.& 7 3-2 6'5, # '&0 #77#61 -#('1 3.&," 34, '2 .&9 7' 61.-, 30#& 13 7 3#0 3&

' &' ()* # 4 "' ,# ?#=9 = -#9 -#,, 3.&@

A&0 #-,1'&0 3&9 1"# -#' ,.& 7.- ' & #B 4#- 32 #&1 6' & "#(4 3& ,#(#613&9

1"# 0 #,39 & ' &0 7. 65,3&9 1"# #77.-1, .7 ' & #B 4# -32# &1=

C#' ,.&, 7.- #B 4#- 32 #&13&9 ' -#<

! +-. ; (#2 D. (: 3& 9 ? E24 -. :3& 9 ' 4 -. 6#,, -#,4 . & ,#@

! F 41323* 3&9 ?G39 "#, 1 ) 3#(0 .- (./ #,1 65,1.2 #- 6.24 ('3&1,@

! C.; 5,1&#,, ?>.&,1'&1 -#,4. &,# 132#@

! D 6-##&3&9 ?H5-1"#- ,6-##&3&9 . 7 1"# 6-3136'( 7#/ 1. 1"# :31' (

7#/ I J, @

K#,39& /"#-# ) .5J-# 9.3&9 L ;# ,5-# ) .5 9 #1 1"#-#Mesign where you

re going - be sure you get there



465


Desired Results of Experiments

Here we have models that are the result of designed experiments. Many have difficulty determiningDOE models from that of physical models. A physical model includes: biology, chemistry, physics

and usually many variables, typically using complexities and calculus to describe. The DOE modeldoesn’t include any variables or complex calculus: it includes most important variables and showsvariation of data collected. DOE will focus on the specific region of interest.

DOE Models vs. Physical Models


! " #$% &' ) #% * +,-

! "#$%$&'() +),)-($.) /01+2-(3 10 3)0.$-)34

! 5)+2-) -6-#) ($%) 1, 7'&+#$&8 (0'&3'-($1&'# /01-)33)34

. /0+'+1 +,-

! 9' (7)%'($-'# %1+)# $3 +)3$0)+ (1 %1.) (7) /01-)33 0)3/1&3)4

! : //10(2&$(6 (1 %))( +$,,)0$&8 -23(1%)0 0);2$0)%)&(3 <3/)- $,$-'($1&3 10

=:>?4

2#$ 340 5& 4+- ,

! @01.$+) -1&3$3()&( /01-)33 10 /01+2-( /)0,10%'&-)4

! A)3)&3$($B ) (7) 12(/2( 0)3/1&3)<3? (1 $&/2( .'0$'C#) -7' &8)3 $&-#2+$&8

D : EF" .'0$'C#)34

! A)3$8 & /01-)33)3 G&1H$&8 H7$-7 $&/2( .'0$'C#)3 '0) +$,,$-2#( (1 %'$&(' $&4

)6"&&,+,-

! @'3( /01-)33 +' (' $3 #$%$()+ 10 3('($3($-' # -1&-#23$1&3 /0).)&()+ 8 11+

&'001H$&8 1, -0$($-'# ,'-(103 $& I&'#6B) @7'3)

78&, +0 "9+,4 +0 !.2 ) :

Designedexperimentsallows us todescribe a

mathematicalrelationshipbetween theinputs andoutputs.However, oftenthe mathematicalequation is notnecessary or useddepending on thefocus of the

experiment.

When it rains it PORS

What are the differences between DOE modeling and physical

models?

– A physical model is known by theory using concepts of physics,chemistry, biology, etc...

– Physical models explain outside area of immediate project needs and

include more variables than typical DOE models.

–

DOE describes only a small region of the experimental space.

The objective is to

minimize the response.

The physical model is

not important for our

business objective. The

DOE Model will focus in

the region of interest.



466


Definition for Design of Experiments

One Factor at a Time is NOT a DOE

Design of Experimentshows the cause and effectrelationship of variables ofinterest X and Y. By way ofinput variables, designedexperiments have beennoted within the AnalyzePhase then are executed inthe Improve Phase. DOEtightly controls the inputvariables and carefullymonitors the uncontrollablevariables.

Let’s assume a Belt hasfound in the Analyze Phasethat pressure andtemperature impact hisprocess and no one knowswhat yield is achieved for the

possible temperature andpressure combinations.

If a Belt inefficiently did a OneFactor at a Time experiment(referred to as OFAT), onevariable would be selected tochange first while the othervariable is held constant,once the desired result wasobserved, the first variable


!"#$%& () *+ ,"- $."& /# !"# $% '( ) (*'+,-'.'* /+-01 2 1.

34) ,,',5 ) ,2 *1,26 *-',5 ) , +7 3+8'/ +,- -0) - 9 ' 44 :'+42

-0+ -86+ *)6 (+;) ,2 ;+..+*- 8+4)- '1,(0 '3 < +-9 ++, -0+ =

>) 8 ') <4+( ),2 -0+ ? >) 8 ')<4+( 1. ',-+8+(-@

"# $ ) 4 419 ( -0+ +7 3+8'/+,-+8 -1 (-62 : -0+ +..+*- 1. / ) ,:

',36- >)8 ')< 4+( -0)- /) : ',.46+,*+ -0+ 3 8126*- 18 381*+((

# $.01/2&"(0#13 A ) ( 9 +44 )( 31 (('< 4+ ',-+8) *-'1, + ..+*-( !.18

+7 ) / 34+ (: ,+8 5 '(-'* +..+*-(%@

B0+ +,2 8+ (64- 1. / ) ,: +7 3+8'/ +,-( '( -1 2+(*8'<+ -0+

8+(64-( )( ) /)-0+/)-'*)4 .6,*- '1,@

: C . !7 %

B0+ 5 1) 4 1. " # $ '( -1 .',2 ) 2+ ('5 , -0) - 9 '4 4 3812 6*+ -0+

',.18/) -'1, 8+D6'8+2 )- ) /','/6/ *1(-@

Properly designed DOE’s are more efficient experiments.

! "# %&'()* & ( & +,-# !" #$%& () * + ,- .,/(0 ,+1* 2 )132, 4 51 +61 *

.2* ++,7 ,- .,/(0 ,+1 6/ 8" 9:

%;, < /*. ;(= );6> ) 3 (, 27 =6+165/) ?6/ * ./6=,)) 1;*1 * /,

5+@ +6> + 16 1;, ,- .,/(0 ,+1,/:

P r e s s u r e

( p s i )

75

80

85

90

95

Yield Contours Are

Unknown To Experimenter

30 31 32 33 34 35

120

125

130

135

Temperature (C)

Trial Temp Press Yield

1 125 30 74

2 125 31 80

3 125 32 85

4 125 33 92

5 125 34 86

6 130 33 85

7 120 33 90

7

2143

6

5 ! "#$%&% $()*#$+$)(

,$#- ! ./0

01&) ! "#$%&% 232 $4254)

,$#- 6! 7

is set at that level and the second variable is changed. Basically, you pick the winner of thecombinations tested.

The curves shown on the graph above represent a constant process yield if the Belt knew thetheoretical relationships of all the variables and the process output of pressure. These contour linesare familiar if you’ve ever done hiking in the mountains and looked at an elevation map which showscontours of constant elevation. As a test we decided to increase temperature to achieve a higheryield. After achieving a maximum yield with temperature, we then decided to change the other factor,pressure. We then came to the conclusion the maximum yield is near 92% because it was thehighest yield noted in our 7 trials.

With the Six Sigma methodology, we use DOE which would have found a higher yield using

equations. Many sources state that OFAT experimentation is inefficient when compared with DOEmethods. Some people call it hit or miss. Luck has a lot to do with results using OFAT methods.



467


Types of Experimental Designs

Value Chain

DOE is iterative innature and may requiremore than oneexperiment at times.

As we learn more aboutthe important variables,our approach willchange as well. If wehave a very goodunderstanding of ourprocess maybe we willonly need oneexperiment, if not wevery well may need a

series of experiments.

Fractional Factorials or screening designs are used when the process or product knowledge is low.We may have a long list of possible input variables (often referred to as factors) and need to screenthem down to a more reasonable or workable level.

Full Factorials are used when it is necessary to fully understand the effects of interactions and whenthere are between 2 to 5 input variables.

Response surface methods (not typically applicable) are used to optimize a response typically whenthe response surface has significant curvature.


!"# % #&#'( ) &*+( +,*& - .#/ +* / #.,% &( +# ( 0-)) 0( 1+*',( )

/#. ,% & ,. % ,2#& 34 5

!6 "#'# 7 ,. +"# &- 8 3#' *0 ,&9-+ 2( ' ,(3 )#. *' 0(1+*'. :

"

; ,. +"# & -8 3#' *0 < )#2#).= +"( + > , )) 3# - .#/ 0*' #( 1"0(1+*':

! ? -( &+,+( +,2# * ' @ -( ) ,+( +,2# 0( 1+*'. 1(& 3# -.#/:

Full factorial designsare generally noted as2 to the k where k isnumber of inputvariables or factors and2 is the number oflevels all factors used.In the table, two levelsand four factors are

shown; by using theformula, how manyruns would be involvedin this design? 16 isthe answer, of course.



468


Visualization of 2 Level Full Factorial

Let’s consider a 2 squareddesign which means we have 2levels for 2 factors. The factorsof interest are temperature and

pressure. There are severalways to visualize this 2 levelFull Factorial design. Inexperimenting we often usewhat’s called coded variables.Coding simplifies the notation.The low level for a factor isminus one, the high level is plusone. Coding is not very friendlywhen trying to run anexperiment so we use uncoded

or actual variable levels. In ourexample 300 degrees is the low

Graphical DOE Analysis - The Cube Plot

The representationhere has two cubeddesigns and 2levels of threefactors and showsa treatmentcombination tableusing coded inputslevel settings. The

table has 8experimental runs.Run 5 shows startangle, stop anglevery low and thefulcrum relativelyhigh.


T P T*P

-1

+1

-1

+1

-1

+1

-1

+1

-1

-1

+1

+1

-1

-1

+1

+1

+1

-1

-1

+1

+1

-1

-1

+1

Temp

300

350

Press

500

600

22

Temp

Press

350F300F

(+1,-1)(-1,-1)500

600 (+1,+1)(-1,+1)

!"#$ &' (&$ )*&+ ,- . $#+/0

! 1& * ( 2 3 4 4 5 6 $ &/ / 2 7 4 4

! 1& * ( 2 3 7 4 5 6 $ &/ / 2 7 4 4

! 1& * ( 2 3 4 4 5 6 $ &/ / 2 8 4 4

! 1& * ( 2 3 7 4 5 6 $ &/ / 2 8 4 4Coded levels for factors

Uncoded levels for factors

level, 500 degrees is the high level for temperature.

Back when we had to calculate the effects of experiments by hand it was much simpler to usecoded variables. Also when you look at the prediction equation generated you could easily tellwhich variable had the largest effect. Coding also helps us explain some of the math involved inDOE.

Fortunately for us, SigmaXL® calculates the equations for both coded and non-coded data.

! " # $ %& ' ( * + , &'$ %-# "# * .*/*012/ 3 3 3

S t o p A n g l e

Start Angle !"#$"%

$"&'"%'

("('

)"$ &"''

%"'

Fulcrum

Run Start Stop Meters

Number Angle Angle Fulcrum Traveled

% *% *% *% $"%!

$ % *% *% !"#!

( *% % *% ("('

& % % *% %"'!

' *% *% % '"%'

+ % *% % $"&!

, *% % % )"$!

) % % % &"''

4 5 ! Response

S t o p A n g l e

Start Angle !"#$"%

$"&'"%'

("('

)"$ &"''

%"'

Fulcrum S t o p A n g l e

Start Angle !"#$"%

$"&'"%'

("('

)"$ &"''

%"'

Fulcrum



% *% *% *% $"%!

$ % *% *% !"#!

( *% % *% ("('

& % % *% %"'!

' *% *% % '"%'

+ % *% % $"&!

, *% % % )"$!

) % % % &"''

4 5 ! Response



% *% *% *% $"%!

$ % *% *% !"#!

( *% % *% ("('

& % % *% %"'!

' *% *% % '"%'

+ % *% % $"&!

, *% % % )"$!

) % % % &"''

4 5 ! Response

6 7* / * (' /7' %#01/$ 8'%#- 9 * #%012*/'& %# /7 %$ &'$ %-# :

;" < 9 * #= (1# $ * (' /7'(' %# /7 %$ '> 0'( %9'# /:



471


Let’s review what is happening here. The dot indicated by the green arrow is the Mean distancewhen the fulcrum is at the low level as indicated by a -1 and when the start angle is at the highlevel as indicated by a 1. Earlier we said the point indicated by the green arrow had the fulcrum atthe low level and the start angle at the high level. Experimental runs 2 and 4 had the process

running at those conditions so the distance from those two experimental runs is averaged andplotted in reference to a value of 1.2 on the vertical axis. You can note the red dotted line shown isfor when the start angle is at the high level as indicated by a 1.

Interaction Plot Creation


-1

1

-1-1 11

1.5

2.5

3.5

4.5

5.5

6.5

Fulcrum

Start Angle

M e a n

Interaction Plot (data means) for Distance

-1

1

-1-1 11

1.5

2.5

3.5

4.5

5.5

6.5

Fulcrum

Start Angle

M e a n

Interaction Plot (data means) for Distance

Run # Start Angle Stop Angle Fulcrum Distance! "! "! "! $%!&! " #" #" $%&$

' "! ! "! '%'(

' " " #" "%($( "! "! ! (%!() " #" " !%'$

) "! ! ! *%$&* " " " '%((

+&%,& - ! %(&./ $ 0 !%$&

+1%(( - $%1&./$ 0 '%1*

Calculating the points to plot the interaction is not as straight forward as it was in the Main EffectsPlot. Here we have four points to plot and since there are only 8 data points each average will becreated using data points from 2 experimental runs. This plot is the interaction of Fulcrum withStart Angle on the distance. Starting with the point indicated with the green arrow above we must

find the response data when the fulcrum is set low and start angle is set high (notice the colorcoding SigmaXL® uses on the right side of the chart). The point indicated with the purple arrow iswhere fulcrum is set high and start angle is high. Take a few moments to verify the remaining twopoints plotted.



472


Graphical DOE Analysis - The Interaction Plots

Based on howmany factorsyou selectSigmaXL® will

create a numberof interactionplots.

Here there are 3factors selectedso it generatesthe 3 interactionplots. These arereferred to as 2-way interactions.

SigmaXL® also plots the mirror images, just in case it is easier to interpret with the variables flipped.These mirror images present the same data but visually may be easier to understand.




473


DOE Methodology

Generate Full Factorial Designs in SigmaXL®

It is easy togenerate FullFactorial Designs in

SigmaXL®. Followthe command pathshown here. This isthe Factorial/Screening Designdialog. The nextslide will explain thedifferent optionsavailable to youthrough this dialogbox.

In the “SelectDesign” drop downselection, you canchoose full factorialor fractional factorialdesigns. ResolutionIII designs are


! " # $% &'$ )*$ +,- .)&.- / +,01/$2

3 " 45)- 1/ &5* )*$ $ 6 +$,&2 $')-/ 01 7$.)&8$

9" :$/$.) )*$ 0;)+;) < ,$5+0'5$= 8-,&-1/$5

>" :$/$.) )*$ &'+;) < &'?$+$'?$')= 8-,&-1/$5

@ " A*00 5$ )*$ /$8$/5 %0, )*$ &'+;) 8- , &- 1 /$5

B " :$ /$.) )*$ $ 6 +$, &2$')- / ?$5 &C '

D " 46 $.;)$ )*$ $6 +$,&2 $') - '? .0/ /$.) ?- )-

E " F ' - /G H $ )* $ ? - )- % ,0 2 )* $ ? $ 5 & C ' $ ? $ 6 + $ , &2 $ ' ) - ' ?

?, - I 5)- )&5)&.-/ .0'./;5&0 '5

J " #,- I + ,- .)&.- / 50/;)&0'5

! K "L$+/ &.-)$ 0, 8- / &?- )$ )*$ $6 +$,&2 $')-/ ,$5;/)5! ! " M2+ /$2$') 50 /;)&0'5

screening designs and should be used with caution. Resolution IV designs can be tricky becausethere are aliased two-way interactions. It is best, if possible, to use Resolution V or higher designs.These design options will be discussed in detail later.



474


Create Three Factor Full Factorial Design

Let’s create a three factor Full Factorial Design using the SigmaXL® command shown at the top ofthe slide. The design we selected will give us all possible experimental combinations of 3 factorsusing 2 levels for each factor.

Be sure to change the “Number of factors:” to 3. Also be sure not to select the “8-Run, 2**3, Full-Factorial” line within the “Designs” box.

In the “Randomize Runs” box, one can change the order of the experimental runs. To view the

design in standard order (not randomized for now) be sure to uncheck the default of “RandomizeRuns”. “Un-checking” means no checkmark is in the white box next to “Randomize Runs”.

Now, we need toenter the names ofthe three factors aswell as the “Low” and “High” valuesthat we want aslevels.

Remember whenwe discussed non-coded levels? Theprocess settings of140 and 180 for thestart angle areexamples of non-coded levels.




475


Three Factor Full Factorial Design

One warning to you as a new Belt using SigmaXL®… never copy, paste, delete or move DOEcolumns, SigmaXL® may not recognize the design you are attempting to use.

Is our experiment done? Not at all. The process must now be run at the 8 experimental set ofconditions shown above and the output or outputs of interest must be recorded yellow column(s). After we have collected the data we will then analyze the experiment. Remember the 11 stepDOE methodology from earlier?

Here is the worksheet SigmaXL® creates. If you had left the “Randomize Runs” selection checked,your design would be in a different order than shown. Notice the structure of the last 3 columnswhere the factors are shown. The first factor, Start Angle, goes from low to high as you read downthe column. The second factor, Stop Angle, has 2 low then 2 high all the way down the column and

the third factor, Fulcrum, has 4 low then 4 high. Notice the structure just keeps doubling thepattern. If we had created a 4 factor Full Factorial Design the fourth factor column would have had8 rows at the low setting then 8 rows at the high setting. You can see it is very easy to create a FullFactorial Design. This standard order as we call it is not however the recommended order in whichan experiment should be run. We will discuss this in detail as we continue through the modules.


Hold on Here we go….



477


Lean Six Sigma

Black Belt Training

Now we will continue with the Improve Phase “Experimental Methods”.

Improve Phase

Experimental Methods



478




DOE Methodology

In this module we will describe the 11 step DOE methodology some basic concepts and lots of

fun and exciting terminology. Once again great content for dinner conversation later tonight!

Within this modulewe will go througha basic introductionto Designing

Experiments

! "#$%&'()*%"#$! "#$%&'()*%"#$

+ *',$+ *',$

-'*."&"/"01-'*."&"/"01

! "## !%& '()*%# + ,-.)*/.0'1! "## !%& '()*%# +, -.)*/.0'1

+ ,-.)*/.0'%# 2.'3(41+ ,-.)*/.0'%# 2.'3(41

5.1*60*06 +,-.)*/.0'15.1*60*06 +,-.)*/.0'1

748%0&.4 9 )(&.11 2(4.#*06:

2; <

748%0&.4 9 )(&.11 2(4.#*06:

2; <

9)(&.11 2(4.#*06: <.6).11 *(09)(&.1 1 2(4.#*06: <.6 ).1 1*(0

=.#&(/. '( >/-)(8.=.#&(/. '( >/-)(8.

! )%&'*(0%# ! %&'()*%# + ,-.)*/.0'1! )%&'*(0%# ! %&'()*%# + ,-.)*/.0'1

=)%- ?- @ 7& '*(0 >'./1=)%- ?- @ 7& '*(0 >'./1

! " #$% &'$ )*$ +,- .)&.- / +,01/$2

3 " 45)- 1/&5* )*$ 46 7$ ,&2$' )- / 8 19$.)&:$

; " <$/$.) )*$ 8 =)7=) > ,$570 '5$? @ - , &-1 /$5

A " <$/$.) )*$ B'7= ) >&'C$7$' C$')? @ - , &-1 /$5

D" E*005$ )*$ F$:$/5 %0, )*$ &'7=) :-, &-1/$5

G " <$/$.) )*$ 46 7$, &2$' )- / #$5&H '

I " 46 $.=)$ )*$ $6 7$ ,&2$' ) - 'C E0 //$.) #- )-

J " K'- /LM$ )*$ C- )- % ,02 )*$ #$5&H'$C 4 6 7$, &2 $') - 'C

C,- N <)- )&5)&.- / E0 './=5&0'5

O " #,- N + ,- .)&.- / <0 /=)&0'5

! P "Q$7/ &.-)$ 0, : - / &C- )$ )*$ $6 7$, &2$' )- / ,$5=/)5

!!"B27/$2$') <0/=) &0'5



479


Questions to Design Selection

So you’ve decided to use Designed Experiments. Shown here are ten basic Project Managementconsiderations before running any experiment. This is obviously not an exhaustive list, but certainlysome important questions to consider and answer.

What is behind some of these questions? Let’s briefly discuss a few aspects individually.1. Access to a process is necessary for proper monitoring and execution of a project. If restrictedaccess for whatever reason exists, then work around must exist.

2.

If the team members or subject matter experts aren’t fully involved, then potential conflicts or

unrealistic designs may be awaiting you for a poor experiment.3. If the Process Owners and stakeholders are unknown to you before execution of an experimentrude awakenings such as cancellations, scheduling conflicts and other nightmares can occur.4.

No one wants to be told what will happen to the process they are managing so if you don’t involvethem in the experimental design even if it involves reviewing the team’s designed experiment, how doyou expect cooperation?5. If the Process Owners don’t understand what your DOE is, how can they assist you?6.

Does your DOE intend to make a wide range of quality product or potentially produce anunacceptable product in the quest to improve the process? If the Process Owner has never knownwhat your DOE intentions were, how can they not be upset if they are surprised by the results of the

DOE?7.

Time and money impact scheduling, randomization, testing concerns. All of these must beconsidered especially when using the actual process.8.

It is often desirable to run DOE’s in a pilot plant or facility but this is not often the case. If a pilotfacility is to be used, do the results match the process when translated outside of the laboratory?9. Noise variables cannot be controlled, by definition, but if ambient weather is considered to have aneffect on your process, why would you execute an experiment when a cold or warm front is passingthrough your area. This is one example of a known disturbance being designed around.10.

Manage your project to know if the DOE is intended to stretch the boundaries of conceived productcreation or work well within a small experimental area.

There are many considerations to consider. Often learning comes through experience so if you are

unsure about your future experiment in this project or another, consult with mentors or Six Sigma belts.




480


Questions to Design Selection (cont.)

These questions need be answered before running an experiment.

DOE Methodology Step 1

First define theproblem in apractical sense.Will we achieve allthat is necessary?Might it requiremultipleexperiments?

Notice an

example of thisshown here.




481



In Step 2, we have to determine the critical characteristics and the desired outcome. This gives usour critical characteristic.

Step 3 is knowing that a DOE is going to be performed, does it makes sense to go an extra mile?Let’s get our money’s worth by measuring more than one output if it could benefit us in any way.





482



Step 4 is to select the Input or independent Variables. At this point you should have a decentunderstanding of the variables that need to be explored as a result of the work accomplished inthe previous phases.


Step 5 is to choosethe levels for theinput variables. Thefactor levels must beconsidered to createthe desired changein the outputresponse as

identified in Step 3.Poor choices forinput variable levelsettings could verywell render anexperiment uselessso be smart.




483


DOE Methodology Step 5 (cont.)

Do not set the levels too wide, this may cause our experiment to lose very valuable output response.Making an assumption by way of drawing what you have in your mind of what it will look like, helps agreat deal.

Be aware you do not want to set the factor levels too low either. We could be shown no difference inoutput to input relationship.




484



slide off such a steep peak, unless your process controls are very tight it would be better to find thenice robust region where the output response is high but flat, meaning that the factor settings canchange a bit, but it does not have much effect on the output response. If the concern for spendingtoo much time on this comes up, also, consider how many defects are taken in when the statisticalsignificance is deemed inadequate.

You might think we have spent too much time on just setting the levels for the input variables orfactors in your experiment. However, consider the learning of others who have had to go back to

their Process Owners or Champions and explain that no factors were deemed statisticallysignificant because the design was inadequate.


Input variable level settingsshould be set far enoughapart to detect a differencein the response and to have

enough statisticalconfidence in the change ofthe output relative to theexperimental noise. Assume this graphic was asketch generated from ourbasic understanding of thetheory. We don’t knowexactly what factor settingwould produce the outputresponse but we do know

the general shape of thecurve. Notice that westayed away from the sharppeak. It is very easy to

Step 6 is to select theExperimental Design.




485



that subject matter experts along with your team members should pay attention to their experienceand the previously gathered and analyzed data. If curvature is suspected, center points are used toconfirm if curvature exists within the experimental region.

Remembering that noise variables can’t be controlled but managed around, blocking is a techniquefor managing your experiment around noise variables considered of importance. Remember, you areinterested in understanding the effects and interactions of your controlled variables so you wantstatistical confidence.

Randomization has animpact on your

statistical confidencebecause yourexperimental Noise isspread across the runs.

What would happen ifanother unknownsignificant variablechanged halfway duringour experiment?

It is possible that anunknown significantvariable such asmachine warm up timecould get confused withthe C variable becausewithout randomizationall the low levels wouldbe generated first andthen all the high levels.

!"#"$%&' "$' )*+,)-)$"# '&./-$. "*& ,/-,#0 &$%)1*"-&' "$' +,&

'&2/$/+/)$ )2 3"#"$%&' "$' )*+,)-)$"# /. %)4&*&' /$ " #"+&* 5)'1#&6

7 &$+&* 8)/$+. "*& 1.&' 2)* /$4&.+/-"+/$- %1*4"+1*& "$' " '4"$%&''&./- $.6 7 &$+&* 8)/$+. "*& %)4&*&' /$ " #"+&* 5)'1#&6

!#)%9/$- %"$ 3& 1.&' +) "%%)1$+ 2)* $)/.& 4"*/"3#&. "$' /. %)4&*&' /$ "

#"+&* 5)'1#&6

!"# % &&'()* +,- -.& /+(0& 1+21.33

Step 6 involvesselecting theExperimental Design.DOE’s can be

designed in many waysbut balanced andorthogonal designs arehighly encouraged.SigmaXL® will alwaysdesign a balanced andorthogonal design ifyou use the program todesign yourexperiment.

Remember our advice


I

m keeping out the Noise coach



486



Select the number of replicates to achieve the accuracy that you require for your DOE. EnsureRandomize Runs is unchecked. This will simplify the interpretation of the worksheet.

Determining sample size is very similar to what we did in the Analyze Phase. There are a fewdistinctions. Much of the values are self-explanatory.

As in the Analyze Phase, we are typically solving for the number of replicates, but you can work the

numbers backwards as we did before and estimate how big an effect could be detected.




487




The replicated designhas double the runs.The design is fullyrandomized wheneverpossible but theabove are shown instandard order tomake the worksheetseasier to interpret.

Notice howexperimental run #1and #9 have the threefactors which are startangle, stop angle andfulcrum, running withthe same combinationof levels and thenexperimental run #9 isa replicate of run #1.

A rep is a replication which is an independent observation of the run that represents variation fromexperimental run to experimental run.

A replication is NOT a duplicate or a repeat. Look at the two designs shown here. The first is a single

replicate design, which means there is only one value for each unique experimental run. Theterminology is a bit confusing, but don’t worry.

Single Replicate

Design

Replicated Design (2)

Replication -



488



Step 7 is to Execute the Experiment and Collect Data.


! " #$ %&'(% (*% #$ + %,-. %/( 0 /1 23 4 4%&( 50(0

! "#$%&$$ ()* *+,*-#.*/(01 $%2,*3 (#.* 0/4 %2$( 5#() ()* ,-2%*$$ 25/*-$,-#2- (2 ()* *+,*-#.*/(6

! 72.* (*0. .*.8*-$ .&$( 8* ,-*$*/( 4&-#/9 ()* */(#-* *+,*-#.*/(6

! :;(*- ()* *+,*-#.*/( )0$ $(0-(*43 0-* <2& 9*((#/9 2&(,&( -*$,2/$*$ <2&*+,*%(*4=

> ?; /2(3 @&#%A1< *B0 1&0(* ;2- C 2#$* 2- 2()*- ;0%(2-$ 0/4 %2/$#4*-$(2,,#/9 2- %0/%*1#/9 ()* *+,*-#.*/(6

! D$* 0 129 822A (2 .0A* /2(*$ 2; 28$*-B0(#2/$3 2()*- ;0%(2- $*((#/9$3 *(%6

! E 2..&/#%0(* 5#() ()* 2,*-0 (2-$3 (*%)/#%#0/$3 $(0;; 082&( ()**+,*-#.*/(01 4*(0#1$ 0/4 5)< ()* *+,*-#.*/( #$ 8*#/9 4#$%&$$*4 8*;2-*-&//#/9 ()* *+,*-#.*/(6

> F)#$ %2..&/#%0(#2/ %0 / ,-*B*/( G)*1,#/9 H 8< ()* 2,*-0(2-$3(*%)/#%#0/$3 *(%6 ()0( .#9)( 40.09* <2&- *+,*-#.*/(01 4*$#9/6

! : 1*-( ()* 1082-0(2-< 2- @&01#(< (*%)/#%#0/$ #; <2&- *+,*-#.*/( 5#11

#/%-*0$* ()* /&.8*- 2; $0.,1*$ 0--#B#/9 4&-#/9 ()* *+,*-#.*/(6




489



Step 8 is to Analyze the data from the Designed Experiment and draw Statistical Conclusions.


Step 9 is to Draw Practical Solutions.

! " # $% &' () +,) - %+% . /01 +,) -) 2 34$) 5 67 8)/ 31)$ +

%$ 5 5 /%9 :+%+32+3;%& <0$ ; &=2 30$ 2

! " #$%&'($ ) + ,$)-.'. &$. $)#/$0- 1//, (23/#/0 ', 4&/ %#/3'25.

6205)/.7

! 85#4&/# $,$)-.'. 29 :#/05(',; < 4&/ 620/) 42 4&/ .';,'9'($,4 4/#6.

=')) 1/ (23/#/0 ', 4&/ ,/>4 6205)/7

! 85#4&/# $,$)-.'. 29 :#/05(',; < 4&/ 620/) 42 4&/ .';,'9'($,4 4/#6.

=')) 1/ (23/#/0 ', 4&/ ,/>4 6205)/7

! ?&/ 9',$) 620/) 9'44',; =')) 2((5#7

! ?/#6. ', 4&/ 9',$) @A B /C5$4'2, =')) &$3/ .4$4'.4'($ ) (2,9'0/,(/-25 ,//0/07

! @'$ ;,2./ 4&/ #/.'05$). .'6')$#)- 42 4&$4 29 D/;#/..'2, +,$ )-.'.7

! @/4$ '). 29 4&'. .4/% $ #/ (23/#/0 ', 4&/ ,/>4 6205)/7

! " #$% & ($% )*+)% , - .,/*+.01

! "#$% '$(( )* +,-*.*/ $0 /*12$( $0 1#* 0*31 4,/5(*6

! 7-*0 $8 1*.4% ,. 82+1,.% 2.* %121$%1$+2 ((9 %$:0$8$+201; 8,. <.2+1$+2 (

%$:0$8$+20+* 1#* 1*.4 4$:#1 )* .*4,-*/6

! =!"#"$%& '$(#)"*+,#-$./01*20/ & 1",4,5/+ > '$(( #*(< 1#* <.,?*+1 1*24

8$0/ '#*.* 1#* -$12( 8*' 82+1,.% 0**/ 1, )* 12.:*1*/ 1, 2+#$*-* 1#*

/*%$.*/ ,51<51 .*%<,0%*6 @ "#$% '$(( )* +,-*.*/ $0 /*12$( $0 1#* 0*31 4,/5(*6

! "#$% %1*< $% #,' 1#* <.,?*+1 1*2 4 /*1*.4$0*% 1#* <.,?*+1A% <,1*01$2 (

%5++*%%6

! B44*/$21*(9 %#2.* 1#* .*%5(1% '$1# 1#* <.,+*%% ,'0*. 8,. 8**/)2+C ,0

$4<(*4*0121$,0 ,8 1#* *3<*.$4*012( .*%5(1%6




490



Step 10 is to Replicate or Validate the Experimental Results.


And the final step is to Implement Solutions. We spend so much time with the 11 stepmethodology for a couple of reasons. One, it is easy to get confused or excited about running aDesigned Experiment. Two, experiments are easy to design with the help of SigmaXL® butdifficult to execute appropriately and achieve statistical results unless you follow a planningapproach as we have discussed here. Overall there is a lot that can be overlooked or not doneproperly, take your time and follow this process, it WILL ensure better results.

You will probably not fully appreciate all the comments in the modules of this phase until you havedesigned, managed, executed and analyzed a few real life experiments for yourself.

! ! " !"# $%" %& ' )* $+ ',* & -

! "# %&' ()*'+%,-' (# %&' './'0,1'2% 34 5 4++(1/6,5&'7 427 %&' 895,2'55

: 45' ,5 54%,5#,'7; %&'2 /0(+''7 %( %&' : (2%0(6 <642 3&,+& ,5 +(- '0'7

,2 %&' : (2%0(6 <&45'=

! >( 2(% *95% 092 './'0,1'2%5 427 2(% ,1/6'1'2% %&' 5(69%,(25=

! ?90%&'0 './'0,1'2%5 14@ 2''7 %( )' 7'5,A 2'7 %( #90%&'0 +&4 2A' %&'

(9%/9% %( 54 %,5#@ %&' 895,2'55 : 45'= B C&,5 /(55,)6' 2''7 #(0 42(%&'0 './'0,1'2% ,5 3&@ 3' 5%4%'7 ,2

'406,'0 1(796'5 %&4% >D EF5 +42 )' 42 ,%'04%,-' /0(+'55=

! " # !"# $ %&'(" *+ , ' $ %- '(" (." /0 # "+ %1" 2(' $ !"34 $(3

! "#$%& #()*()+ $,% -&./$(/. 0 1%230$2 #&45 6$%7 8 9 :%&(#; $,% &%230$2<

= 6%$ $,% #./$4&2 .$ $,% -&./$(/.0 1%230$2 #43)* >($, 6$%7 8 .)* 2%%

(# $,% 7&4/%22 43$73$ &%274)*2 . 2 %?7%/$%*@ A,(2 :%&(#(/.$(4)

&%70(/.$%2 $,% &%230$ 4# $,% %?7%&(5%)$@

= B4 )4$ #4&+%$ ;43& 54*%0 ,.2 245% %&&4&@




491



You have now completed Improve Phase – Experimental Methods.


! Be able to Design, Conduct and Analyze anExperiment

Notes



492


Lean Six Sigma

Black Belt Training

Now we will continue in the Improve Phase with “Full Factorials”.

Improve PhaseFull Factorial Experiments



493


•

There are five or fewer factors.

• You know the critical factors and need to explain interactions.

• Optimizing processes.

Ok, let

s do some

experimenting

Full Factorial designs are used when:

Full Factorial Experiments


Why Use Full Factorial Designs

Two level Full Factorial designs are the most powerful and efficient set of experiments.

They are used to: Investigate multiple factors at only two levels, requiring fewer runs thanmulti-level designs. To investigate large number of factors simultaneously in relatively fewruns. To provide insight into potential interactions. Are frequently used in industrial DOE

applications because of simplicity and ease of analysis. To obtain a mathematicalrelationship between X’s and Y’s. And to determine a numerical, mathematical relationshipto identify the most important or critical factors in the experiments.

In this modulewe will discussthe FullFactorial in

detail.

!"#"$%& "$( ) *+,-.-$"#/+0!"#"$%& "$( ) *+,-.-$"#/+0

1/+ "$( 2/".$-3& 4-(&#1/+ "$( 2/".$-3& 4-(&#

5 &$+&* 6-/$+35 &$+&* 6-/$+3

4"+,&7"+/%"# 4-(&#34"+,&7"+/%"# 4-(&#3

!"## !%&'()*%# +, -.)*/.0'1!"## !%&'()*%# +, -.)*/.0'1

+, -.)*/.0 '% # 2.'3(41+, -.)*/.0 '% # 2.'3(4 1

5.1 *6 0*06 +, -.) */.0 '15.1 *6 0*06 +, -. )*/.0 '1

74 8 % 0& .4 9)(& .11 2(4.# *06 :

2;<

74 8 % 0& .4 9)(& .11 2(4.# *06 :

2;<

9)(&.11 2(4 .# *06 : <.6 ).11*(09)(&.11 2(4. # *06 : <.6 ).11*(0

= .#&(/ . '( >/- )(8.= .#&(/ . '( >/- )(8.

!)%&'*(0% # !%&'()*%#

+, -. )*/.0 '1

!)%&'*(0% # !%&'()*%#

+, -. )*/.0 '1

= )% - ? - @ 7&'*(0 > './1= )%- ?- @ 7 &'*(0 > './1

!"#"$%& "$( ) *+,-.-$"#/+0!"#"$%& "$( ) *+,-.-$"#/+0

1/+ "$( 2/".$-3& 4-(&#1/+ "$( 2/".$-3& 4-(&#

5 &$+&* 6-/$+35 &$+&* 6-/$+3

4"+,&7"+/%"# 4-(&#34"+,&7"+/%"# 4-(&#3

!"## !%&'()*%# +, -.)*/.0'1!"## !%&'()*%# +, -.)*/.0'1

+, -.)*/.0 '% # 2.'3(41+, -.)*/.0 '% # 2.'3(4 1

5.1 *6 0*06 +, -.) */.0 '15.1 *6 0*06 +, -. )*/.0 '1

74 8 % 0& .4 9)(& .11 2(4.# *06 :

2;<

74 8 % 0& .4 9)(& .11 2(4.# *06 :

2;<

9)(&.11 2(4 .# *06 : <.6 ).11*(09)(&.11 2(4. # *06 : <.6 ).11*(0

= .#&(/ . '( >/- )(8.= .#&(/ . '( >/- )(8.

!)%&'*(0% # !%&'()*%#

+, -. )*/.0 '1

!)%&'*(0% # !%&'()*%#

+, -. )*/.0 '1

= )% - ? - @ 7&'*(0 > './1= )%- ?- @ 7 &'*(0 > './1



494


Mathematical Output of Experiments

This may look similar to regression, but the important difference is that DOE is considered truecause and effect because of the controlled nature of experimentation. This is an important tool in

manufacturing environments.

The only difference between the model equation and the prediction equation shown is that theprediction equation is simplified for describing the data gathered in the experiment and using it topredict future events. Just because you end up with a prediction equation in an experiment doesnot mean it is a good predictive model. We will discuss this further when we introduce centerpoints.

! " #$ $&' ($) *+, -. / 0 1 2 3) / 4/,#$4/,35/+ .*&5,3-& ,- '$)5(36$ ,#$

($)*+,) -. ,#$ $78$(34$&,9

! : -( ,#$ ;< :/5,-(3/+ '$) 3=&) ,#3) 4-'*+$ '3)5*)) $) > +3&$/(($+/,3-&)#38) /($ 5-?$($'9

! @++ 4-'$+) A3++ #/?$ ) -4$ $((-( /) )#-A& 6B ,#$ ! 3& ,#$ 6$+-A

$C*/,3-&9

! " #$ 4/,#$4/,35/+ $C*/,3-& 6$+-A 3) ,#$ 8($'35,3-& .(-4 ,#$

$78$(34$&,/+ '/,/9 D-,35$ ,#$($ 3) &- $((-( ,$(4 3& ,#3) .-(49

! 3) ,#$ 8($'35,$' -*,8*, ($) 8-&)$ /) / .*&5,3-& -. ,#$ 3&8*,

?/(3/6+$) *)$' 3& ,#$ $78$(34$&,9

Y




495


Linear Mathematical Model

Linear Models are usually sufficient for most industrial experimental objectives. This goes back tothe difference between a physical model and a DOE model. Just because we know by theory thatthe model should not be linear, it may express itself as sufficiently Linear in the particular design

space.

People can get confused between the concept of curvature and twisted response planes. We donot have enough information (not enough levels for each variable) to describe true curvature.Take a piece of paper which will represent 2 input variables. Lift opposite corners. That is agraphical representation of an interaction. The response plane (paper) is twisted. Now lift up thepaper to eye level and rotate until the projection looks like a curved line. We are simply looking atthe projection of the twisted plane with Linear Models. There may be true curvature in the realworld, we simply can’t describe it with a Linear Model.

HOWEVER, in most manufacturing processes the Linear Model is very powerful because of theconstrained design space. Draw a box on the paper and hold it up by two opposite corners.Depending on how much twist you give the paper and how big the box is you will either see acurve or not in the defined space.

The surface plot on the left has no significant interaction, but both Main Effects are significant.The surface plot on the right shows a significant interaction with T and Cn.

!"# %&'#() *+,#% &- -.//&0&#'1 /+) *+-1 &',.-1)&(% #23#)&*#'1(% +45#01&6#-7

! "# %&'#() *+,#% 0(' #23%(&' )#-3+'-# 3%('#- (', 18&- 1#, )#-3+'- # - .)/(0#-

4#0( .-# +/ &'1#)(01&+'-7 9 ! "# /+%%+8&': &- ( %&'#() 3)#,&01&+' *+,#% .-#, &' ( 18+;%#6#% /.%% +)

/)(0 1&+'(% /(01+)&(%- 7

55

60

% Reacted

-1

0Ct

-1

65

-1

1

0 Cn

1

Cn

Surface Plot of % Reacted

55

60

% Reacted

-1

0Ct

-1

65

-1

1

0 Cn

1

Cn


-1

45

55

0

% Reacted

T

65

-1

1

0 Cn

1

Cn


-1

45

55

0

% Reacted

T

65

-1

1

0 Cn

1

Cn





496


Quadratic Mathematical Model

True curvature can be described using the Quadratic Model. The squared term in the model givesus the ability to describe true curvature. With the ability of describing curvature comes a cost. Theexperiment gets much bigger. Central composite designs are an example of a Quadratic Model.

Here is a surface plot of true curvature in a Quadratic Model. This shape is referred to as a saddlefor obvious reasons.

The nomenclature for 2 level designs is 2 to the K. If you had an experiment with 3 factors it wouldbe a 2 cubed design. If you simply do the math, that is the number of experimental runs in the basicdesign.

Nomenclature for Factorial Experiment

!"# $%#&'( *+$,-. ( #/ 0, +0&#'/,$ 1'&2 $,. '3/. /+& $,.(%'0,$ '/ &2'. 4+$"-,5

!"#$%#&'( *+$,-. ,67-#'/ ("%8#&"%,9 4#6'4"4.9 4'/'4"4. #/$ &1'.&,$

4#6'4"4. #/$ 4'/'4"4. 12,/ '/&,%#(&'+/. #%, #(&'8,5

: ; 2, <+--+1'/3 '. &2, ="#$%#&'( 7%,$'( &'+/ 4+$,- ". ,$ '/ . +4, %,. 7+/. ,

."%<#( , 4+$,-. /+& (+8,%,$ '/ &2'. &%#'/'/35

: ; 2, . '47-,% >? 4+$,-. $+ /+& '/(-"$, ,/+"32 '/<+%4#&'+/ &+ 3,/,%#&,

&2, !"#$%#&'( *+$,-5

-1.

6

11

C6

- . - .-0.5 0.0

0.51. A

- .5 -1.0- .

16

21

- .

.0 -1.5

1.5

1.0.5

0.0 B-0.5- .

1.51.0




497


Treatment Combinations

Standard Order of 2 Level Designs

Dr. Frank Yates created this standard order to aid in calculating the effects of each effect by

hand. Thank goodness we no longer have to perform hand calculations. It is common to draw acube for a 2 cubed design as shown.


The Design Matrix for 2 k factorials are shown in standard order(not randomized).

The low level is indicated by a -

and the high level by a +

.

A 2 2 design has 2 factors at 2 levels.

Meaning - 4 treatment combinations to consider and

analyze.

10 20

50 1 2

100 3 4

Temperature

Pressure

Treatment combinationfor run number 2 is:

Temperature at 20 deg

and Pressure at 50 psi.

No, those are 2 X 4 s

Treatment combinations, or experimental runs, show how to set the levels for each of the factors.Minuses and plusses can be used to indicate low and high factor level settings, Center Points areindicated with zeros. If the process is evaluated with combinations of the temperature set at 10 and20 degrees and pressure at 50 and 100 psi, an example of an experimental run or treatment

combination would be 20 degrees and 50 psi.



498


Full Factorial Design with 4 Factors

Full Factorial Design

Let’s walk through anddesign a 2 cubeddesign again for

practice. You canname the columns A, Band C or any nameyou’d like.

This table created withthe factors is referredto as a table ofcontrasts. Thecontrast columns arethe minus ones and

plus ones in the factorcolumns. In order to

Here we havestandard notation for2 to the 4 design andabove using 2 cubes,a commonrepresentation; nowfor the low levels ofthe 4 the factor andone for the high.


calculate contrast columns for interactions, we need the contrast columns for the main factors.

Warning, whatever you do, do not change the names of the columns by simply typing over thenames. SigmaXL® creates a model that it uses for the analysis later. If it can’t find the columnnames used to generate the worksheet, it will give an error message.



499


Balanced Design

Orthogonal Design

Factorial designs should bebalanced for properinterpretation of themathematical equation.

An experiment is balancedwhen each factor has thesame number ofexperimental runs at bothhigh and low levels.

Summing the signs of thecolumn contrast should yielda zero. In this example,there are 2 minuses and 2plusses.

Balance simplifies the mathnecessary to analyze theexperiment.

An orthogonal designallows each effect inan experiment to bemeasuredindependently, theseare vectors which areat 90 degrees to eachother. When everyinteraction for allpossible variable pairsums to zero, thedesign is orthogonal.


!"#$%&'"( *+,'-., ,/%0(1 2+ 2"(".#+1 3%& 4&%4+& '.$+&4&+$"$'%. %3 $/+

5"$/+5"$'#"( +60"$'%.7

8. +94+&'5+.$ ', 2"(".#+1 :/+. +"#/ 3"#$%& /", $/+ ,"5+ .052+& %3

+94+&'5+.$"( &0., "$ 2%$/ /'-/ ".1 (%: (+;+(,7

<055'.- $/+ ,'- ., %3 $/+ #%(05. #%.$&",$ ,/%0(1 ='+(1 " > +&%7

?"(".#+ ,'54('3'+, $/+ 5"$/ .+#+,,"&= $% "."(=>+ $/+ +94+&'5+.$7

@ A3 =%0 " (:" =, 0,+ $/+ 1+,'-., BAC AD8? DB 4&%;'1+,E $/+= :'(( "(:"=, 2+

2"(".#+17

iX!

A B

1 - -

2 + -

3 - +

4 + +

0 0i

X!

A B

1 - -

2 + -

3 - +

4 + +

0 0

SigmaXL® creates balanced, orthogonal designs. If they aren’t changed, this isn’t a problem.



500


Biomedical Production Example


!" $%&' ()*+,-( .( .&-- .*-/ $%0123% $%( 44 5$(, 67 8 +($%191-13: ;

<%( =&1+(9&>*- ?&0+ &' *$$(+,$&"3 $1 &">0(*'( $%( :&(-9 1? * ',(>&?&>

,01$(&" (),0(''&1" ?10 2'( &" 0('(*0>% =: 2"&@(0'&$&(' *"9

,%*0+*>(2$&>*- >1+,*"&(';

!" #$%&'$ )*$ +,-.)&.-/ +,01/$2

A!">0(*'( $%( :&(-9 =: BC D 1? >200("$ ,0192>$&1"; <%( E(*'20(+("$ 5:'$(+

F "*-:'&' ?10 :&(-9 %*' =((" @(0&?&(9; <%( =*'(-&"( ?10 $%( ,0&+*0: +($0&> 1?

:&(-9 & ' *$ BC D; <%( 1=G(>$&@( 1? $%( H01G(>$ I %*0$(0 0(J2&0(9 $%( $(*+ $1

*>%&(@( *$ -(*'$ * BCD &">0(*'( &" :&(-9;

3" 45)-1 /&5* )*$ 46 7$, &2$' )-/ 8 19$.)&:$

A E*)&+&K( $%( :&(-9;

!" #$%$&' ')$ * +',+' - .$/,01/$2 34 . 546 %$/

! " #$%& () *+(,$#- $.*+$//#(- #/ ,0$ (-%1 (2,*2, () #-,$+$/,3

! 4, #/ &$/#+56%$ ,( 705-8$ ,0$ 1#$%& )+(9 : ;< ,( 5, %$5/, =: <3

7" #$%$&' ')$ 81,+' -519$,$19 $1'2 34 . 546 %$/! >$9*$+5,2+$! ? (-7$-,+5,#(-! ?5,5%1/,! @ (#/$ 5-& (,0$+ A5+#5 6%$/ /270 5/ 596#$-, +((9 ,$9*$+5,2+$ 5-& ,$70-#7#5 -

B#%% 6$ +$7(+&$& &2+#-8 ,0$ $.*$+#9$-,3

:" ;)00 /$ ')$ <$=$%/ >0. ')$ 81,+' 34 . 546 %$/! >0$ )(%%(B#-8 %$A$%/ B$+$ &$,$+9#-$& B#,0 ,((%/ )+(9 ,0$ C-5 %1D $ E05/$ /270

5/ F$8+$//#(-G H(. E%(,/G I 1*(,0$/#/ >$/,#-8 5-& J 75,,$+ E%(,/3 >0$ %$A$%/B$+$ /$, )5+ $-(280 ,( 5,,$9*, %5+8$ 1#$%& 705-8$/ ,( 8$, /,5,#/,#75%7(-)#&$-7$ #- (2+ +$/2%,/3 K >$9*$+5,2+$ ? LM: G N:O K ? (-7$-,+5,#(- < L:G P:O K ? 5,5%1/, LJ2**%#$+ C G J2**%#$+ HO



501


Biomedical Production Example (cont.)

When creating the worksheetin SigmaXL® be sure tochange the default in the“Number of Replicates

” window to 2.

Enter the names of the factorsand their levels here inSigmaXL®. This is where theseare created so remember to doit here, it will not carry throughif you only do it in theworksheet itself.

SigmaXL® V6 does not supportdiscrete factors in DOE so thehigh and low levels must be

coded. We recommend 0,1 asshown.

Type “Yield” in the “ResponseName” as shown. If we hadmore than one response wewould change the “Number ofResponses” and label the“Response Names”.

You will almost always use the

randomization selection whencreating designs for realexperiments. There are someexceptions that we will coverlater in this module.

Again, we will use StandardOrder to make the worksheeteasier to interpret.




502



Here we go…We first need to estimatethe effects for ALL possibleeffects in the design,including all main effectsand all interaction effects.

Then we will decide whichones are important todescribing the variation inthe data set.

We will remove the effectsthat are not important todescribing the variation inthe data set and re-run themodel with only thoseeffects. This is similar to

In the shaded ‘Yield’ field is where we willplace the experimentalresults.

Select the “3 Factor DOE” worksheet which contains thedata shown above.

Note that supplier is coded as0,1. There is no “in between” value for the 2 differentsuppliers.

In an actual experiment youwould type in the yield

response information in thecreated worksheet. Over thenext several slides we will walkthrough the analysis.

the work you have already done in Regression Analysis. After we have run the final model fit we willcheck our Residual Analysis to validate our assumptions, the same as in Regression.




503



The Pareto Chart shows us thesignificant effects based on theselected alpha level.

At this point, Temperature andthe interaction of Temperaturewith supplier are the significanteffects.

Look for the FactorialFit information. Weinterpret this based onthe same way as wehave interpreted aswe do any otherstatistical test.

What does this tellus….there are 2

significant effects thatshould be in thismodel.

Since we have removedthe insignificant factorswe need to go back andrefit the model. Even

though there were onlytwo significant effectswe must include allMain Effects in themodel that are involvedin an interaction.




504


Biomedical Production Example (cont>)

We need to createsome Factorial Plotsbefore evaluating theResiduals. Followthe SigmaXL® pathshown here.

The steep slope on a Main Effects Plot means that variable is significant. Flat lines as shown forconcentration and supplier indicate they are not significant.


The interaction plot shows you all the plots with the variables you selected in the previousSigmaXL® command. The interaction of interest for our example is temperature with supplier. Hereit looks like high temperature with supplier 1 gives the highest yield which in our case is exactly whatwe want.



505


Biomedical Production Example (cont>)

Review the fitted Analysis of Variance table. This provides a lot of information that we will explorelater in the module, for now notice the P-value.


This shows us our Residual plots for yield. The interpretation is the same as we’ve used in the pastfor Regression.



506



The Residuals versus Variables are most important when deciding what level to set an insignificant factor.

A typical guideline is a difference of a factor of 3 in the spread of the Residuals between the low and

high levels of an insignificant input variable.

In this case concentration was not significant, but we still need to make a decision on how to set itfor the process. The low level for concentration has a smaller spread of Residuals, but there is nota difference of 3:1. Other considerations for setting the Variable are cost and reducing cycle time.

Step 9 is to draw yourPractical Solutions.

The Solver Add-in isincluded in theMicrosoft ExcelPackage. To accessit,Click Tools > Add-Ins

(Excel 2007: OfficeButton | Excel Options| Add-Ins > ManageExcel Add-Ins, clickGo…). Ensure thatthe Solver Add-in ischecked. If the Solver Add-in does notappear in the Add-insavailable list, you willneed to re-installExcel to include alladd-ins.




507




Using Excel’s Solver we will find the optimal predicted response. We will select to be changing

cells K26 and K27, the yellow fields. Our optimization will be subject to the following constraints:K27 = Binary - This limits the options for Supplier to 1 or 0.L26 <= 1 - This limits the Temp to ensure our maximum of 45, or the coded value 1L26 >= -1 - This limits the Temp to ensure our minimum of 25, or the coded value -1

By clicking solve, we are given the optimal result.

Please note, we will set Concentration to 5%. Since Concentration is insignificant, we will reduce itto the minimum value to save on cost and potentially to minimize variation.



508



Now that we have completed one example we are going to add to your knowledge base bycovering Center Points and run through another example adding further explanation of thestatistics as well.

Center Points

As you can see in the graphic there may be an unknown hump in the Response Curve, by addingthe Center Point it allows us to calculate an additional statistic. If there is significant curvature in themodel all we know is that the model is not Linear.

We don’t know what it is, just what it is not.




509


Center Point Clues

Pseudo Center Points areused when there arediscrete input variables inthe model.

The model can becollapsed creating realCenter Points if thediscrete input variablesare not significant.

If the desire was tomaximize the response(as shown in graphic) thenthe model doesn’t matter.The model is an important

tool to predict outputresponse inside thedesign space. If theexperimenter decides toset up another experimentto continue in the directionindicated, then predictingis not an issue.

Panel Cleaning Example


! # $%&$' ()*%& *+ , -.,/+ , 0))1 *%+2',%3$ 4)-*3/5 62& *+ 7)+& $88$3&*9$

.:$% , -- &:$ *%42& 8,3&)'+ ,'$ # )%&*%2)2+;

! 02*1$-*%$ *+ &) '2% < => # $%&$' ()*%& '2%+ 1*+&'*62&$1 2%*8)'7-/ &:')20:

&:$ $?4$'*7$%& .:$% ,-- &:$ *%42& 8,3&)'+ ,'$ 3)%&*%2)2+ *% , @2-- )'@',3&*)%,- @,3&)'*,-;

A

?“-” “+”“c”

!" # $%$&' )'*+, -*'A

?“-” “+”“c”

A

?“-” “+”“c”

!" # $%$&' )'*+, -*'

.,'* $/ %"//'0 /1"/

/1' 2 $-'"0 %,3'2 $*

$-"++0,+0 $"/'4

!" $%&' ()* +,-( .( .&-- .*-/ $%0123% $%( 44 '$(, 56 7 +($%181-139 :10* ,* "(- ;-(*"&"3 +*;%&"( 2'&"3 < ("$(0 =1&"$' &" $%( *"* -9'&'> ?%(+*"2:*;$20&"3 :&0+ &' *$$(+,$&"3 $1 '$*0$ 2, * "(. ,*"(- ;-(*"&"3+*;%&"( *"8 .12-8 -&/( $1 3($$&"3 &$ 02""&"3 @2&;/-9> ?%(9 %*A((),(0&(";( .&$% $%&' $9,( 1: +*;%&"(B C2$ $%(9 81 "1$ %*A( (),(0&(";(.&$% $%&' ,*0$&;2-*0 +18(- 1: (@2&,+("$>

! " !"# $%" '(" ) *+,'$,+- )*. /-"0

D E$*0$ $%( "(. (@2&,+("$ *' (::&;&("$-9 *' ,1''&C-(> ?%( "((8 :10 $%( "(.(@2&,+("$ .*' 8($(0+&"(8 &" $%( F"*-9G( =%*'(>

D F H(*'20(+("$ E9'$(+ F"*-9'&' %*' C((" ;1+,-($(8 *"8 +18&:&(8 $1 C0&"3.&$%&" *;;(,$*C-( 32&8(-&"('>

# " 12'+/ -$2( '(" 13 4 "*$0 "% '+ - 5 /6",'$7 "

D I&$ * $*03($ :10 J &8$% 1: KL MN O P>

D H&"&+&G( A*0&*$&1" *' +2;% *' ,1''&C-(>



510


Panel Cleaning Example (cont.)

Na2S2O8 is SodiumPersulfate; pleaseuse that any timeyou see that

notation.

Center Points not only tell us something about how well the linear model works, but is also areality check for our data. By eyeballing the Center Point data as our experiment progressed wecan see if anything has effected our experiment that we were not expecting. If your Center Pointsare dramatically different from each other, you’ve got a problem -- somewhere. They should befairly close in magnitude, at least within normal variation.


! " #$%$&' ')$ * +',+' -.$/,0 1/$2 3 4. 546 %$/

! " #$%& () *(+$,*%(- #. %&/ (+01 -/.2(+./3

7 " #$%$&' ')$ 81,+ ' - 519$ ,$1 9$1 '2 34. 546 %$/! 45/00 6#7/

! 6/72/-8%,-/

! 9 8 :;:< =

! 6&/ />2/-%. ?/0#/@/ %&8% 87?#/+% %/72/-8%,-/ 8+$ &,7#$#%1 5#00 &8 @/+( /))/*% (+ %&/ 2-(*/..3 A(+#%(-. 5#00 ?/ 208*/$ #+ %&/ -((7 %(-/*(-$ %/72/-8%,-/ 8+$ &,7#$#%13

:" ;)00/$ ')$ <$=$%/ >0. ')$ 81,+' 34. 546%$/

B 45/00 6#7/ C D E F G 7#+,%/.

B 6/72/-8 %,-/ CDH E =HG I

B 9 8 :;:< = CJ3=E :3D G K7L 0#%

Use the “Panel Cleaning DOE” worksheet

You actually know the answer already since the sample size is the same as the previous exampleand they were both 2 cubed designs. Look at your worksheet and find the Center Point runs. Whyare the Center Points uniformly distributed?



511


Creating Designs with Center Points

You most likely already know how to create a design with Center Points added. Simply go throughthe usual steps to create a design and include Center Points.

Your design should look different than the one in the illustration because we more likely than not havea different random seed that generated the designs. It is possible that our designs are the same, buttrying to calculate the odds of that occurring is not worth the bother. You should have 19 rows in yourdesign, so if you do not, go back and fix it.




512


Creating Designs with Center Points

Let’s continue with the Panel Cleaning Example. Use the “Panel Cleaning DOE” worksheet.

Do the same for theCenter Point you want inthe middle and end of thedesign. We have color

coded our example forease of understanding.The rows you move mostlikely will be different.

Use Excel’s Sort to sortthe worksheet by RunOrder (Data>Sort).

You should now have aworksheet that has a

Center Point at or nearthe beginning, middleand end. If your originaldesign had the CenterPoints roughly in thosepositions, great thatsaved a little work.





513


Analyze the experimentin SigmaXL®. For funsince you’ve alreadydone this once in this

module, stop readingand work on your ownfor a while. When youthink you know whatshould be removed fromthe model, go aheadand do it.


So how did it go?Looks like thesignificant effects areSodium Persulfate,temperature, theinteraction of tempwith SodiumPersulfate and dwelltime in that order ofimportance.


The P-values from the analysis in the session agree as well.



514



Re-fit the model byremoving the insignificantfactors if you have notalready done this. Be

sure to generate thenecessary StandardizedResidual Plots.

The Residual error is broken into 2 sources. The 3 degrees of freedom for lack of fit are from the 3interaction effects that were removed from the model because they were not significant in explainingthe variation of the data. The 10 degrees of freedom come from replication. The 8 runs from theoriginal design generated 8 degrees of freedom, in this case there were 2 replicates minus 1 equals1 degree of freedom for each run in the design. Add to that 2 degrees of freedom from the CenterPoints (3 Center Points minus 1 equals 2 degrees of freedom) and we have a total of 10 degrees offreedom for pure error. Pure error can be defined as the failure of things treated alike to act alikewhich are the replicates.


Here we are going to define the calculations in the ANOVA table.

When working with 2 level designs you will always have 1 degree of freedom for each effect(including interactions) which is calculated as 2 levels minus 1 equals 1 degree of freedom. In the ANOVA table for Main Effects we have 3 degrees of freedom for the 3 Main Effects placed in themodel. There is one degree of freedom for the temperature Sodium Persulfate interaction.



516


Prediction Equation


Take a fewminutes to studythe equations.They really are

simply“plug and

chug”.

Please note, wehave takenliberties withrounding numbers!You won’t actuallyhave to do this byhand because thatis exactly what theresponse optimizer

does in SigmaXL®.

The most interesting thing to look at here is the interaction plot. The temperature with SodiumPersulfate interaction shows there is very little difference in the predicted response as long asSodium Persulfate is held at the high level. But if the concentration of Sodium Persulfate islowered, temperature and in particular 40 degrees lowers the width more rapidly than iftemperature was set at 80 degrees.




517



There are no assumption violations within the plots shown here.

As depicted here the Residuals Versus Factor Plots do NOT show any differences in the

variation of the data from the low to the high values.




518



Here we will use Excel’sSolver (Data>Solver) todraw some PracticalConclusions. Play with

Solver and see what youcan do remembering thatthe original objective wasto hit a target of 40 +/- 5for the width.


It looks like we can get close, but we can’t hit the target. We know our lower specification limit is 35and it looks like we can get to 38 with the Sodium Persulfate at the low level, temp and dwell timehigh. Is the good enough? Maybe, maybe not. If you knew the spread of the data or variation and itwas small you could capitalize on that capability by using 38 as the target instead of 40 and stillguarantee your customer they would never see any product with widths smaller than 35.

Imagine if you were working with gold or platinum. What effect could that have on the bottom line?

Are there other solutions? Explore your options by modifying the constraints in Solver or through experimentation withthe PredictedResponseCalculator. Solverdoes an excellent jobof optimizing

according to thedata. What it doesnot know are all thequirks of yourequipment, cost ofraw materials,increasingthroughput, etc.

Is it possible toachieve the targetvalue of 40 withSodium Persulfateset at the minimumvalue (to minimizecost)?



519






520



It’s awrap…….Fun stuff,

right?!


Now we will look at SigmaXL®’s Contour/Surface Plots to visualize the solution set of input variablelevel settings in order to achieve the desired result.

As shown here we generate 3 different graphs as a result of changing the set point for dwell time.

The areas highlighted in red (produced manually to aide interpretation) are the solution set foradjusting temperature and Sodium Persulfate to get a predicted response between 35 and 45. Thisis an alternative to the Response Optimizer.



521


You have now completed Improve Phase – Full Factorial Experiments.


! Understand how to create Balanced and OrthogonalDesigns

! Explain how Fit, Diagnose and Center Points factor into

an Experiment


Notes



522


Lean Six Sigma

Black Belt Training

Now we will continue with the Improve Phase “Fractional Factorial Designing Experiments”.

Improve PhaseFractional Factorial Experiments



523


Fractional Factorial Experiments


Why Use Fractional Factorial Designs?

We’ve shown two 4 factor designs side by side so you can contrast the two designs. Notice theFractional Factorial Design requires only a fraction of the experimental runs to evaluate 4 inputfactors. In this case, it is a half fraction. As with most things in life there is a price to be paid forreducing the number of runs required which we will go through in detail in this module.

Within this module wewill explore how toconduct a FractionalFactorial Experiment.

! "#$%&'(! "#$%&'(

)#(#"$%'"*)#(#"$%'"*

! '(+',(-&(. 0 1 #* '2,%&'(! '(+',(-&(. 0 1 #* '2,%&'(

3#*&.(*3#*&.(*

! "## !%& '()*%# + ,-.)*/.0'1! "## !%& '()*%# + ,-.)*/.0'1

+ ,-.)*/.0'%# 2.'3(41+ ,-.)*/.0'%# 2.'3(41

5.1*60*06 +,-.)*/.0'15.1*60*06 +,-.)*/.0'1

748%0&.4 9)(&.1 1 2(4.#*06:

2; <

748%0&.4 9)(&.1 1 2(4.#*06:

2; <

9)(&.1 1 2(4.#*06: <.6 ).1 1 *(09)(&.1 1 2(4.#*06: <.6 ).1 1 *(0

=.#&(/. '( >/-)(8.=.#&(/. '( >/-)(8.

! )%&'*(0%# ! %&'()*%# + ,-.)*/.0'1! )%&'*(0%# ! %&'()*%# + ,-.)*/.0'1

=)%- ?- @ 7& '*(0 >'./1=)%- ?- @ 7& '*(0 >'./1

FractionalFactorialDesigns are apowerful sub-setof FactorialDesigns. As thename implies,you may expectthey are somefraction of the

original FactorialDesigns – andyou’d becorrect. Thequestion is whatfraction?



525


Nomenclature for Fractional Factorials

The general notation for aFractional Factorial issimilar to that of a FullFactorial. Take a few

moments and read throughthe definitions for thenotation.

Let’s look at the 2 to the 5minus 1 example here:How many factors are inthe experiment? That is thefirst number in the exponentor in this case, 5.

At this point we are notready to discuss theresolution since we havenot covered it yet.

Half-Fractional Experiment Creation

How many runs if no repeats or replicates? Simply do the math. 2 to the 5 minus 1 is the same as2 to the fourth which is 8 runs.

What Fractional Design is this? Since this design uses only half the number of runs as a FullFactorial with 5 factors it is a half fraction.

!"# % #& #'( ) & *+( +,*& -*'

.'( /+,*& ( ) .( /+*',( )0 ,01

! " $ %&'()* +, ,- ./+*0 /+ () 1%2)0/13- /)4

! 5 $ %&'()* +, ,-./+*0 - 0013%)4 /+ -% 1%/)*-./1+% . +6&'% 7- 60+ .- 66)4

84)3*)) +, ,*-./1+%-/1%39 :1/; <$< = >? > $< = @?A $< = B? )/.CD

! E $ 4)013% *)0+6&/1+% 7FFF? FG? G? )/.CDC F/ 4)/-160 -'+&%/ +,

.+%,+&%41%3 /+ .+'5-*) 4)013% -6/)*%-/12)0

! > "H5 $ /;) %&'()* +, )I5)*1')%/-6 *&%0

J;) )I-'56) .6-*1,1)0 ;+: /+ &0) /;) %+')%.6-/&*)C

K L+: '-%M ,-./+*0 1% /;) )I5)*1')%/N

K L+: '-%M *&%0 1, %+ *)5)-/0 +* *)561.-/)0N

K O ;-/ ,*-./1+%-6 4)013% 10 /;10 7<= B? <= @ +* <= >DN

22kk--pp

RR22

kk--pp

RR

2255--11

VV22

55--11

VV22

55--11

VV




526


Half-Fractional Experiment Creation

Having 4 runs can not project 4 factor therefore, this would have 3 degrees of freedom, so theanswer is a big fat NO.

Why would we call this a half fraction? Because half the number of runs is necessary as apposedto that of a Full Factorial.

Graphical Representation of Half-Fraction

!"# %& '"( )(&%*+, & "-.+ /& -0/+*( 0-.& , 1/22() / 3"/245 40/1'%-+6 7"%& %& '"( )(& %*+

89& ' 1 0(/'() -+ '"( :0(; %-9& & 2%) (< 7 "%& %& / "/24 40/1 '%-+ & %+ 1 ( / 4922 => => => = 4/1 '-0%/2.-92) '/?( @A 09+& < !%'" '"( "/24 40/1'%-+ .( 1 /+ (& '%B/'( '"( ( 44(1'& -4 C 4/1 '-0& %+ D

09+& < !"/' %& '"( 1-& '6 !( 2-& ( '"( /E%2%'# '- & '9)# '"( "%* "( 0 -0)(0 %+'(0/1'%-+

%+)(:(+)(+'2#F

Half Fraction:

Alias Structure:

D = ABC

Note D settings

are the same as

the ABCinteraction

G -92) .( 1 0(/'( / H9/0'(0 40/1'%-+ (>:(0%B(+' -9' -4 '"( /E-;(

B/'0%> /+) & '%22 &'9)# 4-90 4/1'-0& /' -+1(6

!"# -0 ."# +-'6

A B C D AxB AxC BxC AxBxC

-1 -1 -1 -1 1 1 1 -1

1 -1 -1 -1 -1 -1 1 1

-1 1 -1 -1 -1 1 -1 1

1 1 -1 -1 1 -1 -1 -1

-1 -1 1 -1 1 -1 -1 1

1 -1 1 -1 -1 1 -1 -1

-1 1 1 -1 -1 -1 1 -1

1 1 1 -1 1 1 1 1

-1 -1 -1 1 1 1 1 -1

1 -1 -1 1 -1 -1 1 1

-1 1 -1 1 -1 1 -1 11 1 -1 1 1 -1 -1 -1

-1 -1 1 1 1 -1 -1 1

1 -1 1 1 -1 1 -1 -1

-1 1 1 1 -1 -1 1 -1

1 1 1 1 1 1 1 1

!" $%&" '()*+) )"' $%,-.-/%* 0(12%, 3 45"/(6"20%, 7") (82) -1/ 9 -%*01/) :

; $" 8/%5$(*% , /"5/")"20%0(12 )$1<) 0$" = /+2) <" */"%0"' 12 0$" 5/"&(1+) >

),('")?

@ "6"6A"/ 0$%0 7 () *12-1+2'"' <(0$ 0$" BC D (20"/%* 0(12 (2 0$() $%,-.-/%*0(12%,

'")(82?

A

B

C

C

+

-

+

+

+

-

-

-

D- +

A +-A

B

C

C

+

-

+

+

+

-

-

-

D- +

A +-!"# %&'( ") #*(+&",- - %&.(




528


Design Generators (cont.)

SigmaXL® Aliasing

This SigmaXL® output gives thesummary of whatyou did on theprevious slides much

quicker than we cando by hand. Thereason we have youdid things manuallyearlier is to being toappreciate andunderstand theSigmaXL® outputgenerated below thedata table after youcreate a Fractional

Factorial design with4 factors, halffraction with noCenter Points or replicates and the number of blocks equal to 1. You should get the same output.Try it.

Notice after the design structure an alias structure is indicated. We can see the AB 2-way interactionis Confounded with the CD 2-way interaction meaning we cannot distinguish if the interaction isstatistically significant whether it is a result of the AB or CD interaction or a combination.




529


So What is “Confounding ”?

Using more enhance visuals, here is another Fractional Design structure, notice how the Aliasstructure A is Confounded with the two way interaction. The light green box indicates this to be truethe most obvious.

Confounded Effects With Fractionals

! "#$"%#&'#( '* +,- ."#*-/%-#.- 0 # -12-3'4-#+-3 0. .-2+* $"3 #"+ 3%##'#( 05%66 50.+"3'06 7-*'(#8

9 ,-# %*'#( +,- :! "#$"%#&'#( ; "3 :< 6'0*; 20 ++-3# =- 0**%4- +,0+ +,-,'(,-3 "3&-3 '#+-30.+'"#* '# 0 ! "#$"%#&-& -$$-.+ 03- #"+ *'( #'$'.0#+8

> ?20 3*'+@ "$ -$$-.+* 23'#.'26- '#&'.0+-* +,0+ ,'( ,-3 "3&-3 '#+-30.+'"#*03- A-3@ 303-8

B ! " #$ %& $()&*+,)$-(. +*& $/0 -*)+() )#&1 2- (-) + 3- 4(2 5 6$( )&* + ,)$- ( . )# + ) + * & / - * & ,- / 0 %&7 )# + ( )# - .& $( 8 - %8 $( 9): - ;+ ,)- * . + * & * + * &< =# - / + . > ? >+ * @ &*

C# +,- 20 *+ -10 426-D +,- 7 $0.+"3 =0* ! "#$"%#&-& ='+, +,- < E! F G=0 @'#+-30.+'"#8 9 ,-# +,- -$$-.+ '* 0**'(#-& +" 7 =,'., '* ! "#$"%#&-& ='+,< E! D =- 0 **%4- H-.0%*- "$ +,- *20 3*'+@ "$ -$$-.+* 23'#.'26- +,- -$$-.+ '*-#+'3-6@ H-.0%*- "$ +,- 7 $0.+"38

I-4-4H-3 =,-# +=" '+-4* *%., 0* 0# '#+-30.+'"# ='+, 0 J0'# K$$-.+ 03-! "#$"%#&-&D "#- .0 ##"+ &'*+'#(%'*, '$ +,- *+0+'*+'.0 6 *'(#'$'.0 #.- '* 0 3-*%6+"$ +,- J0'# K$$-.+ "3 +,- '#+-30.+'"# "3 0 ."4H'#0+'"#8

! "#$ %#&' #% $ &) *+,- *,-. /)- 0 1) &/)2 &3 #&' 4 5




530


Experimental Resolution

!!

""##$$

%%!!

""##$$

%%

%&'&'(&) % +, -.& ,/'&,012-3)& )&4&)&,0&5 -.& %&6/13-+/,7

8.+6 36&431 9+6321 2+5 )&'&'(&)6 5&4+,+-+/,6 /4 -.&

: /,4/3,5+,; 5&6+; ,2-&5 (< -.& %&6/13-+/,7

Resolution IV

Next hold up four fingers

The Confounding is main effects with

three way interactions or !

Two way interactions Confounded with

other two way interactions.

Main EffectsMain Effects Two Way InteractionsTwo Way Interactions

Resolution III

Hold up Three Fingers, One on one

hand and Two on the other. This

illustrates the Confounding of main

effects with two way interactions.

Main EffectsMain Effects Three Way InteractionsThree Way Interactions

Two Way InteractionsTwo Way Interactions Two Way InteractionsTwo Way Interactions

Fully Saturated Design

Main EffectsMain Effects

Three Way InteractionsThree Way Interactions

Four Way Interactions

Resolution V

Hold up Five Fingers, One on one hand and

Four on the other. This illustrates the

Confounding of main effects with four way

interactions or!

Two way interactions Confounded with

three way interactions.

Two Way InteractionsTwo Way Interactions

!"# %&'()* )&+ &' '",-. /"0,(1" 2#',*(/&,. 34

22

kk--pp

RR22

kk--pp

RR




531


SigmaXL® Fractional Factorial Design Creation

We have already seenthis SigmaXL® after aFractional FactorialDesign was created.SigmaXL® automatically tells usthe Resolution and ifwe use the handstechnique toremember the Aliasingtype of structure, wecan save time. TheResolution can getvery complicated withthose screening

Fractional FactorialDesigns with factorsmore than 5 so thishelps is desirable.

2 V(5 -1) Fractional Design Resolution V

B

CA

D

E

! #$%&'() *+$,- .##/%&)0

12 345$6 ,-&/($%&,'-)

+$,- .##/%&) '-76 8 '-#'9-:/:

5,&; ($(/ < 45$ 6 ,-&/($% &,'-)

1= &(,$7) &' >/& ! +$,- .##/%&)

3-: '(:/( ,-&/($%&,'-) $(/

8 '-#'9-:/: 5,&; ?(: '(:/(

Run A B C D E

1 -1

2 1

3 -1

4 1

5 -1

6 1

7 -1

8 1

9 -1

10 1

11 -1

12 1

13 -1

14 1

15 -1

16 1

-1

-1

1

1

-1

-1

1

1

-1

-1

1

1

-1

-1

1

1

-1

-1

-1

-1

1

1

1

1

-1

-1

-1

-1

1

1

1

1

-1

-1

-1

-1

-1

-1

-1

-1

1

1

1

1

1

1

1

1

1

-1

-1

1

-1

1

1

-1

-1

1

1

-1

1

-1

-1

1

! " # $ % # & $

B

CA

D

E

! #$%&'() *+$,- .##/%&)0

12 345$6 ,-&/($%&,'-)

+$,- .##/%&) '-76 8 '-#'9-:/:

5,&; ($(/ < 45$ 6 ,-&/($% &,'-)

1= &(,$7) &' >/& ! +$,- .##/%&)

3-: '(:/( ,-&/($%&,'-) $(/

8 '-#'9-:/: 5,&; ?(: '(:/(

Run A B C D E

1 -1

2 1

3 -1

4 1

5 -1

6 1

7 -1

8 1

9 -1

10 1

11 -1

12 1

13 -1

14 1

15 -1

16 1

-1

-1

1

1

-1

-1

1

1

-1

-1

1

1

-1

-1

1

1

-1

-1

-1

-1

1

1

1

1

-1

-1

-1

-1

1

1

1

1

-1

-1

-1

-1

-1

-1

-1

-1

1

1

1

1

1

1

1

1

1

-1

-1

1

-1

1

1

-1

-1

1

1

-1

1

-1

-1

1

Run A B C D E

1 -1

2 1

3 -1

4 1

5 -1

6 1

7 -1

8 1

9 -1

10 1

11 -1

12 1

13 -1

14 1

15 -1

16 1

-1

-1

1

1

-1

-1

1

1

-1

-1

1

1

-1

-1

1

1

-1

-1

-1

-1

1

1

1

1

-1

-1

-1

-1

1

1

1

1

-1

-1

-1

-1

-1

-1

-1

-1

1

1

1

1

1

1

1

1

1

-1

-1

1

-1

1

1

-1

-1

1

1

-1

1

-1

-1

1

! " # $ % # & $

.@$AB7/ '# $ C/(6 9)/#97 D($%&,'-$7 E/),>- '#&/- 9)/: #'( )%(//-,-> :/),>-)F




533


Fractional Factorial Example

This is a two to the eighth minus four power design with a resolution four design. This design has16 runs as you see in the slide with all eight factors at two levels.




534


Fractional Factorial Example (cont.)

Take a look at what Confounding exists before you jump into analysis. SigmaXL® does not reportConfounding with 3-way interactions.




535



We chose to set alpha to 0.1 initially but this is not required. We find the factors with important MainEffects are E, H and B. The 2-way interactions AC, AF and AE seem important at an alpha level of0.1.




536






537




Statistical Conclusions to maintain terms in the model must cons ider: ! Maintaining hierarchical order

! A 2 - way interaction must have the involved factors in the model also ! High statistical confidence with the P - value less than your alpha risk ! A higher R - sq or model explanation of the process changes is desired ! Proper residuals and few to no unusual observations

Statistical Conclusions to maintain terms in the model must consider: ! Maintaining hierarchical order ! A 2 - way interaction must have the involved factors in the model also ! High statistical confidence with the P -value less than your alpha risk ! A higher R - sq or model explanation of the process changes is desired ! Proper residuals and few to no unusual observations

No, no unusual

observations here … No, no unusual

observations here…



538






539




Practical Conclusions to keep in the model include:! Simple models can be useful depending on the project or process

requirements! Terms with practically large enough significance even if statistically

significant

! Impact of R-sq by removing a term with low effects

! Ability to set and control the controllable inputs in the model may

decide on the use of terms

! Robust designs or minimal variation requirements may require

close inspection of interactions effects on the Y

! If multiple outputs are involved in the process requirements,

balancing of requirements will be necessary

That

s a lot of juggling…

10. Replicate or Validate the Experimental Results

!

After we have determined with 95% statistical confidence, we mustreplicate the results to confirm our assumptions; such as which 2-way

interactions were significant among the Confounded ones

! If the results do not match the expected results OR the project goal,

further experimentation may be needed

! In this case, we were able to achieve 29.8 on average with the

process setting of B, E and H and so the results are considered

successful in the project

We win, we win…



540



! ! " #$ %&'$ '() +,&-).,(/

! ! "#$ &'() ()* +#",*-- . &/*#- 0/1 1*2*3"4 ()* 5 "/(#"3 +30/-

(" -6-(0'/ 7"6# -6,,*--

Fractional Factorial Exercise




541



• Explain why & how to use a Fractional Factorial Design

•

Create a proper Fractional Factorial Design

• Analyze a proper model with aliased interactions

You have now completed Improve Phase – Fractional Factorial Experiments.


Notes

Not that kind of model



542


Lean Six Sigma

Black Belt Training

Congratulations on completing the training portion of the Improve Phase. Now comes theexciting and challenging part…implementing what you have learned to real world projects.

Improve PhaseWrap Up and Action Items



543



Improve Phase Overview—The Goal

Improve Phase Action Items

Before beginning the Control Phase you should prepare a clear presentation that addresses eachtopic shown here.

This is a summary ofthe purpose for theImprove Phase. Avoid getting into

analysis paralysis,only use DOE’s asnecessary. Mostproblems will NOTrequire the use ofDesignedExperimentshowever to qualify asa Black Belt you atleast need to havean understanding of

DOE as described inthis course.

!"# % &' ( &) *"# +, -.& /# 0"' 1# 21 *&3

! "#$#%&'(# $*# +,$'&-. .#/#.0 +1 $*# /-%'-2.#0 3*'4* -%# 0'5('1'4-($.6'&,-4$'(5 6+7% 8%'&-%6 9#$%'4:

! "#&+(0$%-$# - 3+%;'(5 ;(+3.#<5# +1 &+<#.'(5 -0 - &#-(0 +1

,%+4#00 +,$'&'=-$'+(:

! "#$%&' )&*+, - .& %/& 012.+3& 4/-$& '&*#3&.-)*&$ %/-% &-5/ 5-6'#' -%&

,#** 2.&$&6% #6 - 4+,&. 4+#6% 2.&$&6%-%#+6 -% %/& )&7#66#67 +8 %/&

9 +6%.+* 4/-$& %.-#6#67:

! ;% %/#$ 2+#6% <+= $/+=*' - ** =6'&.$%-6' ,/-% #$ 6&5&$$-.< %+ 2.+3#'&

%/&$& '&*#3&.-)*&$ #6 <+=. 2.&$&6%-%#+6:

> ?&-1 @&1)&.$ A?&-1 @&&%#67 ; %%&6'-65&B

> 4.#1-.< @&%.#5

> C&5+6'-.< @&%.#5A$B

> DE2&.#1&6% F=$%#8#5-%#+6

> DE2&.#1&6% 4*-6 G H )I&5 %#3&

> DE2&.#1&6% J&$=*%$

> 4.+I&5% 4*-6

> 0$$=&$ -6' K- ..#&.$

!"#$ & '() $*'+,t s your show



544


Six Sigma Behaviors

Improve Phase - The Roadblocks

Each phase will have roadblocks. Many will be similar throughout your project.


! "#$%& (#%)*$+,-. *+,/)&#+,-

! "#$%& /$&+/+,-. 0$-*$12$%#0

! 3)4$%& 0)()56)-#0 0#*$-$+%-

! 786/)*$%& *9)%&# : *+%($%,+,- 2#)/%$%&

! ;9)/$%& 6#-( 1/)*($*#-

!"#$ & ' (" ) *+, -. /$* 0 -1 0 -23 " ' +4#*55 3 65/ 7*

8 9 : ;! <: =!;

>4 + /$ * 0 -1 0 -2 3 " #6 (/6 +* ?

!"#$!"#$ & & ' (" ) * + ' (" ) *+ , , -. /$* 0 -1 0 -23 " ' +4#*55 3 65/ 7*-. /$* 0 -1 0 -23 " ' +4#*55 36 5/ 7*

8 9 : ;! <: =!; 8 9 : ;! <: =!;

>4 + /$ * 0 -1 0 -2 3 " #6 (/6 +* ? >4 + /$ * 0 -1 0 -2 3 " #6 (/6 +* ?

!"#$

&'(

!"#$)

!""# %"& '() *"')+',-. &"-/0."1#2 -+/ *.-+ '" -//&)22 '()3 0)%"&) '()40)1"3) *&"0.)325

6 !-1# "% /- '-

6 7- '- *&)2)+')/ ,2 '() 0)2' 89)22 04 %9+1',"+-. 3-+- 8)&2

6 :)-3 3)30)&2 /" +"' (-;) '() ',3) '" 1"..)1' /-'-

6 <&"1)22 *- &',1,*-+'2 /" +"' *- &',1,*-') ,+ '() -+-.42,2 *.- ++,+8

6 !-1# "% -11)22 '" '() *&"1)22

Walk

the

Walk



545


DMAIC Roadmap

Improve Phase

The objective of the Improve Phase is simple – utilize advanced statistical methods to identifycontributing variables OR more appropriately optimize variables to create a desired output.

Over 80% of projects will realize theirsolutions in the Analyze Phase –Designed Experiments can be extremelyeffective when used properly, it isimperative that a Designed Experiment is justified. From an application andpractical standpoint, if you can identify asolution by utilizing the strategy and toolswithin the Measure and Analyze Phases,then do it. Do not force DesignedExperiments.

Remember, your sole objective inconducting a Lean Six Sigma project is tofind a solution to the problem. Youcreated a Problem Statement and anObjective Statement at the beginning ofyour project. However you can reach asolution that achieves the stated goals inthe Objective Statement, than implementthem and move on to another issue –

there are plenty!


!"#$%&'( *+,-.#/ 0 +#1

022#22 3 %1-&.&%(4 5 161- &.&%( 1$" 7#128+#/#$% 3(2%#/2

!"#$%&'( 1$" *+&,+&%&9# 0.. :;2

*+,<#=>&26+,<# !/61?% :;2 @1<# A $ *+,-.#/

!"#$%&'(4 *+&,+&%&9#4 3#.#?% 3,.8%&,$2 5 ,$%+,. ,+ B.&/&$1%# :;2 51 82&$C *+,-.#/2

!/6.#/#$%3 ,.8%&,$2 %, 5 ,$%+,. ,+ B.&/&$1%# :2 5 182&$C *+,-.#/2

!/6.#/#$% 5 ,$%+,. *.1$ %, B$28+# *+,-.#/ >,#2$ ;% D#%8+$

E#+&'( F&$1$?&1. !/61?%

>#%#+/&$# 066+,6+&1%# *+,G#?% F,?82

B2%&/1%# 5A *H

B2%1-.&2I J#1/

5 I 1 / 6 & , $ =

* + , ? # 2 2 A K $ # +

> # ' & $ #

7 # 1 2 8 + #

0 $ 1 . ( 9 #

! / 6 + , < #

5 , $ % + , .

!"#$%&'( *+,-.#/ 0 +#1

022#22 3 %1-&.&%(4 5 161- &.&%( 1$" 7#128+#/#$% 3(2%#/2

!"#$%&'( 1$" *+&,+&%&9# 0.. :;2

*+,<#=>&26+,<# !/61?% :;2 @1<# A $ *+,-.#/

!"#$%&'(4 *+&,+&%&9#4 3#.#?% 3,.8%&,$2 5 ,$%+,. ,+ B.&/&$1%# :;2 51 82&$C *+,-.#/2

!/6.#/#$%3 ,.8%&,$2 %, 5 ,$%+,. ,+ B.&/&$1%# :2 5 182&$C *+,-.#/2

!/6.#/#$% 5 ,$%+,. *.1$ %, B$28+# *+,-.#/ >,#2$ ;% D#%8+$

E#+&'( F&$1$?&1. !/61?%

>#%#+/&$# 066+,6+&1%# *+,G#?% F,?82

B2%&/1%# 5A *H

B2%1-.&2I J#1/

!"#$%&'( *+,-.#/ 0 +#1

022#22 3 %1-&.&%(4 5 161- &.&%( 1$" 7#128+#/#$% 3(2%#/2

!"#$%&'( 1$" *+&,+&%&9# 0.. :;2

*+,<#=>&26+,<# !/61?% :;2 @1<# A $ *+,-.#/

!"#$%&'(4 *+&,+&%&9#4 3#.#?% 3,.8%&,$2 5 ,$%+,. ,+ B.&/&$1%# :;2 51 82&$C *+,-.#/2

!/6.#/#$%3 ,.8%&,$2 %, 5 ,$%+,. ,+ B.&/&$1%# :2 5 182&$C *+,-.#/2

!/6.#/#$% 5 ,$%+,. *.1$ %, B$28+# *+,-.#/ >,#2$ ;% D#%8+$

E#+&'( F&$1$?&1. !/61?%

>#%#+/&$# 066+,6+&1%# *+,G#?% F,?82

B2%&/1%# 5A *H

B2%1-.&2I J#1/

5 I 1 / 6 & , $ =

* + , ? # 2 2 A K $ # +

> # ' & $ #

7 # 1 2 8 + #

0 $ 1 . ( 9 #

! / 6 + , < #

5 , $ % + , .

!"# $%&'& ) *+,$-.-

/0-".'1% 2-3 4'.#$ 56&

78,-9'+-". .* : ,.'+';- 4# $<- *1 56&

='+<$#.- .>- ? -3 @9*A-&&

4#$'0# .- ?-3 @9*A-&&

/+,$-+-". ? -3 @9*A-&&

B-#0% 1*9 ) *".9*$



546


Improve Phase Checklist

These are questions that the participant should be able to answer in clear, understandable languageat the end of this phase.

Planning for Action


!"#$$%$& ()* +%",( -#"%.#(%,$ /,0 10*#2()0,3&)

!0*4*$( 4(#(%4(%5#" +0,6%4* (, +0,5*44 ,7$*0

8 ,$5"3.* ,$ *9+*5(*. /%$#$5%#" 1 *$*/%(4

:5)*.3"* 0*4,305*4; /,0 %6+"*6*$(#(%,$ (%6*"%$*

!0*+#0* /,0 %6+"*6*$(#(%,$ ,/ /%$#" 6,.*"

< 1(#%$ 6#()*6#(%5#" 6,.*" (, 0*+0*4*$( +0,5*44

=$# ">4%4 ,/ 0*43"(4 /,06 >,30 ?< @

@9*53(%$& >,30 +"#$$*. ?< @

:5)*.3"%$& >,30 *9+*0%6*$(#" +"# $

= ? < @ (, 6**( >,30 +0,1"*6 4,"-%$& 4(0#(*&>

! " ## ! $ & " '# ! $# ! ( &# ! "# ! ) '

!"#$$%$& ()* +%",( -#"%.#(%,$ /,0 10*#2()0,3&)

!0*4*$( 4(#(%4(%5#" +0,6%4* (, +0,5*44 ,7$*0

8 ,$5"3.* ,$ *9+*5(*. /%$#$5%#" 1 *$*/%(4

:5)*.3"* 0*4,305*4; /,0 %6+"*6*$(#(%,$ (%6*"%$*

!0*+#0* /,0 %6+"*6*$(#(%,$ ,/ /%$#" 6,.*"

< 1(#%$ 6#()*6#(%5#" 6,.*" (, 0*+0*4*$( +0,5*44

=$# ">4%4 ,/ 0*43"(4 /,06 >,30 ?< @

@9*53(%$& >,30 +"#$$*. ?< @

:5)*.3"%$& >,30 *9+*0%6*$(#" +"# $

= ? < @ (, 6**( >,30 +0,1"*6 4,"-%$& 4(0#(*&>

! " ## ! $ & " '# ! $# ! ( &# ! "# ! ) '

Over the last decade of deploying Six Sigma it has been found that the parallel application of thetools and techniques in a real project yields the maximum success for the rapid transfer ofknowledge. Thus we have developed a follow up process that involves planning for action betweenthe conclusion of this phase and the beginning of the Control Phase. It is imperative that you

complete this to keep you on the proper path. Thanks and good luck!



547


At this point, you should:

You have now completed Improve Phase – Wrap Up and Action Items.

! Have a clear understanding of the specific action items

!

Have started to develop a project plan to complete the

action items

! Have identified ways to deal with potential roadblocks

! Be ready to apply the Six Sigma method within your

business


Notes

You re on your way



548


Lean Six Sigma

Black Belt Training

Now that we have completed the Improve Phase we are going to jump into the Control Phase.Welcome to Control will give you a brief look at the topics we are going to cover.

Control PhaseWelcome to Control



549


Welcome to Control

Overview

DMAIC Roadmap

These are the moduleswe will cover in theControl Phase as weattempt to insure that

the gains we havemade with our projectremain in place..


!"# !"% & ' () *+,)- .-' */!"# !"% & ' () *+,)- .-' */

01213+ ()*+,)-/01213+ ()*+,)-/

41'* ()*+,) -/41'* ()*+,) -/

5 6 7 ' * 31 6 ( ' 8 ' 9 " -"+:5 6 7 ' * 31 6 ( ' 8 ' 9 "-"+:

5 6 7 ' * 316 ; # 8 1, "& 1* +/5 6 7 ' * 316 ;# 8 1, "& 1* +/

< 1-3)&1 +) ()* +,)-< 1-3)& 1 +) () *+,)-

!+' +"/+"3' - .,)31/ / ( )*+,)-

= !. ( >

!+' +"/+"3' - .,)31// () *+,)-

= !. ( >

< ,' 8 ?8 @ 5 3+")* A +1& /< ,' 8 ?8 @ 5 3+")* A+1& /

!"#$%&'( *+,-.#/ 0+#1

022#22 3%1-&.&%(4 5 161 -&.&%(4 1$" 7#128+#/#$% 3(2%#/2

!"#$%&'( 1$" *+&,+&%&9# 0.. :;2

*+,<#= >&26+,<# !/61?% :;2 @1 <# A $ *+,-.#/

!"#$%&'(4 *+&,+&%&9#4 3#.#?% 3,.8%&,$2 5 ,$%+,. ,+ B.&/&$1%# :;2 5 182&$C *+,-.#/2

!/6.#/#$%3 ,.8%&,$2 %, 5, $%+,. ,+ B.&/&$1%# :;2 51 82&$C *+,-.#/2

!/6.#/#$% 5 ,$%+,. *.1$ %, B$28+# *+,-.#/ >,#2$;% D#%8+$

E#+&'( F&$1$?&1. !/61?%

>#%#+/&$# 066+,6+&1 %# *+,G#?% F,?82

B2%&/1%# 5A *H

B2%1-.&2I J#1/

5 I 1 / 6 & , $ =

* + , ? # 2 2 A K $ # +

> # ' & $ #

7 # 1 2 8 + #

0 $ 1 . ( 9

#

! / 6 + , < #

5 , $ % + , .

!"#$%&'( *+,-.#/ 0+#1

022#22 3%1-&.&%(4 5 161 -&.&%(4 1$" 7#128+#/#$% 3(2%#/2

!"#$%&'( 1$" *+&,+&%&9# 0.. :;2

*+,<#= >&26+,<# !/61?% :;2 @1 <# A $ *+,-.#/

!"#$%&'(4 *+&,+&%&9#4 3#.#?% 3,.8%&,$2 5 ,$%+,. ,+ B.&/&$1%# :;2 5 182&$C *+,-.#/2

!/6.#/#$%3 ,.8%&,$2 %, 5, $%+,. ,+ B.&/&$1%# :;2 51 82&$C *+,-.#/2

!/6.#/#$% 5 ,$%+,. *.1$ %, B$28+# *+,-.#/ >,#2$;% D#%8+$

E#+&'( F&$1$?&1. !/61?%

>#%#+/&$# 066+,6+&1 %# *+,G#?% F,?82

B2%&/1%# 5A *H

B2%1-.&2I J#1/

!"#$%&'( *+,-.#/ 0+#1

022#22 3%1-&.&%(4 5 161 -&.&%(4 1$" 7#128+#/#$% 3(2%#/2

!"#$%&'( 1$" *+&,+&%&9# 0.. :;2

*+,<#= >&26+,<# !/61?% :;2 @1 <# A $ *+,-.#/

!"#$%&'(4 *+&,+&%&9#4 3#.#?% 3,.8%&,$2 5 ,$%+,. ,+ B.&/&$1%# :;2 5 182&$C *+,-.#/2

!/6.#/#$%3 ,.8%&,$2 %, 5, $%+,. ,+ B.&/&$1%# :;2 51 82&$C *+,-.#/2

!/6.#/#$% 5 ,$%+,. *.1$ %, B$28+# *+,-.#/ >,#2$;% D#%8+$

E#+&'( F&$1$?&1. !/61?%

>#%#+/&$# 066+,6+&1 %# *+,G#?% F,?82

B2%&/1%# 5A *H

B2%1-.&2I J#1/

5 I 1 / 6 & , $ =

* + , ? # 2 2 A K $ # +

> # ' & $ #

7 # 1 2 8 + #

0 $ 1 . ( 9

#

! / 6 + , < #

5 , $ % + , .



550


Control Phase Finality with Control Plans

Welcome to Control

!"#$%&'"'() +','-)'.

/'&',%# 0$12(2(3 4,1(

!"#,'"'() 0$12(2(3 4,1(

/'&',%# /%-5"'()1)2%( 4,1(

!"#,'"'() /%-5"'()1)2%( 4,1 (

/'&',%# 6%(2)%$2(3 4,1(

!"#,'"'() 6%(2)%$2(3 4,1(

7 % )% 8 '9) 4$%:'-)

/'&',%# ;'<#%(<' 4,1(

!"#,'"'() ;'<#%(<' 4,1(

/'&',%# 4,1( )% =,23( +><)'"< 1(. +)$5-)5$'<

=,23( +><)'"< 1(. +)$5-)5$'<

?'$2@> A2(1(-21, !"#1-)

!"#$%&'"'() +','-)'.

/'&',%# 0$12(2(3 4,1(

!"#,'"'() 0$12(2(3 4,1(

/'&',%# /%-5"'()1)2%( 4,1(

!"#,'"'() /%-5"'()1)2%( 4,1 (

/'&',%# 6%(2)%$2(3 4,1(

!"#,'"'() 6%(2)%$2(3 4,1(

7 % )% 8 '9) 4$%:'-)

/'&',%# ;'<#%(<' 4,1(

!"#,'"'() ;'<#%(<' 4,1(

/'&',%# 4,1( )% =,23( +><)'"< 1(. +)$5-)5$'<

=,23( +><)'"< 1(. +)$5-)5$'<

?'$2@> A2(1(-21, !"#1-)



551


Lean Six Sigma

Black Belt Training

Now we will continue in the Control Phase with “ Advanced Experiments”.

Control PhaseAdvanced Experiments



552


Advanced Experiments

Overview

Beginnings of Control Phase

This module is the Advanced DOE module. At first thought, you might wonder why this is covered inthe Control Phase instead of the Improve Phase. We include the Advanced DOE in this ControlPhase to emphasize the iterative nature of Design of Experiments. The iterative nature can includea quick, statistically based technique for finding the highest or lowest response output known as the

steepest ascent or descent. We cover this methodology in depth including an example andsummary.

You’ve already narrowed to the “vital few” with the Define, Measure, Analyze and Improve Phases.

Just because you’ve found the “vital few”, may not mean you have the final results desired fromthe project scope.

The Control Phase involves controlling the X’s where you need the Y to perform.

If you haven’t achieved the output desired, one more DOE tool exists to help find where the inputsshould be.



553


Reminder of Iterative Nature for DOE

Purpose

The purpose of performing a Designed Experiment is to determine:#

The mathematical relationship Y=F(x1, x2, x3,…).#

Which X's most impact Y, and therefore need to be controlled#

The level of each X to achieve the desired mean Y# The level of each X to minimize the variability of Y

A DOE is needed only if this information cannot be obtained from passive analysis of the process.#

The danger of NOT running a Designed Experiment is the ability to prove cause and effect.!

Regressions, correlations or multi-linear regressions show relationships butcannot prove cause-effect relationships!

DOE’s prove cause and effect because variables are changed and the effect ismeasured in the output(s) of interest

Steepest ascent/descent designs use proven cause-effect relationships and achieve quickimproving results for a project.

DOE is an iterative process, the approach taken depends on the information that is known.

Steepest ascent/decent is another method used to increase our knowledge and is used inconjunction with factorials and/or response surface methods.




554


Steepest Ascent

This methods starts with a Full or Fractional Factorial as the base to determine the direction ofsteepest ascent/decent.

#

This method works best when there is no significant curvature in the model used todetermine direction, linearity is an assumption

The direction of ascent is determined using the coefficients in the Prediction Equation. This

method works best with a small number of variables; just 2 or 3.

Steepest Ascent/Descent

The method of steepestascent guides you toward atarget outside the originalinference space.

The method takes the mosteconomical or shortest routetowards the target by stayingon the path of steepestascent.

How can the PredictionEquation from the original

experiment miss the mark?


Inference Space



555


2-Factor Example for Steepest Ascent


Stepping Along the Path of Steepest Ascent

Our simulated process will be run atthe dotted points along the line sowe can observe the “Y” or theoutput.



556


Steepest Ascent Steps

At some point, once a localmaximum has been detected,another factorial DOE may be

necessary to determine the nextdirection.

Taking a New Direction When Appropriate

Step 1: Obtain the coefficients for the prediction equation from a factorial DOE (must use coded

variables)

Step 2: Select the Base factor:•

Most difficult to adjust•

Discrete levels•

Largest coefficient (This is recommended)

Step 3: Determine the step size, in coded units, that you will move in the direction of the BaseFactor

Step 4: Determine the step size for the other factors

Step 5: Move along the path and run the process at each step, continue along the path until eitherthe target value is achieved, or until a local maximum is reached

Step 6: If necessary, conduct another DOE to determine a new steepest ascent path, and repeatsteps 1-5


3322110 X bX bX b bY +++=



557


Example of Projection Vector Method

Choosing the Step Size




558


Other Factor Step Size


Work through each step to find the optimum result.



559


Process Results from Steepest Ascent




560



Notes

You have now completed Control Phase – Advanced Experiments.

! Use the results of a DOE to determine how to furtheroptimize a process using the steepest ascent/descent method




561


Lean Six Sigma

Black Belt Training

Now we will continue in the Control Phase with “ Advanced Capability”.

Control PhaseAdvanced Capability



562


Advanced Capability

Overview

Beginnings of Control Phase

Within this module we will explore using Process Capability to show a difference in processperformance as a result of your project efforts as well as review it as a monitoring tool to ensuresustainability of improved efforts.

You’ve already narrowed to the “vital few” with the Define, Measure, Analyze and Improve Phases.Just because you are able to achieve results with your project or through a DOE does not mean youhave Process Capability.

This module in the Control Phase gives you tools and ideas to tackle Special Causes that may behampering your Process Capability even if you found your “vital few” to get an improved average.

By this time you should have made improvements with your project. How do you know? Well theobvious is by continually monitoring your primary metric, which we know you have been doing,

right? Within this module we are going to look at another method to prove your project’s impact onthe process with a more quantified approach. We will compare the Capability established in the

Measure Phase to a Capability Analysis here in the Control Phase. Ready to have some fun…



563


Capability and Monitoring

Capability Studies

!

Are intended to be periodic, estimations of a process’s ability to meet its requirements

!

Can be conducted on both Discrete and Continuous Data!

Are most meaningful when conducted on stable processes

!

Can be reported as Sigma Level which is optimal (short term) performance

!

These concepts should be remembered from using the Six Sigma toolset applied so far:

#

Customer or business specification limits

$ Business specification limits cannot be wider than the specification limits of a

final product

# Nature of long term vs. short term data

#

Mean and Standard Deviation of the process (for Continuous Data)

#

The behavior and shape of the distribution of Continuous Data

#

Procedure for determining Sigma level

#

Relevance of data

You may want to take a moment to review the key components of Capability taught in the MeasurePhase. Here in the Control Phase Capability Studies are meaningful on stable processes. Ifrandom events are occurring frequently, then predictability will be less secure.

!

If the project was important enough to warrant the time and attention of you and your team, it is

important enough to ensure that performance levels are maintained

!

Monitoring the improved process is a key element of the Control Plan

!

Reporting Capability and Stability should be used together as primary components of the

monitoring plan

!

In the Measure Phase, Capability was used to establish baseline performance by assessing

what had occurred in the relevant past

! In the Control Phase, Capability becomes a predictive (inferential) tool to predict the expected

process performance, usually based on a sample.

Your project is clearly important, so much so that time and resources were allocated to it! Oneaspect that is absolutely critical to your Control Phase action items and project closure is

Capability Analysis as a predictive measure. Recall in the Measure Phase we emphasized“taking a snapshot” not worrying about Stability. Well now that you have fixed some stuff it’stime to be concerned about Stability to ensure your efforts stick.

Advanced Capability



564



Shown here is the roadmap for Capability within the Control Phase. Here we are going to teachyou how to perform Capability Analyses on both Continuous and Attribute Data. Remember toalways VALIDATE those spec limits!

Capability for the Control Phase

As in the MeasurePhase, understandingwhether you are dealing

with long term or shortterm data is an importantfirst step.

If the process is stable,short term data providesa quick estimate of trueprocess potential sincespecial causes areminimal.

Advanced Capability

Recall the difference between short and long term. The long term is the variation across the

subgroups and within the subgroups. Think of it in terms of Population versus Sample. Subgroupsor Lot represent Short Term; Overall represents Long term. You will have to slice and dice yourdata in respect to your business / process and determine what long term & short term are for yourprocess.



565


Discrete Capability: Binomial

Advanced Capability

SigmaXL® does not include a tool for Binary Process Capability Analysis. However the abovecharts can be created using SigmaXL®'s P-Chart, Histogram and Scatter Plot tools.

It

ll get ya there

Notes



566


Example of Defectives

Advanced Capability

Here we are reporting the Capability relative to Late Reports. The subgroup size is varying as isthe number of reports we analyze at each time frame for lateness.

From the Summary Stats we see the following. The % Defective of the process is nearly 18%.

Can you see that p bar is equal to 0.1756 PPM Def? This graph is a P-Chart which will becovered in more detail later. The red dot in this graph indicates a Special Cause showing theproportion of reports to be late to be excessively high and considered out of control.



567


Discrete Capability: Binomial Output

The upper left graph, is the plot of Proportion Defectives versus Sample Size. If this was widelyvarying and with a non-level slope, we might conclude our detection of late reports depends on thenumber of reports checked.

The last graph in the lower right shows a histogram of the % defective or late in our example. Youcan see the target line of 10% and see that most if not all are above our target; the lower spec.

The summary stats are there for our help although in this example, we have no question that ourprocess is not capable with a target of less than 10% late reports. However, let’s consider thedetails of the summary stats box in the middle. The summary stats gives the % defective which wasequal to the p bar shown in the upper left slide. Confidence intervals are given for the percent late.

The ppm defective is just the p bar multiplied by a million. The process Z is determined from thepercent defective and is shown with confidence intervals also. Remember if this data was long term,then the sigma level of the process would have a value added to this Z to obtain the sigma level. Doyou remember what value is assumed that separates Z short term and Z long term? Rememberwhen a process Z long term is used to estimate the Z short term, you add 1.5. In our example,assuming this data is from a long term capability analysis, the sigma level of the process would be2.43 with an upper confidence interval of 2.49 and a lower confidence interval of 2.38. Rememberthat the summary stats do not indicate the percent of groups larger than the target but indicates thepercent defective as a whole.

Advanced Capability



568


Discrete Capability: Poisson

More Capability Analysis

Advanced Capability

You can do aCapability Analysis using

the PoissonDistribution inSigmaXL® ifyou aretracking thenumber ofdefective units.

This Capability Analysis for defects per unit is similar to the binomial Capability Analysis.However, there is no Z value stated for this Capability Analysis. Remember we had a desire for theprocess to have less than one defect per unit. If you look at the lower right graph, you can see thelarge majority of samples show less than 1.0 dpu. In this example even if the dpu never settled outat some value, it is clear the average dpu is much less than 1.0. In fact, we have 95% confidencethat the upper confidence interval for the dpu is about 0.59.

Still works….



569


Continuous Capability: Normal

Advanced Capability

This should lookfamiliar from theMeasure Phase. Here

we are treating thedata as individualobservations. Laterwe will re-analyze thedata using CapabilityCombination Report(Subgroups) using“filler2” for NumericData Variable (Y) and“time” for SubgroupColumn or Size.

Continuous Capability: Normal Output Review

The black curve is

the predictedNormalDistribution for allof the data usingthe Overall (LongTerm) StDev.

The StDev(Within, ShortTerm) iscomputed usingthe Individuals

Chart MR-Bar/d2estimate. Thisgives us ourpotential StDev,i.e. “entitlement”.

If we had used Capability Combination Report (Subgroups), the StDev (Within, Short Term) wouldbe computed using the X-Bar & R or X-Bar & S Control Chart methods for within subgroup variation.



570


Continuous Capability: Normal Output Review

Advanced Capability

Note:ConfidenceIntervals for

ProcessCapabilityIndices may becalculated using“SigmaXL>BasicProcessCapabilityTemplates>Process Capability &ConfidenceIntervals”

Normal Capability Sixpack

Notice the

Capability Ploton the bottomright. Thisshows theoverall andwithin variationrelative to theplacement andwidth in thespecificationlimits.



571


Individual Distribution Identification Output

Advanced Capability

Recall from theMeasure Phase thatyou should alwaystake a look at your

data graphically; apicture is worth a1000 words. Youcan almost alwaysuse SigmaXL® tohelp you identifywhat type ofdistribution you aredealing with and tocreate a graphicalview of your data.

Also, this is a greatway to determineProcess Capabilitywithout transformingdata.

Continuous Capability: Non-Normal

This is the output which you will use to determine your distribution. The P-values shown on each graphare used to evaluate if the distribution an appropriate predictor. Since most decisions require only an

alpha risk of less than 5%, the P-values should be above 0.05. However, do not assume that a higherP-value means one distribution is better than another. There is just less error of that being theappropriate distribution to select.



572


Continuous Capability: Non-normal

Advanced Capability

Now that you have the distribution identified run a Capability Analysis as shown here. In theCapability Combination Report (Individuals- Non-normal) select “Cycletime” as Numeric DataVariable (Y). Ensure “Weibull(2 Parameter)” is selected for “Specify Distribution”.

Technical note from SigmaXL®'s workbook:

Z-Score Method (Default)

The Z-Score method for computing process capability indices are obtained by using the inversecdf of the normal distribution on the cdf of the Non-normal Distribution. Normal based capabilityindices are then applied to the transformed z-values. This approach offers two key advantages:the relationship between the capability indices and calculated defects per million is consistentacross the normal and all Non-normal Distributions, and short term capability indices Cp and Cpkcan be estimated using the standard deviation from control chart methods on the transformed z-values. The Z-Score method was initially developed by Davis Bothe and expanded on by AndrewSleeper. For further details, see Sleeper, Six Sigma Distribution Modeling .

Percentile (ISO) Method

The Percentile method to calculate process capability indices uses the following formulas:Ppu = (USL – 50th percentile)/(99.865 percentile – 50th percentile)Ppl = (50th percentile – LSL)/(50th percentile – 0.135 percentile)Ppk = min(Ppu, Ppl)Pp = (USL – LSL)/( 99.865 percentile – 0.135 percentile)

References for Process Capability Indices:

Bothe, D.R. (1997). Measuring Process Capability , McGraw-Hill, New York.Sleeper, A. (2006). Six Sigma Distribution Modeling , McGraw-Hill, New York.



573


Continuous Capability: Non-normal Output

Advanced Capability

Continuous Capability: Non-normal Output

This should look a bit more familiar. Since the data was Long Term, the sigma level of the processwould be adjusted by 1.5 and result in a sigma value of 1.48. Review the differential betweenobserved performance and expected performance, what does this tell you?



575


Practical Sustainability in Control Phase

Advanced Capability

Final Results of Control Phase

By eliminating Outliers your variation will reduce and your Median could shift. It is even possible thatyou could Normalize your distribution.

Within the later phases of the methodology you can use Capability to identify Special Causes orOutliers as shown here. If you can minimize them over time then the Process Capability willimprove!



576


Capability for the Control Phase

Advanced Capability

In summary be sure to capture the correct information to, one, prove the improvement in yourprocess and two, hand off the right information to the process owner for monitoring and measuringthe improved process.



577



You have now completed Control Phase – Advanced Capability.

! Understand the importance of Capability Analysis as it isapplied in the Control Phase

!

Select the appropriate method for Capability Analysis basedon the type of data distribution of your process

! Interpret the output of SigmaXL®’s Capability functions

! Understand how the use for Capability Analysis may alter

through the DMAIC phases

Advanced Capability

Notes



578


Lean Six Sigma

Black Belt Training

Now we will continue in the Control Phase with “Lean Controls”.

Control PhaseLean Controls



579


Lean Controls

Overview

Lean Controls

You can see in this section of the course we will look at the Vision of Lean, Lean Tools andSustaining Project Success.


!"#$ &''( )*+,(*+,-.!"#$ &''( )*+,(*+,-.

/0'1"2- 34.-#*$"5 3422"../0'1"2- 34.-#*$"5 3422"..

6*.*'$ '7 !"#$ 3488'0-*$+ 3*9 3*+:#6*.*'$ '7 !"#$ 3 488'0-*$+ 3 *9 3 *+:#

!"# !"% &' ()* +,)- . -' */!"# !"% & ' ()* +,)- . -' */

01213+ ()* +,)-/01213+ ()*+,)-/

41'* ()*+,) -/41'* ()*+,) -/

5 6 7 ' * 3 1 6 ( ' 8 ' 9 " -" +:5 6 7 ' * 3 16 ( ' 8 ' 9 " -" +:

56 7' *316 ;# 81, "& 1*+/56 7' *316 ;# 81, "& 1*+/

< 1-3)&1 +) ()* +,)-< 1-3)&1 +) ()* +,)-

!+'+ "/+"3'- .,)31/ / () *+,)-

=!.(>

!+'+ "/+"3'- .,) 31// ( )*+,)-

=!.(>

< ,' 8 ?8 @ 5 3+")* A+1& /< ,'8 ? 8 @ 53+ ")* A +1& /

You’ve begun the process of sustaining your project after finding the “vital few” X’s.

In Advanced Process Capability, we discussed removing some of the Special Causes causingspread from Outliers in the process performance.

This module gives more tools from the Lean toolbox to stabilize your process.

Belts, after some practice, often consider this module’s set of tools a way to improve someprocesses that are totally “out of control” or of such poor Process Capability before applying the SixSigma methodology.

The tools we are going to review within this module can be used to help control a process. They canbe utilized at any time in an improvement effort not just in Control. These Lean concepts can beapplied to help reduce variation, effect outliers or clean up a process before, during or at theconclusion of a project.

Grab a tool and

get busy



580


The Vision of Lean Supporting Your Project

What is Waste (MUDA)?

The first step toward waste elimination is waste identification which you did originally with your ProjectCharter and measured with your primary metric even if you didn’t use the term waste. All Belt projectsfocus efforts into one (or more) of these seven areas.

Remember, the goal is to achieve and the SUSTAIN our improvements. We discussed 5S in theDefine Phase but we are going to review it with a twist here in the Control Phase.

Lean Controls

p ! " $%&&'( )*)(%+&

, %& -% & . +(/'*(

, %+0"& 1

p ! " $%&&'( )*)(%+& %

2+)*% 3 4%$('56 . +(/'*( 78 1

p ! " $%&&'( )*)(%+&

8(%&9 %59 +0"9 ! '5: . +(/'*( %

;+)*%3 <%$('561

p ! " $%&&'( )*)(%+& , %+0"&

=8+> 8+? @% A . +(/'*(

8(%&9 %59 +0"9 ! '5: 1

B"%& (''3) % 99 9 +)$ +C 3 +&" 5"D*+5"9 (' 4*5(/"5 ) *)(% +& ? % +&)

5"% 3+0 "9 . +(/ 8 +> 8+? @ % E"3( F5' G"$()1

!"# % &'( )'*&*+ , &-. !"# % &'( )'*&*+ , &-. //

0* +(-)')'1 2#+*.(+0* +(-)')'1 2#+* .(+

3)+*- . 4-5(&67 3)+*- . 4-5(&67

0 (- ' 8 - 6 8 )9 #8 : & 6 ; 0 (- ' 8 - 6 8 )9 #8 : & 6 ;

< -)9#'< -)9#'

< - ' = - '< - ' = - '

! " #$% '# ()$%* $+% ,(($ () "*- . '/ . '0 1 " 2,(3%4$5 6+% 7 8 " #'4% 9%1%*$# () : " #$% ;1<= " '* >" 2" *%#%? '*4 9<=%@

! A<=" () B(,,%4$'(*

! A<=" () C D %,2,(= <4$'(*

! A<=" () E,(4%## '*0

! A < = " ( ) B ( * D % - " * 4%

! A<=" () F*D %*$(,-

! A<=" () A($'(*

! A<= " () ! " '$'*0

6+% #2%4') '4# () $+% AG HI : %,% ='#4<## %= '* $+% H%)'*% E+" #%@

! 6+% ,%=<4$'(* () AG HI 4" * ,%=<4% -( <, (<$9 '%,# " *= +%92: '$+ =% )%4$ 2, %D %*$'(*5 C <$9'%,# 8 %4" <# % () ='))%,'*0 : " #$%" 1 (*0 2,( 4%=<,%#J 1 " 4+'*%#J %$45

K%$ $+"$ 0 ",8"0% (<$$" +%,%Let that garbage outta here



581


The Goal

The term “5S” derives from theJapanese words for five practicesleading to a clean andmanageable work area. The five“S” are: ‘Seiri ' means toseparate needed tools, parts, andinstructions from unneededmaterials and to remove thelatter. 'Seiton' means to neatlyarrange and identify parts andtools for ease of use. 'Seiso'means to conduct a cleanupcampaign. 'Seiketsu' means toconduct seiri, seiton, and seiso atfrequent, indeed daily, intervals tomaintain a workplace in perfectcondition. 'Shitsuk e' means to

S - Workplace Organization

Remember that any projectneeds to be sustained. Muda(pronounced like mooo dah)are wastes than can reappear

if the following Lean tools arenot used. The goal is to haveyour Belts move onto otherprojects and not be used asfirefighters.

Lean Controls

!"#$ % '"() *% %+* ) ", - . . / 01%,2#2#) 3" 0( 4("5*6% 7 +26+ *- 282#, %*1

9 : ! ; <

= 2%+ %+21 2# 8 2#>? 7 * 7 2 -- 2#%(">0 6* , #> (*@2*7 1"8 * "' %+* A*, #

%""-1 01*> %" 101%,2# 3"0( B("5*6% 1066*11C

! "# %&'() *+& ,-./01'2& 3)21&'(4 *+&.& 3) ' 01'2& 5-.&6&.7*+3(8 '(9 &6&.7*+3(83) 3( 3*) 01'2&:

! "# 3) *+& )*'.*3(8 0-3(* 5-.3%01&%&(*3(83%0.-6&%&(*) *- ' 0.-2&)):

! ;- &()<.& 7-<. 8'3() '.&)<)*'3('=1&4 7-< %<)* )*'.*,3*+ ' 53.% 5-<(9'*3-(:

! >*) )*.&(8 *+ 3) 2-(*3(8 &(*<0-( *+& &%01-7&&) '(92-%0'(7 =&3(8 2-%%3**&9*- %'3(*'3(3(8 3*:

form the habit of always following the first four S’s.

On the next page we have translated the Japanese words to English words. Simply put, 5Smeans the workplace is clean, there is a place for everything and everything is in its place. The5S will create a workplace that is suitable for and will stimulate high quality and high productivitywork. It will make the workplace more comfortable and a place that you can be proud of.

Developed in Japan, this method assumes no effective and quality job can be done without cleanand safe environment and without behavioral rules. The 5S allow you to set up a well adaptedand functional work environment, ruled by simple yet effective rules. 5S deployment is done in alogical and progressive way. The first three S’s are workplace actions, while the last two aresustaining and progress actions.

It is recommended to start implementing 5S in a well chosen pilot workspace or pilot process andspread to the others step by step.



582


S Translation - Workplace Organization

Lean Controls

!"# $ &' $' (# )# * +"# , ' - ., ' () -' "+/( 0(1 -+)2

! "# $ 3 4 !"#$# % &"'$#() +, !-$.#()

! "# $ 5 4 !"#.-( / $)'(#0 #() !.$'#)1."(#()

! "# $ 6 4 !"#2- % &"'(#() !1#(#()

! "# $ 7 4 ! "3".24 ! .' (5' $5#0 #() ! .' (5' $5#0 #()

! "# $ 8 4 !1#.243" 6$'#(#() 7 8#29#,&#(" !42.'#(#()

!"# $ &' $' (# )# * +"# , ' - ., ' () -' "+/( 0(1 -+)2

! "# $ 3 4 !"#$# % &"'$#() +, !-$.#()

! "# $ 5 4 !"#.-( / $)'(#0 #() !.$'#)1."(#()

! "# $ 6 4 !"#2- % &"'(#() !1#(#()

! "# $ 7 4 ! "3".24 ! .' (5' $5#0 #() ! .' (5' $5#0 #()

! "# $ 8 4 !1#.243" 6$'#(#() 7 8#29#,&#(" !42.'#(#()

9/:;) /( ;)+(1 "2# 0(1 -+)2 < /,=) > ? ;:2 #' )+#, "/ ,#? #? @# ,A

The English translations are:

Seiri = SortingEliminate everything not required for the current work, keeping only the bare essentials.

Seiton = Straightening Arrange items in a way that they are easily visible and accessible.

Seiso = ShiningClean everything and find ways to keep it clean. Make cleaning a part of your everydaywork.

Seketsu = StandardizingCreate rules by which the first three S’s are maintained.

Shitsuke = SustainingKeep 5S activities from unraveling



584


A Method for Sorting

STRAIGHTENING – Arranging Necessary Items

After you have determined the usefulness of an item, set three classes for determining where to store anitem based on the frequency of use and the distance to travel to get the item. “ A” is for things which areto be kept close at hand, because the frequency of use is high. “B” is if the item is used infrequently butapproximately on a weekly basis. Do no put it on your work surface, rather keep in easy walkingdistance, i.e. on a bookshelf or in a nearby cabinet, usually in the same room you are in. For “C” items itis acceptable to store in a somewhat remote place, meaning a few minutes walk away.

By rigorously applying the sort action and the prescribed method, you will find that the remainder of the5S items will be quite easy to accomplish. It is very difficult to order a large number of items in a givenspace and the amount of cleaning increases with the number of items. Your workplace should onlycontain those items needed on a daily to weekly basis to perform your job.

The second stage of5S involves theorderly arrangementof needed items sothey are easy to useand accessible for“anyone” to find.Orderliness eliminateswaste in productionand clerical activities.

Lean Controls

Frequency of

Utilization Class

Keep within arms

reach

Keep in local

location

Keep in remote

location

Daily or several times

a day A YES MAYBE NO

Weekly B MAYBE YES NO

Monthly or quarterly C NO NO YES

A

BC F

r e q u e n c y

o f U s e

Distance

A

BC

A

BC F

r e q u e n c y

o f U s e

Distance

! " # %& '" ( ) * + & * " * ( # , # )* - ( . '/ #

01) / #2'/',( 3 &#)# %1 "%1)# '%#4 "

* -1,( 3 '%& %&# %*5 -# 5# -13 6

!"#$%$&$'%(

! "# %&&%'( ) %** ')+),,% &- ./)0,1

! "# 2%3) % 4),.('%/)4 5*% +)

6#& )3)&-/2.'(1

! 7 5*% +) 6#& )3)&-/2.'( %'4)3)&-/2.'( .' ./, 5*%+)1

! 8% ,.*- 3.,.9 *) %'4 %++),,.9*)1

) *+ (

! :.,;%**- ,2#<, <2% / ., &)=;.&)4#& ., #;/ #6 5*%+)1

! >#&) )66.+.)'/ /# 6.'4 ./)0, % '4

4#+;0)'/, ?,.*2#;)//),@ *%9)*,A1

! B%3), /.0) 9- '#/ 2%3.'( /#

,)%&+2 6#& ./)0,1

! B2#&/)& /&%3)* 4 .,/%'+),1

,*$%- . &' 0"1 "12 "0

C "2.'(, ;,)4 /#( )/2)&

,2#;*4 9) D)5/ /#()/2)&1

C E,) *%9)*,F /%5)F 6*##&

0%&D.'(,F ,.(',F %'4

,2%4#< #;/*.'),1

C B2% &%9*) ./)0, ,2#;*4 9)

D)5/ %/ % +)'/&%* *#+%/.#'

?)*.0.'%/)4 )G+),,A1

,*$%- . &' 0"1 "12 "0

C "2.'(, ;,)4 /#( )/2)&

,2#;*4 9) D)5/ /#()/2)&1

C E,) *%9)*,F /%5)F 6*##&

0%&D.'(,F ,.(',F %'4

,2%4#< #;/*.'),1

C B2% &%9*) ./)0, ,2#;*4 9)

D)5/ %/ % +)'/&%* *#+%/.#'

?)*.0.'%/)4 )G+),,A1



585


SHINING – Cleaning the Workplace

STANDARDIZING – Creating Consistency

The third stage of5S is keepingeverything clean

and swept. Thismaintains a saferwork area andproblem areas arequickly identified. An important part of“shining” is “MessPrevention.” Inother words, don’tallow litter, scrap,shavings, cuttings,etc., to land on thefloor in the firstplace.

The fourth stage of5S involves creatinga consistentapproach forcarrying out tasksand procedures.Orderliness is thecore of“standardization” and is maintained byVisual Controlswhich might consistof: Signboards,

Painted Lines, Color-coding strategiesand Standardizing“Best Methods” across theorganization.

Lean Controls

!"#$%$&$'%(

! " #$%& $($)*+,-&. %&/0-&/ 1%*2 +3 4$$5 -+

6#$%&7 ! 8% 4$ 6#$% &-&. % 5% )+

30 *39) $($)*/%* 13)47

) *+ (

! : 6#$% & 13)45#% 6$-&/-6%+$2 % ;9%#-+*5)3/96+ %&/ 5)36$227

! <92+ % &/ /-)+ 6%92$5)3/96+ 63&+%=-&%+-3&%&/ 53+$&+-%# ,$%#+,,%>%)/27

! : 6#$% & 13)45#% 6$

,$#52 -/$&+-0* %?&3)=%#63&/-+-3&27

,*$%- . &' 0"1 "12 "0

@ AB($)*+,-&. -& -+2 5#%6$C 0)$$2 95

+-=$ 03) 6#$%&-&.7

@ D2$ %& 300-6$ 3) 0%6 -#-+* #%*39+ %2 %

(-29%# %-/ +3 -/$&+-0* -&/-(-/9%#

)$253&2-?-#-+-$2 03) 6#$%&-&.7 E,-2

$#-=-&%+$2 A&3 =%&F2 #%&/7C

@ " #$%&-&. +,$ 13)4 %)$% -2 #-4$?%+,-&.7 G+ )$#-$($2 2+)$22 %&/ 2+)%-&H

)$=3($2 21$%+ %&/ /-)+H %&/

5)$5%)$2 +,$ ?3/* 03) +,$ &$I+ /%*7

,*$%- . &' 0"1 "12 "0

@ AB($)*+,-&. -& -+2 5#%6$C 0)$$2 95

+-=$ 03) 6#$%&-&.7

@ D2$ %& 300-6$ 3) 0%6 -#-+* #%*39+ %2 %

(-29%# %-/ +3 -/$&+-0* -&/-(-/9%#

)$253&2-?-#-+-$2 03) 6#$%&-&.7 E,-2

$#-=-&%+$2 A&3 =%&F2 #%&/7C

@ " #$%&-&. +,$ 13)4 %)$% -2 #-4$

?%+,-&.7 G+ )$#-$($2 2+)$22 %&/ 2+)%-&H

)$=3($2 21$%+ %&/ /-)+H %&/

5)$5%)$2 +,$ ?3/* 03) +,$ &$I+ /%*7

!"#$%$&$'%(

! "# %&'()&'( )*+ ,#-./0& 1+

&) & 0+2+0 )*&) 3(1#2+-4

/-#50+%4 &(6 %&.+4 )*+%

#52'#347

! "# 1#()'(3#3408 '%/-#2+

8#3- #99'1+ #- 9&1'0')8 58

1#()'(3#34 &44+44%+() &(6

&1)'#(7

) *+ (

! "# 434)&'( 4#-)'(: ; 4)#-&:+

&(6 4*'('(: &1)'2')'+4 +2+-86&87

,*$%- . &' 0"1"1 2"0

< = + %34) .++/ )*+ ,#-. /0&1+ (+&)

+(#3:* 9#- 2'43&0 '6+()'9'+-4 )# 5+

+99+1)'2+ '( 3(1#2+-'(: *'66+(

/-#50+%47

< >+2+0#/ & 484)+% )*&) +(&50+4

+2+-8#(+ '( )*+ ,#-./0&1+ )# 4++

/-#50+%4 ,*+( )*+8 #113-7

,*$%- . &' 0"1" 12 "0

< = + %34) .++/ )*+ ,#-. /0&1+ (+&)

+(#3:* 9#- 2'43&0 '6+()'9'+-4 )# 5+

+99+1)'2+ '( 3(1#2+-'(: *'66+(/-#50+%47

< >+2+0#/ & 484)+% )*&) +(&50+4

+2+-8#(+ '( )*+ ,#-./0&1+ )# 4++

/-#50+%4 ,*+( )*+8 #113-7



586


SUSTAINING – Maintaining the 5S

The Visual Factory

This last stage of 5Sis the discipline andcommitment of allother stages.

Without“sustaining”, yourworkplace can easilyrevert back to beingdirty and chaotic.That is why it is socrucial for your teamto be empowered toimprove andmaintain theirworkplace. Keeping

a 5S program vital inan organizationcreates a cleanerworkplace, a saferworkplace. Itcontributes to how

A visual factory canbest be represented bya workplace where arecently hiredsupervisor can easilyidentify inventorylevels, extra tools orsupplies, scrap issues,downtime concerns or

even issues with setupsor changeovers.

Lean Controls

!"#$%$&$'%(

! "# %&'()&'( #*+

,'-.'/0'(12 31 (11, )#

/+&.)'.1 &(, +1/1&) *()'0

') 41.#%1- & 3&5 #6 0'617

) *+ (

! "# 4*'0, 89 '()# #*+

1:1+5,& 5 /+#.1--7

,*$%- . &' 0"1 "12 "3

; <1:10#/ -.=1,*01- &(,

.=1.> 0'-)-7

; ? ##, =&4')- &+1 =&+,

)# 1-)&40'-=7

; @ #%%')%1() &(, ,'-.'/0'(1

)#3&+, =#*-1>11/'(A &+1

1--1()'&0 6'+-) -)1/- )#3&+,41'(A 3#+0, .0&--7

,*$%- . &' 0"1 "1 2"3

; <1:10#/ -.=1,*01- &(,

.=1.> 0'-)-7

; ? ##, =&4')- &+1 =&+,

)# 1-)&40'-=7

; @ #%%')%1() &(, ,'-.'/0'(1

)#3&+, =#*-1>11/'(A &+1

1--1()'&0 6'+-) -)1/- )#3&+,41'(A 3#+0, .0&--7

we feel about our product, our process, our company and ourselves. It provides a customershowcase to promote your business and product quality will improve – especially by reducingcontaminants. Efficiency will increase also. When employees take pride in their work andworkplace it can lead to greater job satisfaction and higher productivity.

The basis and foundation of a Visual Factory are the 5S Standards.

A Visual Factory enables a process to manage its processes with clear

indications of opportunities. Your team should ask the following questions if looking for a project:

– Can we readily identify Downtime Issues?

– Can we readily identify Scrap Issues?

– Can we readily identify Changeover Problems?

– Can we readily identify Line Balancing Opportunities?

– Can we readily identify Excessive Inventory Levels? – Can we readily identify Extraneous Tools & Supplies?

Exercise:

– Can you come up with any opportunities for “VISUAL” aids in your

project?

– What visual aids exist to manage your process?



587


What is Standardized Work?

Affectedemployeesshouldunderstand thatonce theytogether havedefined thestandard, theywill be expectedto perform the job according tothat standard.

Prerequisites for Standardized Work

The steps in developing CTQ’s are identifying the customer, capturing the Voice of the Customerand finally validating the CTQ’s.

Lean Controls

If the items are organized and orderly, thenstandardized work can be accomplished.

–

Less Standard Deviation of results

–

Visual factory demands framework ofstandardized work.

The one best way

to perform each

operation has been identified and agreed

upon through general consensus (notmajority rules)

– This defines the Standard

work

procedure

5S - Workplace Organization

Visual Factory

We cannot sustain

Standardized Work

without 5S and the

Visual Factory.

Standardized Work

Standardized work does not happen without the Visual Factory which

can be further described with:

Availability of required tools (5S). Operators cannot be expected to

maintain standard work if required to locate needed tools

Consistent flow of raw material. Operators cannot be expected to

maintain standard work if they are searching for needed parts

Visual alert of variation in the process (Visual Factory ). Operators,material handlers, office staff all need visual signals to keep standard

work a standard

Identified and labeled in-process stock (5S). As inventory levels of in-process stock decrease, a visual signal should be sent to the material

handlers to replenish this stock



588


What is Kaizen?

Prerequisites for Kaizen

A Kaizen event is very similar to a Six Sigma project. A Six Sigma project is actually a Kaizen.By involving your project team or other in an area to assist with implementing the lean control orconcepts you will increase buy in of the team which will effect your projects sustainability.

A Kaizen event can be small or large in scope. Kaizens are improvement with a purpose ofconstantly improving a process. Some Kaizens are very small changes like a new jig or placement ofa product or more involved projects. Kaizens are Six Sigma projects with business impact.

Lean Controls

•

Definition*: The philosophy of continualimprovement, that every process can and

should be continually evaluated and

improved in terms of time required,resources used, resultant quality and otheraspects relevant to the process.

• Kaikaku are breakthrough successes which

are the first focus of Six Sigma projects.

* Note: Kaizen Definition from: All I Needed ToKnow About Manufacturing I Learned

in Joe s Garage. Miller and Schenk,

Bayrock Press, 1996. Page 75.

Visual Factory

Standardized Work

Kaizen


Kaizens need the following cultural elements:

Management Support. Consider the corporate support which is the reason why

Six Sigma focus is a success in your organization

Measurable Process. Without standardized work, we really wouldn

t have a

consistent process to measure. Cycle times would vary, assembly methods

would vary, batches of materials would be mixed, etc!

Analysis Tools. There are improvement projects in each organization whichcannot be solved by an operator. This is why we teach the analysis tools in the

breakthrough strategy of Six Sigma.

Operator Support. The organization needs

to understand that its future lies in the

success of the value-adding employees.

Our roles as Belts are to convince operators

that we are here for them--they will then be

there for us.



589


Two Types of Kanban

What is Kanban?

This is a building block. A Kanban needs to be supported by the previous steps we have reviewed. IfKanbans are abused they will actually backfire and effect the process in a negative manner.

There are two categories of Kanbans, finished good Kanbans and incoming material Kanbans asdepicted here.

Lean Controls

!" #$ & ' ( )* )+,$- . //- + 0 1 *21 *+

! 3 ) . * 1 4 0 1 * 2 1 * ' 3 , / 5 4 - 2 $#/ +6$- 1 6 6,$ $*- /7 6,$#8/9$++ )*. 1 8$1 6/ + ). *1 4 7/8#8/ -5 96)/* 6/ 2$ . )*:

! ; : <: 0 0 1 * 2 1 * ' =+ $- 7/8 1 > 5 9,>/8$ 8$7 )*$- 4$?$4 /7 )*?$*6/8"

9/*68/4 : 0 1 *21 * )+ #/+6$- 1+)*?$*6/8" )+ - $#4$6$- 6,5+)*+58 )*. / *4" 6,$ >)*)>5>1 4 4/@ 1 24$ 4$? $4 /7 # 8/-5 96 ) +> 1) * 6 1 ) * $- :

!" #$ A ' <*9/> )*. B16$8 )1 4 0 1 *21 *+

! =+ $- 6/ # 5 8 9, 1+ $ > 1 6$8 )1 4 +7 8/> 1 + 5 # # 4 " ) * . - $# 1 8 6> $* 6$)6,$8 )*6$8*1 4 /8 $C 6$8*1 4 6/6,$ /8. 1 *)D 1 6)/*: E$. 541 6$+6,$ 1 >/ 5*6 /7 F <; )*?$*6/8"4/916$- 16 1 #186 )95418 #8/9$++ :

<*6$8<*6$8 GG ;8/9$++;8/9$++

! " #$ % & ' ( ' ) ! " #$ % & ' ( ' )

3 5##4 ) $ 83 5##4 ) $ 8

"#$%##& $%()*(+#,,#,

*+#&'*+#&' ,, - & . /0 1 1 - & . /0 1 1

; :<:0 :; :<:0 :

3 ). *1 43 ). *1 4

-*(./+$0(&1&,$*/+$0(& 23&43&

There are two main categories of Kanbans:

Kanbans are the best control method of inventory which impactssome of the 7 elements of MUDA shown earlier.

Kanban provides production, conveyance, and delivery

information. In it

s purest form the system will not allowany goods to be moved within the facility without an

appropriate Kanban (or signal) attached to the goods.

–

The Japanese word for a communication signal

or card--typically a signal to begin work

–

Kanban is the technique

used to pull

products andmaterial through and into

the lean manufacturing system.

–

The actual Kanban

can be a

physical signal such as an empty

container or a small card.


Visual Factory

Standardized Work

Kaizen

Kanban



590


Prerequisites for a Successful Kanban System

It is not possible to implement a viable Kanban system without a strong support structure made upof the prerequisites. One of the most difficult concepts for people to integrate is the simplicity of theLean tools… and to keep the discipline. Benchmarks have organizations using up to seven years to

implement a successful Kanban System all the way through supplier and customer supply chain.

Kanbans shouldsmooth out inventoryand keep productflowing but use them

cautiously. If youprematurelyimplement a Kanbanit WILL backfire.

Warnings Regarding Kanban

Lean Controls

!"#$# & '#($ $)* *+,' $)--#$$.)/ 0 1 23 1 2$4

! 5(*,+6 # -"1 27 #+6#, *,+-#8),#$9

! :#/1' &6#/; $'1 3/# 8#( 1 28 -; -/#9

! < ) (3 #, + . * 1, '$ * #, 0 1 2 3 1 2 =-1, 8 > ?@A! 3 # $'1 2 8 1 , 8 1 2 8

AB C @DE 3# F #*' '+ 1 $ .#G 1 $ *+$ $&3 /# *1,'$ *#, -1,8 9

! A( 1 / / 1 ( +)2' +. 61, &1 '&+2 =+, 8#.#-'$> 9

! < #1 , H#,+ 8 #.#-'$ $"+)/8 3 # $#2' '+ '"# 1 $$#( 3/; * ,+-#$$

=:#$)/' +. #1 ,/ &#, 3 #/' *,+I#-'$>9

! J+2$&$'#2' -;-/# '&(#$ 8 #. &2#8 3 ; A'128 1 ,8&H#8 K +,F 9

! ?1 '#, &1/ "1 28/#,$ () $' 3# ',1&2#8 &2 '"# +,7 1 2&H1 '&+2 +. '"#

',12$*+,'1' &+2 $;$'#(9

If you do NOT have 5S, Visual Factory, standardizedwork and ongoing Kaizens –

Kanbans cannot succeed!

Kanban systems are not quick fixes to large inventory

problems, workforce issues, poor product planning,

fluctuating demand cycles, etc...

Don t forget that

weakest Link

thing



591


The Lean Tools and Sustained Project Success

The 5 Lean concepts are an excellent method for Belts to sustain their project success. If you haveoutliers, declining benefits or dropping process capability, you need to consider the conceptspresented in this module.

Class Exercise

Lean Controls

!"# %#& ' ())*+ "#*, +-+(& .' ,/)0#1( +-11#++2 !"# 3 & .' *#++)'+ 4 )-+" ) - * 5 1) ' + .5 #/ & /# 6

7 2 !"# !89: + ")-*5 ; < ("# ,/)0#1( & /#& & '5 = #> .' .'(#> /& (.'> ? .+-&*

@&1()/4 .'5.1& ()/+ 2 ! A'5.1& (.)'+ )@ ("# '##5 @)/ ;< & /#6

! B -( *.#/+ .' 4) -/ , /)0#1( 3 #(/ .1

! %)++ ) @ .'.(.& * > & .'+ @/)3 ,/) 0#1( @ .'5.'> +

C 2 !"# !89: +")-*5 5#?#*), <(&'5 & /5.D#5 E )/F A'+(/-1(.)'+

! !"#4 & /# /#G-./#5 () +-+(& .' 4 )-/ +4+(#3 =#'#@ .(+ 2

! H )I #? #/J /#3 #3 =#/ I .(") -( & ' )/> & '.D #5 I )/F ,*& 1# I .("; < +(&' 5& /5.D #5 I )/F .'+(/-1(.)'+ I )' K( 1/#& (# 1)'+ .+(#'14

L 2 M & . D # ' K + & ' 5 M & ' = & ' K + 1 & ' ' ) ( = # & ((# 3 , (# 5 I . (" ) - ( ) / > & ' . D # 5

I )/F ,*& 1#+ & '5 )/> & '.D# 5 I )/F .'+(/-1(.)'+2 ! N# 3 # 3 = # / (" # ' # # 5 @) / ; < & ' 5 < (& ' 5 & / 5 . D # 5 E ) / F

A'+(/-1(.)'+ () +- ,, )/( )-/ , /)0#1(+2

O 2 P/)0#1( <1),# 5 .1(& (#+ ")I @&/ -, ("# %#&' ())*+ *& 55 #/ 4)- '##5() .3,*#3#'( 3#&+-/#+ () +-+(&.' &'4 ,/)0#1( +-11#++ @ /)3 4)-/Q:9AR #@@)/(+2

!" $%& ' ()"* + , -&. /(, 0 (), 1 ,(2&3$ .3(1&4 5 -6& .(7 &

&8 + 7 19&. (/ :&+ " $((9. -" (1 &,+ $-(";

! < $%&,. 3+ " 9&+ ," / ,(7 $%(.& - $&7 . 0 () 3(". -*&, ' + . -3;

: -.$ ($%&, :&+ " $((9. 0 () + ,& 7 (.$ -"$&,&.$&* -" + 11 90-"5 $(

.).$+-" 0 (), 1,( 2&3$ ,&.)9$. ;

=( 5 &"& ,+ $& $%& >8 &,3-.& -"/(,7 + $-(" 3(". -*&, ? + 9@ -"5+ ,()" * 0 (), /+3- 9- $0 4 &.1 &3-+ 9 90 - / -$ -. A < = + 7 + ")/+ 3$),-"5

("&4 + "* 3(". -*&, ? %&,& + 6 -.)+ 9 /+ 3$(,0 ? ()9* ' & ).&/)9

+ 9("5 ? -$% $%& ($%&, B :&+ " 3(" 3&1$. ,& 6-&? &*;



592



You have now completed Control Phase – Lean Controls.

! Describe some Lean tools

!

Understand how these tools can help with project

sustainability

! Understand how the Lean tools depends on each other

! Understand how tools must document the defect prevention

created in the Control Phase

Lean Controls

Notes



593


Lean Six Sigma

Black Belt Training

Now we will continue in the Control Phase with the “Defect Controls”.

Control PhaseDefect Controls



594


Defect Controls

Overview

Purpose of Defect Prevention in Control Phase

With Defect Prevention we want to ensure that the improvements created during the project stay in place.

In an effort to put in place Defect Controls we will examine Tolerances, Process Automation andPoka-Yoke.


!"# ! "% & ' () *+,)- .-' */!"# ! "% & ' () *+,)- .-' */

01213+ ()* +,)-/01213+ ()* +,)-/

41'* ()*+,)-/41'* ()*+,)-/

5 6 7 '* 3 1 6 ('8 '9 " - " + :5 6 7 '* 3 1 6 ('8 '9 " - " + :

5 67 ' *316 ;# 81, "&1*+/56 7' *316 ;# 81, "&1*+/

< 1-3)&1 +) ()* +,)-< 1-3)&1 +) ()* +,)-

!+'+ "/+ "3'- . ,)31// ()* +,)-

=!.(>

!+'+ "/+"3' - .,)31/ / ( )*+,)-

=!.(>

< ,' 8 ? 8 @ 5 3+")* A+1& /< ,' 8 ?8 @ 5 3+")* A +1&/

!"#$%&'%( *+$",#-(" #-. /%0 /%12# 3"&%1-!"#$%&'%( *+$",#-(" #-. /%0 /%12# 3"&%1-

4,+("&& 56'+2#'%+- +, 7-'",,68'%+-4,+("&& 56'+2#'%+- +, 7-'",,68'%+-

4+9#:;+9"4+9#:;+9"

!"#$%&& ()* "#+ %) %,- %..#"-& #.-%, ./0-%" 12" (,3 ()*0%) %,-/-(#, # .

,%4 #*%"/ -(,3 )%-5#1& 0%/ ",%1 (, -5% 6 ,/ 07 8 % / ,1 9)* "#+ %

! 5 / & % & :

;2 &-/ (,/ <0% ()* "#+%) %,-& $/ , ,#- <% / $5(%+%1 4 (-5#2- $#,-"#0

-/ $-($& -# 3 2/ "/ ,-%% * %") / ,%,$7 :

=%.%$- !"%+ %,-(#, &% %> & -# 3 / (, *%") / ,%,$7 <7 %0 ()(,/ -(,3 #"

" (3 (1 07 1 %.(,(,3 52) / , (,-%"+%, -(#, (, / * "#$%&&:

? %& &("@ 4% /"% (, ABCDE BF GYes sir, we are in CONTROL



595


Copyright OpenSourceSixSigma.com

Defect Controls

Sigma Level for Project Sustaining in Control

5-6 Six Sigma product and/or process design eliminates an errorcondition OR an automated system monitors the process andautomatically adjust Critical X

s to correct settings without human

intervention to sustain process improvements

4-5 Automated mechanism shuts down the process and preventsfurther operation until a required action is performed

3-5

: Mistake Proofing prevents a product/service from passing ontothe next step

3-4

: SPC on X

s with the Special Causes are identified and actedupon by fully trained operators and staff who adhere to the rules

2-4 SPC on Y

s

1-3 Development of SOPs and process audits

0-1 Training and awareness

BEST

WORST

Our objective is to achieve the highest sigma level at acceptable costs.



596


Sigma Level for Project Sustaining in Control

6s Product/Process Design

The best approach to Defect Prevention is to design Six Sigma right into the process.

Defect Controls

!"#$% &$&% ()*+ ,-.# / &+ ( )*-"##"# #, -0 .0/ . .0" *,.(,. 1 2 "".# *)

"3 -""+# .0" ./ )% ". -/( / 4$5$.6 7

! "#$ &#'()$($) *"# +,-* .- +-./#''0 '+#/(1(/,*(.$' .$ 2 ,-# '#* '3/" *",* *"#

*,-)#* /,+,4(5(*6 .$ 7 (' ,/"(#8#&9

:.*" *"# *,-)#* ,$& *.5#-,$/# .1 *"# 2 ;3'* 4# ,&&-#''#& ($ *"# '+#/ 5(;(*'9

2019181716151413121110

24

22

21

19

17

Distribution of X

Distribution

of Y

<#5,*(.$'"(+

7 = >?@A S p e c i f i c a t i o n

o n

Y

2019181716151413121110

24

22

21

19

17

Distribution of X

Distribution

of Y !"#$%&'()*&+

- . /012

S p e c i f i c a t i o n

o n

Y

3++"4

54"6&7%&'(

8(%"49$#

:';"4

54"6&7%&'(

8(%"49$#

! " $%& '& ()$ *+,-%*. / &$0 &&, 1 ) ,2 3 *- &4.*' *5) ( (6 2&7 &(+.&2

$%'+ 89 % '&9 '&--*+,- +' :; <=- 8,5&'$)*,$6 &> *-$-?

@- ) '&-8($A 5+," *2&,5& *,$&'7) (- -%+8(2 /& 8 -&2 0 %&, &-$)/ ( *-%*,9

$%& -.&5*"*5)$*+,- "+' 1 ?



597


-30 -20 -10 0

0

5

10

Input2

O u t p u t 2

Y = 2.32891 - 0.282622X

R-Sq = 96.1 %

Regression

95% PI

Regression Plot

0 5 10

0

10

20

30

40

50

60

70

80

90

Input

O u t p u t

Y = 7.75434 + 5.81104X

R-Sq = 88.0 %

Regression

95% PI

Regression Plot

0 5 10

0

10

20

30

40

50

60

70

80

90

Input

O u t p u t

Y = 7.75434 + 5.81104X

R-Sq = 88.0 %

Regression

95% PI

Regression Plot

! "#$% ' () * "+ #,+# -,$. ."/ /$.#-

0 (#* #", 1 (/$ (/ 2" #* .3 -$- 4

5"0 $6 (/,+ # -,$.

!"#$% '() (*')*' ")+, -+'+./#$+" 0 #%0 (. 1(2 '(1+.3$ ,+ 4(. #$)*'

- +) +$ - #$ % ( $ " 1( ) + ( 4 . +% . +"" #( $

Product/Process Design Example

Usually we use the prediction band provided by SigmaXL®. This is controllable by manipulation ofthe confidence intervals. 90%, 05%, 99%, etc. Play with adjusting the prediction bands to see theeffect it has.

Defect Controls



598


Poor Regression Impacting Tolerancing

5 – 6 Full Automation

Automation can be an option as well which removes the human element and its inherentvariation. Although use caution to automate a process, many time people jump into automationprematurely, if you automate a poor process what will that do for you?

Defect Controls

!"# # % "&'() &*'+, !"#$%&# $()$ &*+,$*- $(% .-*/%## )+0 )1$*&)$,/)22")031#$ /-,$,/)2 45# $* /*--%/$ #%$$,+6#

7 8 1$*&)$,/ 6 )16 ,+6 ) +0 #"#$%& )0 31#$&%+$#

7 8 1$*&)$,/ 0%$%/$,*+ )+0 #"#$%& )/$,9)$,*+ #"#$%&# : 2)+0,+6 6%)-

%;$%+#,*+ <)#%0 *+ ),-/-)=$ #.%%0 )+0 .*>%- #%$$,+6

7 !"#$%&# $()$ /*1+$ /"/ 2%# )+0 )1$*&)$,/) 22" &)?% )031#$&%+$# <)#%0

*+ )+ *.$,&1& +1&<%- *= /"/2%#

7 8 1$*&)$%0 $%&.%-)$1-% /*+$-*22%-# =*- /*+$-*22,+6 (%)$,+6 )+0 /**2,+6

#"#$%&#

7 8 +$,:@*/? <-)?,+6 #"#$%&#

7 8 1$*&)$,/ >%20%- /*+$-*2 1+,$# =*- 9*2$#A )&.# )+0 0,#$)+/% $-)9%2%0

*+ %)/( >%20 /"/2%

Mr. Correlation

is poor



599


Full Automation Example

Defect Controls

4 – 5 Process Interruption

!"#$%&& ()*%""+,*-#). !"#$%&'() '&(+%,,"- +$%+ ($.+( -/0& +$"

12/#"(( %&- 12"3"&+( 4.2+$"2 /1"2%+'/& .&+', % 2"5.'2"- %#+'/& '(

12"4/2)"-6

7 8 2/.&- 4%.,+ #'2#.'+ 92"%:"2(

7 ; $',- 12//4 #%1( /& )"-'#%+'/&(

7 </4+0% 2" 2/.+'&"( +/ 12"3"&+ .&-"('2%9," #/))%&-(

7 <%4"+= '&+"2,/#:( /& "5.'1)"&+ (.#$ %( ,'> $+ #.2+%'&(? -.%, 1%,)

9.++/&(? 2%) 9,/#:(

7 @2%&(4"2 (=(+") >.'-"( /2 4'A+.2"( +$%+ 12"3"&+ /3"2 /2 .&-"2('B "-

1%2+( 42/) 12/#""-'&>

7 @")1"2%+.2" #/&3"=/2 '&+"2,/#:( /& /3"&(

7 !'(('&> #/)1/&"&+ -"+"#+'/& +$%+ (+/1( +$" 12/#"(( 0$"& +2'>>"2"-

Don

t worry boss, it

s automated



600


4 – 5 Process Interruption (cont.)

3 – 5 Mistake Proofing

Mistake Proofing isgreat because it isusually inexpensiveand very effective.Consider the manyeveryday examples ofMistake Proofing.You can not fit thediesel gas hose intoan unleaded vehiclegas tank. Pretty

straightforward, right?

Defect Controls

! " # $ % & ' (

! ! # $% &' # ($) *+ , -.' */0 - / $% 1/ &2*/0 % / (, ($(&).*& 3. *4( 1/*)-/ % ).% / +5( . +6 +)(7

" 8 /( &-77 -/ 5% * $1.( 7- 3( -5 )2( +6 +)(7 *+ % 9(% . */0 5% * $1.(-/ )2( 7 % */ 7-)-. +2% 5)

" : ) , % + 3 ()(.7 */(3 )2% ) % 2*0 2 ; .(++ 5 *) %) 9(% .*/0*/+)% $ $% )*-/ , % + &% 1+*/0 )2(+( 5% * $1.(+

" <2( .--) &%1+ ( -5 )2( ;.- 9$(7 )1./(3 -1) )- 9( 1 /3(.+*=(39(% . */0 + 5 .-7 )2( +1; ;$ *(.

! >/ )* $ )2( +1 ;; $*(. &-1$3 9 ( 9.- 10 2) */)- &-/).-$ -. .(;$% &(3? )2 ()(% 7 *7; $(7(/)(3 % ; .(++ $-% 3 7 -/*)-. %) )2( 9(% . */0 ;.(++, *)2 % */3 *&%)-.

" : 5 )2( 7 -/*)-. 3 ()(&)+ % ;.( ++ $-% 3 2*0 2(. )2% / )2( +() ;- */)?*) +2 1)+ 3- , / )2( ;. (++ % /3 , *$ $ /- ) % $$-, )2( 1 /*) )- 9 (.(7 -4 (3 5.-7 ;.(+ + 1/)*$ % / */)(.$-&' ' (6 *+ )1./(3 % /3 )2(.% 7 .( +( ) */ )2 ( 7% / 1 % $ 7-3 (

" 8 / $6 )2( $*/( $(% 3 ; (.+-/ % /3 )2( +1; (.4 *+-. 2% 4( ' (6 + )-)2( */ )(.$- &'

" <2( /-/ @&-/5-.7 */0 ; % .) *+ %1 )-7 % )*&% $ $6 7 % .' (3 , *)2 .(33 6 (

A.- &(++ :/)(..1; )*-/

!"#$%& ' )*+ +,"-. !" $%"& '%(!)%' *"+

, -"!). /!"'012 !). %)3!&42 05 "%5%)'!6!&4 &0 75%* &% '%8!7%"

*990/!). * :;;< '%(%7& (5%% "&%6 :;;< 0( &=% &!1%

>0?*@A0?% !" &=% B*6*)%"% &%51 (05 1!"&*?% 6500(!). 05 &0 *80!'

C40?%350D !)*'8%5&%)& %5505" C60?*DE

1

6

5

432

7 8

! "" $% & '( )*+%$+, -." /'0 *1

2 '0 "34

See if you

can find the

Poka- Yokes



601


Traditional Quality vs. Mistake Proofing

Styles of Mistake Proofing

This clearlyhighlights thedifference betweenthe two

approaches. Whatare the benefits tothe SourceInspection method?

Defect Controls

!"#$%& %'(#) +(,-./&%'(

0.,1)&

! "#$%# "#'()*+,% -##"#

.",/0 ."1,20*+,3

.%4%)0+5%6"#0

1 0 7 0*%#60%8

.+9)"5%#

-##"#:($% 1)0+",;

<%%=>()$

? ".%4%)0

2'1"/. +(,-./& %'(3 4 556 5007 02 807 9

!:0; +; < +; !7 =585> !2?

?%@060%8?%@060%8

!""# " % &# '( (# # )) '"

*!+!)( % &# '( (# # )) '",-./01231456

7 % "8 98 : ; 9: 8 % <

)# 8 ("# < = +!!*&% )>

;? '(*# 7 8,;34@ # @/ .A 31456

!""# " ?% ; # ))'""!*

*!+!)( ? %; # ))'""!*,*/3/231456

7 % "8 98 : ; 9: 8 % <

)# 8 ("# < = +!!*&% )>

;? '(*# 7 8,;34@ # @/.A 31456

(B/./ A ./ C D3A 3/D 4 E A 0/E/23 F B12B A ./ A 00 ./DD/0 F 1 3B

G 1D3A H / @.4 4E15I J



602


Mistake Proofing Devices Design

The very best approaches make creating a defect impossible, recall the gas hose example, youcan not put diesel fuel into an unleaded gas tank unless you really try hard or have a hammer.

Types of Mistake Proof Devices

Defect Controls

! "#$% $' ()*+ ,) %"- # . / "%$. 0 ) + 1''2"#- ,) 3"4)5

! 6 "/+*)

! 7#)8 +)#% "3) ! 9 "3) + 1'/ +$ 2)),: . 40

! 9 "3) +1' / +$ .4$"'# ;+1)3 )#$"'#<

! ='4>%), .++* "4.$ "'#

! ! . 3) $() 1 "- ($ +)'+ *)?% "#+ >$

!"#$ """#$%&' )* )#+,'')-.& /,0 &00,0' *, ,1120

!"$$"& 3 3 $ ..,4' /,0 5&*&1*),6 47).& &00,0 )' -&)68 #$5&

'(() """5&*&1*' 5&/&1* -&/,0& )* 1,6*)62&' *, *7& 6&9* ,+&0$*),6

!" #$%&$ ()$*"+ ! !"# $%&' ( *+ ,-,+. # &*-/' &/

0 %/" 1+ *2 3&/

" 4%5 %/ $0 %/&",$

" !" */*6,(,&/+%& 7,' 5 $

,-. )+ / %01) ()$*"+

! 8 35 7,+ *9 1 ' +/$ /* 7,

' //' &",2: ' $$,57 (,2 ,/&;

' +, &* -$/' -/

! 8 35 7,+ * 9 $ /,1$ 2 * -,

%- *1,+'/ %*-" 4%5 %/ $0 %/&",$

("$-"# 23$)4 ()$*"+

! <",&= $ 9*+ &*++,&/ $,>3,- &%-.

! <" ,&= $ 9*+ &*++,&/ /%5%- .

" !"*/*6,(,&/+%& $0 %/&",$

'-2 / %5,+$

11Guide Pins of

Different #$%&'

22Error Detection

and Alarms

33 Limit Switches

44 Counters

55 Checklists

11Guide Pins of

Different #$%&'

22Error Detection

and Alarms

33 Limit Switches

44 Counters

55 Checklists



603


Mistake Proofing Examples

Advantages of Mistake Proofing as a Control Method

Let’s considerexamples ofmistake proofingor Poka-Yoke

devices even inthe home. Have adiscussion aboutthem in the workenvironment aswell.

To see a much more in-depth review of improving the product or service quality by preventing defectsyou MUST review the book shown here. A comprehensive 240 Poka-Yoke examples are shown andcan be applied to many industries. The Poka-Yoke’s are meant to address errors from processing,assembly, mounting, insertion, measurement, dimensional, labeling, inspection, painting, printing,misalignment and many other reasons.

Defect Controls

!"#$%&' % #) '* +,#- ./ * 0-1'2 #3+$../ 0456

! ! " # $

" %& '"#( '$) +,&'"--+ ". $/$0'120

0"--$$ 3"'+

" 41" & .) -(&/ ' 0 210&2 ' 51$( 6$1+ -" 1

5(',1""# 2. "1 "&'+2)$ $/$0'120

0210&2'+

" 7 2 /" '/$++ 8( + 1(.8 $+ (.) ," '

9 ('$1 , $( '$1+

" :,2 /) 31" " - 0(3+ " . #$)20(' 2" .+

" ;&'(.$ / 28,'$1+ 9 2', +(-$'<

5&''".

! :" #3&'$1+

" ="&+$ 2.+$1' 2".

" >?; 0(5 /$ 0"..$0'2".

" ;( ''$1< 2.+$1' 2".

" 7" 9 $1 +(@ $ -$('&1$

! %&'" #" 52 /$

" ?$( ' 5$/'+

" % 2 1 5 ( 8 +

" :(1 $.82.$ 9 (1.2.8 / 28,'+

! A --20$

" ?3$ / / 0,$06 2. 9 " 1) 31" 0$++ 2.8

+"-'9 (1$

" B&$+' 2" .2.8 C D" <" & 9 (. ' '"

)$/$'$E (-'$1 )$31$++2.8 ',$

CD$/$'$E 5&''" . " . <" & 1

0" #3&'$1

! F(0'"1<

" D&(/ 3(/# 5&''" .+ (.) " ',$1

8 & ( 1 ) + " . # ( 0 , 2 . $ 1<

! G$'(2 /

" H ( # 3 $ 1 3 1 " " - 3 ( 0 6 ( 8 2 . 8

!"#$%& ' )*++, "-. % /0% -$% . '# "-1 23/'4

! 5 - 26 # "7 82' $*% "- "-. 8 *+. *%7 # %*' *'93"*'/

! :-#8'1$ "+- +8'*%$"+-# %*' '2 "7"-%$'/ %-/ $;' 8*+1'## "# # "782", "'/

! <'2 "'0'# +8 '*% $+*# ,*+7 *'8'$"$"0' $% #& # +, $6 8"1%2 0"#3% 2 "-#8 ' 1$"+-

! ) *+7 +$'# 1*'%$"0 " $6 % -/ 0% 23' %//"-. % 1$"0 " $"'#

! <'#3 2$# "- /',' 1$ ,*'' = +*&

! <'93"*'# "7 7 '/"%$' %1$"+- = ;'- 8*+> 2'7 # % * "#'

! )*+0"/'# ?@@A "-#8'1$ "+- "-$'*-%2 $+ $;' +8'*%$"+-

B;' >'#$ *'#+3*1' ,+* 8"1$+*"% 2 'C % 7 82'# +, !"#$%& ' )*+ +, "-. "# 4

)+& % DE +& ' 4 :78*+0 "-. )*+/31$ F3 % 2" $6 >6 )*'0'-$ "-. G','1$# H

5 0'*0 "'= >6 I "*+6 3& " I "*% -+H )*+/31$"0 "$6 ) *'## J ?K L L H M



604


Class Exercise

Defect Prevention Culture and Good Control Plans

Defect Controls

!"#$ % '()* +* ," -"* ,. / $( 0 0'/1,// 2 '/)$ % # ."**3 '(- /+ /)#2 /1,""#()4+ $ ) + *, " 3$ 1'4 ')'#/

50#()' 3+ *(# $ ,)*2 $ )'*( #6 $ 2 .4# $ (0 *(# . "*1#// '()#"",.) '*(#6 $ 2 .4 # . #" - " *,.

!# . "#.$ "#0 )* ."#/#() 7*)8 #6 $ 2 .4#/ )* )8# 1 4$//

9 (/: #" )8# 3*4 4*: '(- ;,#/ )'*(/ $ / . $ ") *3 )8# 0 '/1,// '*( $ (0."#/#()$) '*(<

! = *: : $ / )8# (##0 3*" )8# 1*()"*4 /+ /)#2 '0#( )'3'#0> 53 $1"')'1$ 4 ? '/ 2'/)$ % # ."* *3#0 @ 8*: : $ / ') '0#( )'3'#0 $ / 7# '(-1"')'1$ 4>

! = *: $ " # )8#+ 2$ '()$ '(#0>

! = *: $ "# )8#+ A#" ' 3 '#0 $ / : *"% '(- ."*. #" 4+ >

! 9 " # )8#+ #A #" 0 ' / $7 4 #0>

B * , 8 $ A # C D 2 ' ( ,)# / E

Prepare a probable defect prevention method to apply to yourproject.

List any potential barriers to implementation.

All of the Defect Prevention methods used must be documented in your FMEA and the ControlPlan discussed later in the Control Phase.

Tic toc…..



605



You have now completed Control Phase – Defect Controls.

! Describe some methods of Defect Prevention

!

Understand how these techniques can help with project

sustainability:- Including reducing those outliers as seen in

the Advanced Process Capability section- If the vital X was identified, prevent the cause

of defective Y

! Understand what tools must document the Defect Prevention

created in the Control Phase

Defect Controls

Notes



606


Lean Six Sigma

Black Belt Training

We will now continue in the Control Phase with “Statistical Process Control or SPC”.

Control PhaseStatistical Process Control



607


Statistical Process Control

Overview

Statistical techniques can be used to monitor and manage process performance. Processperformance, as we have learned, is determined by the behavior of the inputs acting upon it in theform of Y=f(X). As a result it must be well understood that we can only monitor the performance of aprocess output. Many people have applied Statistical Process Control (SPC) to only the processoutputs. Because they were using SPC, their expectations were high regarding a new potential level

of performance and control over their processes. However, because they only applied SPC to theoutputs, they were soon disappointed. When you apply SPC techniques to outputs, it isappropriately called Statistical Process Monitoring or SPM.

You of course know that you can only control an output by controlling the inputs that exert aninfluence on that output. This is not to say that applying SPC techniques to an output is bad, thereare valid reasons for doing this. Six Sigma has helped us all to better understand where to applysuch control techniques.

In addition to controlling inputs and monitoring outputs, Control Charts are used to determine theBaseline performance of a process, evaluate measurement systems, compare multiple processes,compare processes before and after a change, etc. Control Charts can be used in many situations

that relate to process characterization, analysis and performance.

To better understand the role of SPC techniques in Six Sigma, we will first investigate some of thefactors that influence processes, then review how simple probability makes SPC work and finallylook at various approaches to monitoring and controlling a process.

!"# ! "% & ' () *+,)- .-' */!"# ! "% & ' () *+,)- .-' */

01213+ ()*+,)-/01213+ ()*+,)-/

41'* ()*+,)-/41'* ()*+,)-/

5 6 7 '* 3 1 6 ('8 '9 " - " + :5 6 7 '* 3 1 6 ('8 '9 " - " + :

56 7' *316 ;# 81, "&1*+/5 67 ' *316 ;# 81, "&1*+/

< 1-3)&1 +) ()* +,)-< 1-3)&1 +) () *+,)-

!+'+ "/+ "3'- .,)31/ / ( )*+,)-

=!.(>

!+'+ "/+ "3'- .,)31/ / ( )*+,)-

=!.(>

< ,' 8 ?8 @ 5 3+")* A +1&/< ,' 8 ?8 @ 5 3+")* A +1&/

!"#$%&%'%()!"#$%&%'%()

*'"+",#- /,& 0123%-"*'"+",#- /,& 0123%-"

43"56/' 7 /1-" 8"-#-43"56/ ' 7 /1-" 8"-#-

*9/+3'"-*9/+3'"-



608


SPC Overview: Collecting Data

you should error on the side of taking extra samples, and then, if the process demonstrates its ability tostay in control, you can reduce the sampling rate.

Using rational subgroups is a common way to assure that this does not happen. A rational subgroup isa sample of a process characteristic in which all the items in the sample were produced under verysimilar conditions and in a relatively short time period. Rational subgroups are usually small in size,typically consisting of 3 to 5 units to make up the sample. It is important that rational subgroups consistof units that were produced as closely as possible to each other, especially if you want to detectpatterns, shifts and drifts. If a machine is drilling 30 holes a minute and you wanted to collect a sampleof hole sizes, a good rational subgroup would consist of 4 consecutively drilled holes. The selection ofrational subgroups enables you to accurately distinguish Special Cause variation from Common Causevariation.

Make sure that your samples are not biased in any way, meaning that they are randomly selected. Forexample, do not plot only the first shift’s data if you are running multiple shifts. Don’t look at only onevendor ’s material if you want to know how the overall process is really running. Finally, don’tconcentrate on a specific time to collect your samples; like just before the lunch break.

If your process consists of multiple machines, operators or other process activities that producestreams of the same output characteristic you want to control, it would be best to use separate ControlCharts for each of the output streams.

If the process is stable and in control, the sample observations will be randomly distributed around theaverage. Observations will not show any trends or shifts and will not have any significant outliers fromthe random distribution around the average. This type of behavior is to be expected from a normallyoperating process and that is why it is called Common Cause variation. Unless you are intentionallytrying to optimize the performance of a process to reduce variation or change the average, as in atypical Six Sigma project, you should not make any adjustments or alterations to the process if it isdemonstrating only Common Cause variation. That can be a big time saver since it prevents “wildgoose chases.”

If Special Cause variation occurs, you must investigate what created it and find a way to prevent it fromhappening again. Some form of action is always required to make a correction and to prevent future

occurrences.


!"#$%&'(")*

! " # %#&'(% )(*+, *- *./%0&1 &23& 234% .%%# 536 % *( 7'88 .%

536% 0*#&3'#'#) 3 023(30&%('1&'0 *- '#&%(%1&

+&,# %- *

! " 135,8% '1 3 1+.1%& *- &2% ,*,+83 &'*# *- '#&%(%1& ! 92% )(*+, *- *./%0&1 30&+388: 5%31+(%6 '# 3 1&3&'1&'038

1&+6:

! ;35,8%1 3(% +1%6 &* %1&'53&% &2% &(+% , *,+83&'*#

,3(35%&%(1

!"#$%&' (")

*&+#%,

*&+#%,

*&+#%,

!"#$%&'(")

*&+#%,*&+#%,

*&+#%,*&+#%,

*&+#%,*&+#%,

Control Charts are usually derivedfrom samples taken from thelarger population. Sampling mustbe collected in such a way that it

does not bias or distort theinterpretation of the Control Chart.The process must be allowed tooperate normally when taking asample. If there is any specialtreatment or bias given to theprocess over the period the datais collected, the Control Chartinterpretation will be invalid. Thefrequency of sampling dependson the volume of activity and the

ability to detect trends andpatterns in the data. At the onset,



609


SPC Overview: I-MR Chart

Individuals (I) and Moving Range (MR) Charts are used when each measurement represents one

batch. The subgroup size is equal to one when I-MR Charts are used. These charts are verysimple to prepare and use. The graphic shows the Individuals Chart where the individualmeasurement values are plotted with the Center Line being the average of the individualmeasurements. The Moving Range Chart shows the range between two subsequentmeasurements.

There are certain situations when opportunities to collect data are limited or when grouping thedata into subgroups simply doesn't make practical sense. Perhaps the most obvious of thesecases is when each individual measurement is already a rational subgroup. This might happenwhen each measurement represents one batch, when the measurements are widely spaced intime or when only one measurement is available in evaluating the process. Such situationsinclude destructive testing, inventory turns, monthly revenue figures and chemical tests of a

characteristic in a large container of material.

All of these situations indicate a subgroup size of one. Because this chart is dealing with individualmeasurements it, is not as sensitive as the X-Bar Chart in detecting process changes.




610


SPC Overview: Xbar-R Chart

An XBar-R Chart is used primarily to monitor and control the stability of the average value. The XBarChart plots the average values of each of a number of small sampled subgroups. The averages ofthe process subgroups are collected in sequential, or chronological, order from the process. TheXBar Chart, together with the R Chart shown, is a sensitive method to identify assignable causes ofproduct and process variation and gives great insight into short-term variations.

These charts are most effective when they are used together. Each chart individually shows only aportion of the information concerning the process characteristic. The upper chart shows how theprocess average (central tendency) changes. The lower chart shows how the variation of the processhas changed.

It is important to control both the process average and the variation separately because differentcorrective or improvement actions are usually required to effect a change in each of these twoparameters.

The R Chart must be in control in order to interpret the averages chart because the Control Limits arecalculated considering both process variation and center. When the R Chart is not in control, the

control limits on the averages chart will be inaccurate and may falsely indicate an out of controlcondition. In this case, the lack of control will be due to unstable variation rather than actual changesin the averages.

XBar and RBar Charts are often more sensitive than I-MR, but are frequently done incorrectly. Themost common error is failure to perform rational sub-grouping correctly.

A rational subgroup is simply a group of items made under conditions that are as nearly identical aspossible. Five consecutive items, made on the same machine, with the same setup, the same rawmaterials and the same operator, are a rational subgroup. Five items made at the same time ondifferent machines are not a rational subgroup. Failure to form rational subgroups correctly will makeyour XBar-R Charts dangerously wrong.




611


SPC Overview: U Chart

The U Chart plots defects per unit data collected from subgroups of equal or unequal sizes. The“U” in U Charts stands for defects per Unit. U Charts plot the proportion of defects that areoccurring.

The U Chart and the C Chart are very similar. They both are looking at defects but the U Chart doesnot need a constant sample size like the sample size like the C Chart. The Control Limits on the UChart vary with the sample size and therefore they are not uniform, similar to the P Chart which wewill describe next.

Counting defects on forms is a common use for the U Chart. For example, defects on insuranceclaim forms are a problem for hospitals. Every claim form has to be checked and corrected beforegoing to the insurance company. When completing a claim form, a particular hospital must fill in 13fields to indicate the patient’s name, social security number, DRG codes and other pertinent data. A blank or incorrect field is a defect.

A hospital measured their invoicing performance by calculating the number of defects per unit foreach day’s processing of claims forms. The graph demonstrates their performance on a U Chart.

The general procedure for U Charts is as follows:1. Determine purpose of the chart2. Select data collection point3. Establish basis for sub-grouping4. Establish sampling interval and determine sample size5. Set up forms for recording and charting data and write specific instructions onuse of the chart6. Collect and record data.7. Count the number of nonconformities for each of the subgroups8. Input into Excel or other statistical software.

9. Interpret chart together with other pertinent sources of information on the process and take corrective action if necessary




612


SPC Overview: P Chart

The P Chart plots the proportion of nonconforming units collected from subgroups of equal orunequal size (percent defective). The proportion of defective units observed is obtained by dividingthe number of defective units observed in the sample by the number of units sampled. P Charts

name comes from plotting the Proportion of defectives. When using samples of different sizes, theupper and lower Control Limits will not remain the same - they will look uneven as exhibited in thegraphic. These varying Control Chart limits are effectively managed by Control Charting software.

A common application of a P Chart is when the data is in the form of a percentage and the samplesize for the percentage has the chance to be different from one sample to the next. An examplewould be the number of patients that arrive late each day for their dental appointments. Anotherexample is the number of forms processed daily that had to be reworked due to defects. In both ofthese examples, the total quantity would vary from day to day.

The general procedure for P Charts is as follows:1. Determine purpose of the chart

2. Select data collection point3. Establish basis for sub-grouping4. Establish sampling interval and determine sample size5. Set up forms for recording and charting data and write specific instructions onuse of the chart6. Collect and record data. It is recommended that at least 20 samples be used tocalculate the Control Limits7. Compute P, the proportion nonconforming for each of the subgroups8. Load data into Excel or other statistical software9. Interpret chart together with other pertinent sources of information on theprocess and take corrective action if necessary




613


SPC Overview: Control Methods/Effectiveness


The most effective form of control is called a type 1 corrective action. This is a control applied to theprocess which will eliminate the error condition from occurring. The defect can never happen. Thisis the “prevention” application of the Poka-Yoke method.

The second most effective control is called a type 2 corrective action. This a control applied to theprocess which will detect when an error condition has occurred and will stop the process or shutdown the equipment so that the defect will not move forward. This is the “detection” application ofthe Poka-Yoke method.

The third most effective form of control is to use SPC on the X’s with appropriate monitoring on theYs. To be effective, employees must be fully trained, they must respect the rules and managementmust empower the employees to take action. Once a chart signals a problem, everyoneunderstands the rules of SPC and agrees to take emergency action for special cause identificationand elimination.

The fourth most effective correction action is the implementation of a short-term containment whichis likely to detect the defect caused by the error condition. Containments are typically audits or100% inspection.

Finally you can prepare and implement an S.O.P. (standard operating procedure) to attempt tomanage the process activities and to detect process defects. This action is not sustainable, eithershort-term or long-term.

Do not do SPC for the sake of just saying that you do SPC. It will quickly deteriorate to a waste oftime and a very valuable process tool will be rejected from future use by anyone who wasassociated with the improper use of SPC.

Using the correct level of control for an improvement to a process will increase the acceptance ofchanges/solutions you may wish to make and it will sustain your improvement for the long-term.

Type 1 Corrective Action = Countermeasure: improvement made to the processwhich will eliminate the error condition from occurring. The defect will never be created.This is also referred to as a long-term corrective action in the form of mistake proofingor design changes.

Type 2 Corrective Action = Flag: improvement made to the process which will detect when the error condition has occurred. This flag will shut down the equipment so thatthe defect will not move forward.

SPC on Xs or Ys with fully trained operators and staff who respect the rules. Once achart signals a problem everyone understands the rules of SPC and agrees to shutdown for Special Cause identification. (Cpk > certain level).

Type 3 Corrective Action = Inspection: implementation of a short-term containment which is likely to detect the defect caused by the error condition. Containments aretypically audits or 100% inspection.

SPC on Xs or Ys with fully trained operators. The operators have been trained and

understand the rules of SPC, but management will not empower them to stop forinvestigation.

S.O.P. is implemented to attempt to detect the defects. This action is not sustainableshort-term or long-term.

SPC on Xs or Ys without proper usage = WALL PAPER.



614


Purpose of Statistical Process Control

SPC has its uses because it is known that every process has known variation called Special Cause andCommon Cause variation. Special Cause variation is unnatural variability because of assignablecauses or pattern changes. SPC is a powerful tool to monitor and improve the variation of a process.This powerful tool is often an aspect used in visual factories. If a supervisor or operator or staff is able

to quickly monitor how its process is operating by looking at the key inputs or outputs of the process, thiswould exemplify a visual factory.

SPC is used to detect Special Causes in order to have those operating the process find and remove theSpecial Cause. When a Special Cause has been detected, the process is considered to be “out ofcontrol”.

SPC gives an ongoing look at the Process Capability. It is not a capability measurement but it is a visualindication of the continued Process Capability of your process.


Causes of Variation are either:

–

Common Cause: Reoccurring variability

– Special Cause: Unusual variability

•

Assignable: Reason for detected Variability

• Pattern Change: Presence of trend or unusual pattern

SPC is a basic tool to monitor variation in a process.

This is a special cause



616


Understanding the Power of SPC

The Control Chart Cookbook


!"# $%"& !() %$* +#,+-) $. / (.# ) 0%" -.** +* 1 "2$ "3 -"#$%"&4 "% .5 (+6+$+#7 *0.-+) & -) 2*.

8) %+)$+"# 62 $ 9 : ; / (< =

>?! -()%$* +#-"%0"%)$. 200 .% ) #, &"/ .% -"#$%"& & +@+$* A

! ;(. & +@+$* ) %. $<0 +-) & &< BC D E 3%"@ $(. -.#$.% & +#.A

! ;(.*. &+@+$* %.0%.*.#$ FF AGE H "3 #)$2%)& 8) % +)6+ & +$< 3"% #"%@) & ,+*$% +62$+"#*A

>?! -() %$* )& &"/ / "%I .%* )#, *20.%8 +* +"# $" @) +#$) +# +@0 %"8., 0 %"-.** 0.%3"%@) #-.

3%"@ > +5 >+7 @) 0%" J.-$*A

K*. "3 >? ! -() %$* -)# 6. ) 00& +., / +$( ) & & 0%"-.**.*A

! >.%8 +-.*L @) #23) -$2%+#7 L )#, %. $) +& ) %. J2*$ ) 3./ +#,2 *$%+.* / +$( >?!

)00& +-)$ +"#*A

! !) 2$+"# @ 2*$ 6. $)I .# / +$( 2*. "3 >?! 3"% #"#D#" %@) & 0%"-.**.*A

!"#$%"& &+@+$* , .*-% +6. $(. 0%"-.** 8 ) % +)6+ & +$< ) #, ) %. 2#%.&)$., $" -2*$"@.%*0. -+3+-)$+"#* A MN"+-. "3 $(. ?%" -.** +#*$.), "3 N "+-. "3 $(. ! 2*$"@.%O

! P# 2# ,.*+%) 6&. *+$2) $+"# +* () 8+#7 -"#$%"& & +@+$* / +,.% $() # -2*$"@. %

*0.-+3+-)$+"# & +@+$*A ;(+* / + & & .5 +*$ 3"% 0" "%&< 0 .%3"%@ +#7 0%" -.**.* / +$( ) !0

&.** $() # Q AR

S) #< >?! -()%$* .5 +* $ ) #, *.&.-$+"# @ 2*$ 6. ) 00%"0 % +)$. 3"% .33.-$+8.#.** A

General Steps for Constructing Control Charts

1. Select characteristic (critical X or CTQ) to be charted.

2. Determine the purpose of the chart.

3. Select data-collection points.

4. Establish the basis for sub-grouping (only for Ys).

5. Select the type of Control Chart.

6. Determine the measurement method/criteria.

7. Establish the sampling interval/frequency.

8. Determine the sample size.

9. Establish the basis of calculating the Control Limits.

10. Set up the forms or software for charting data.

11. Set up the forms or software for collecting data.

12. Prepare written instructions for all phases.

13. Conduct the necessary training.

Stirred or

Shaken



617


Focus of Six Sigma and the Use of SPC

Control Chart Anatomy

This concept should be very familiar to you by now. If we understandthe variation caused by the X’s,then we should be monitoring withSPC the X’s first.

By this time in the methodology youshould clearly understand theconcept of Y=f(x). Using SPC weare attempting to control the CriticalX’s in order to control the Y.

Statistical Process Control (SPC)involves the use of statisticaltechniques, to interpret data, to controlthe variation in processes. SPC is usedprimarily to act on out of controlprocesses, but it is also used to monitorthe consistency of processes producingproducts and services.

A primary SPC tool is the Control Chart- a graphical representation for specificquantitative measurements of aprocess input or output. In the ControlChart, these quantitativemeasurements are compared todecision rules calculated based on

probabilities from the actual measurement of process performance.

The comparison between the decision rules and the performance data detects any unusual variationin the process that could indicate a problem with the process. Several different descriptive statisticscan be used in Control Charts. In addition, there are several different types of Control Charts that

can test for different causes, such as how quickly major vs. minor shifts in process averages aredetected.

Control Charts are Time Series Charts of all the data points with one addition. The StandardDeviation for the data is calculated for the data and two additional lines are added. These lines areplaced +/- 3 Standard Deviations away from the Mean and are called the Upper Control Limit (UCL)and the Lower Control Limit (LCL). Now the chart has three zones: (1) The zone between the UCLand the LCL which called the zone of Common Cause variation, (2) The zone above the UCL which azone of Special Cause variation and (3) another zone of Special Cause variation below the LCL.

Control Charts graphically highlight data points that do not fit the normal level of expected variation.This is mathematically defined as being more than +/- 3 Standard Deviations from the Mean. It ’s allbased off probabilities. We will now demonstrate how this is determined.


!" $%& '%()*&(+ (,")*- .% /"0)( ")' 1%,234"' "5 &,% 6 "' 78

6

9%:%5-%5&

; )&:)&

<//%0&

=>?:&"?

@"54&"'

7A B B B 7C

D5-%:%5-%5&

D5:)&

E 2)(%

F'"1*%?

E "5&'"*

D/ .% /45- &,% G34&2 * /%.H 7I(+ /4'(& 0"5(4-%' )(45$ = FE

"5 &,% 7I( &" 20,4%3% 2 -%(4'%- 68

! " #$% &



618


Control and Out of Control

Control Charts provide you with two basic functions; one is to provide time based information on theperformance of the process which makes it possible to track events affecting the process and thesecond is to alert you when Special Cause variation occurs. Control Charts graphically highlight datapoints that do not fit the normal level of variation expected. It is standard that the Common Causevariation level is defined as +/- 3 Standard Deviations from the Mean. This is also know as the UCL

and LCL respectively.Recall the “area under the curve” discussion in the lesson on Basic Statistics, remembering that +/-one Standard Deviation represented 68% of the distribution, +/- 2 was 95% and +/- 3 was 99.7%.You also learned from a probability perspective that you would expect the output of a process wouldhave a 99.7% chance of being between +/- 3 Standard Deviations. You also learned that sum of allprobability must equal 100%. There is only a 0.3% chance (100% - 99.7%) that a data point bebeyond +/- 3 Standard Deviations. In fact, since we are talking about two zones; one zone above the+ 3 Standard Deviations and one below it. We have to split 0.3% in two, meaning that there is only a0.15% chance of being in one of the zones.

There is only a .0015 (.15%) probability that a data point will either be above or below the UCL or

LCL. That is a very small probability as compared to .997 (99.75%) probability the data point will bebetween the UCL and the LCL. What this means is there must have been something special happento cause a data point to be that far from the Mean, like a change in vendor, a mistake, etc. This iswhy the term the term Special Cause or assignable cause variation applies. The probability that adata point was this far from the rest of the population is so low that something special or assignablehappened. Outliers are just that, they have a low probability of occurring, meaning we have lostcontrol of our process. This simple, quantitative approach using probability is the essence of allControl Charts.




619


Size of Subgroups

Remember the ControlLimits are based on yourPAST data and depending

on what sources ofvariation you haveincluded in yoursubgroups, the controllimits which detect theSpecial Cause variationwill be affected. You reallywant to have subgroupswith only Common Causevariation so if othersources of variation aredetected, the sources willbe easily found instead ofburied within yourdefinition of subgroups.

The Impact of Variation


!"#$%&' )*+,-.*# )$/0) &-0 1234 5.- 6&-$&+'0 7&8&9

: ;5 7$55$%*'8" .5 , &8<0-$=, )&>#'0 .- 0?#0=)0 .5 80)8$=, 0?$)8)@ 8<0 )$/ 0@ =@ $))>&''0-

: 1@ A@ &=7 3B &-0 8<0 >.)8 %.>>.= )$/ 0 .5 )*+,-.*#) +0%&*)0 .5 0& )0 .5%& '%*'&8$.=) C<0= DEF $) 7.=0 C$8<.*8 %.>#*80-)G

D$/0 .5 )*+,-.*#) &$7 $= 7080%8$.= .5 )<$58) .5 >0&= $=7$%&8$=, )#0%$&' %&*)00?$)8)G !<0 '&-,0- 8<0 )*+,-.*# )$/0@ 8<0 ,-0&80- %<&=%0 .5 7080%8$=, & )#0%$&'%&*)0G D*+,-.*# )$/0 5.- H88-$+*80 I&8& $) .580= AB : 4BBG

Lot 1

Lot 2

Lot 3

Lot 4

Lot 5

Short-term studies

Long-term study

Lot 1

Lot 2

Lot 3

Lot 4

Lot 5

Short-term studies

Long-term study

Let’s consider if you were tracking delivery times for quotes on new business with an SPC chart. If you decided to not include averaging across product categories, you might find product categoriesare assignable causes but you might not find them as Special Causes since you have includedthem in the subgroups as part of your rationalization.

You really want to have subgroups with only Common Cause variation so if other sources ofvariation are detected, the sources will be easily found instead of buried within your definition ofsubgroups.

- Natural Process Variationas defined by subgroup

selection

- Natural Process Variation- Different Operators

Sources of Variation

- Natural Process Variation- Different Operators

- Supplier Source

And, of course, if two additional

sources of variation arrive, we willdetect that, too!

First, select a spread to

declare as the Natural

Process Variation

so that

whenever any point lands

outside these Control

Limits

an alarm will sound

So, when a second

source of variationappears, we will know!

If you base your limits on all three sources of variation, what will sound the alarm?

-UCL

-LCL



620


Frequency of Sampling


Sampling Frequency is a balance between cost of sampling and testing versus cost of not detectingshifts in mean or variation.

Process knowledge is an input to frequency of samples after the subgroup size has been decided.

- If a process shifts but cannot be detected because of too infrequent sampling, thecustomer suffers- If choice is given of large subgroup samples infrequently or smaller subgroupsmore frequently, most choose to get information more frequently.- In some processes, with automated sampling and testing frequent sampling iseasy.

If undecided as to sample frequency, sample more frequently to confirm detection of process shiftsand reduce frequency if process variation is still detectable.

A rule of thumb also states “sample a process at least 10X more frequent than the frequency of ‘outof control’ conditions”.

Sometimes it can be a struggle how often to sample your process when monitoring results. Unlessthe measurement is automated, inexpensive and recorded with computers and able to be chartedwith SPC software without operator involvement, then frequency of sampling is an issue.

Let’s reemphasize some points. First, you do NOT want to under sample and not have the ability tofind Special Cause variation easily. Second, do not be afraid to sample more frequently and thenreduce the frequency if it is clear Special Causes are found frequently.



621


SPC Selection Process

meaning. When these Control Charts are used to control the Critical X input characteristic it is calledStatistical Process Control (SPC). These charts can also be used to monitor the CTQ’s, the importantprocess outputs. When this is done it is referred to as Statistical Process Monitoring (SPM).

There are two categories of Control Charts for Continuous Data: charts for controlling the processaverage and charts for controlling the process variation. Generally, the two categories are combined.The principal types of Control Charts used in Six Sigma are: charts for Individual Values and MovingRanges (I-MR), charts for Averages and Ranges (XBar-R), charts for Averages and StandardDeviations (XBar-S) and Exponentially Weighted Moving Average charts (EWMA).

Although it is preferable to monitor and control products, services and supporting processes withContinuous Data, there will be times when Continuous Data is not available or there is a need tomeasure and control processes with higher level metrics, such as defects per unit. There are manyexamples where process measurements are in the form of Attribute Data. Fortunately, there arecontrol tools that can be used to monitor these characteristics and to control the critical process inputsand outputs that are measured with Attribute Data.

Attribute Data, also called discrete data, reflects only one of two conditions: conforming or

nonconforming, pass or fail, go or no go. Four principal types of Control Charts are used to monitorand control characteristics measured in Attribute Data: the p (proportion nonconforming), np (numbernonconforming), c (number of non-conformities), and u (non-conformities per unit) charts. Fourprinciple types of Control Charts are used to monitor and control characteristics measured in DiscreteData: the p (proportion nonconforming), np (number nonconforming), c (number of non-conformities),and u (non-conformities per unit) charts. These charts are an aid for decision making. With ControlLimits, they can help us filter out the probable noise by adequately reflecting the Voice of the Process.

A defective is defined as an entire unit, whether it be a product or service, that fails to meetacceptance criteria, regardless of the number of defects in the unit. A defect is defined as the failure tomeet any one of the many acceptance criteria. Any unit with at least one defect may be considered tobe a defective. Sometimes more than one defect is allowed, up to some maximum number, before theproduct is considered to be defective.


! "##$ % ' (() #() * + ,%

!#-,)#. !"+),

typeof data

type of

attribute

data

subgroupsize

I – MR

Chart

X –R

Chart

X –R

Chart

X –S

Chart

X –S

Chart

CumSum

Chart

EWMA

Chart

C Chart U ChartNP

ChartP Chart

type

of defecttype of

subgroups

ATTRIBUTE CONTINUOUS

DEFECTS DEFECTIVES

VARIABLECONSTANT CONSTANT VARIABLE

1 2-5 10+

Number of

Incidences

Incidences

per Unit

Number of

Defectives

Proportion

Defectives

Individuals& Moving

Range

Mean &Range

Mean &Std. Dev.

Cumulative

SumExponentially

Weighted Moving Average

SPECIAL CASES

Sample size

The Control Charts youchoose to use willalways be based firston the type of data you

have and then on theobjective of the ControlChart. The firstselection criteria will bewhether you have Attribute or ContinuousData.

Continuous SPC refersto Control Charts thatdisplay process input

or outputcharacteristics basedon Continuous Data -data where decimalsubdivisions have



622


Chart Selection Process

SigmaXL® includes a Control Chart Selection Tool to simplify the selection process.


Notes



623


Understanding Variable Control Chart Selection

Understanding Attribute Control Chart Selection

The P Chart is the most common type of chart in understanding Attribute Control Charts.


!" # $ & ' ( ) * +, - ) $. / & " & 0 . $ $/ 1,2

u !"#$ %&'(#) (+ , (- ,." /# 0%1.2 3 0 0#4 + 5"# &.++ 1. 3 ) 3 )$ / 3 "(36( 0 ('7

'# 6 . / (.4 .$ 3 )$ 3 ++.++. $ '#- .',."2 1 #". +3 1 50 ()- ',3 ) 4 ( ',

8)$(/ ($%3 0+ &,3" ' 9 8: 3)$ ;#/ ()- <3 )- . &,3 "'+ 9;<: 6%' 4 ,.)+%6 - "#%5 + 3 ". $ .+( ".$= > %'0 (."+ &3 ) &3 %+. ( ++%.+ 4 ( ', < 3 )- . 9<:

&,3"'+ +# ?'3)$3"$ @./(3' (#) &,3"'+ 9?: %+.$ ()+'.3$ ( A &#)&.").$=

u !"#$%&'(#) (+ 0#4 /#0%1. #" &7&0. ' (1. '# 6%( 0$ 5"#$%&' (+ 0#)- #"

,#1 #- .).#%+ +3 1 50. ".5 ".+.)'+ .)' (". 5 "#$% &' 963'&, .'& =:2

+3 1 50 ()- 3 )$ '.+'()- ( + &#+'07 +# +%6 - "#%5 + 3 ". )#' $.+( ".$=

B#) '"#0 0(1('+ 3" . 4 ($." ',3 ) C D3 " &,3"'+ = E+.$ A#" ? !B #) 1 #+'

()5%'+=

u ?.'F%5 (+ &" ( '(&3 0 G #" &#+' #A +.'%5 +&"3 5 (+ , (-,= E+. A#" #%'5%'+

u ?1 3 0 0 +,( A' )..$ + '# 6. $ .'.&'.$G #A'.) 6.&3 %+. #A 3 %'#&#"".03' (#)

#A ',. #%'5%' ".+%0'+ = E+.$ # )07 A#" ()$(/ ($%3 0+ #" 3/ ."3 - .+ #A

> %'5%'+= 8)A".H%.)' 07 %+.$ 6.&3 %+. # A &3 0&%03'(#) &#1 50.I ( '7 =

u ?3 1 . ".3 +#)+ 3 + JK ;L 9JI 5#) .)'(3 0 07 K .(- ,'.$ ;#/()- <3 )- .:

.I &.5' ',. 53 +' $3 '3 ( + 3+ (1 5# "'3 )' 3 + 5".+. )' $3 '3 =

L / . " 3 - . M

<3 )- . # " ?

9C D 3 " 3 ) $ < #"C D 3 " 3 ) $ ? :

8)$ ( / ( $%3 0 3 )$

;#/ ()- < 3 )- .

!".FB#)'"#0

JI 5# ).) '(30 07

K .(- ,'. $

; # / ( ) - L / . " 3 - .

B%1 %0 3 '( / . ? %1

; # +' &# 11 # )

N .+ + B # 1 1 # )

u ! ""# %& %'()* %+" ,'( )%-&. &, #",")%-/"

0.- %1 2 1( 34 5" 1 - 6" -1 /( ' -( 7 5" ( .# 010( 5 58 9 : ;

u < +". 8 &0 = ( .% %& %'()* %+" .0 3 7"' & , #",")%-/"

0.-%1 4"' 107 > '&042 1( 34 5" 1 -6" -1 010( 5 58

) &.1%( . % ( .# 010( 5 58 9 : ;

u < +". 8 &0 = ( .% %& %'()* %+" .0 3 7"' & , #",")%1

4"' 107 > '&04 & , 0.-%1 4'&# 0)"#2 1(3 45" 1 -6" -1

)&.1%(.%

u < +". 8 &0 = ( .% %& %'( )* %+" .03 7"' &,

#",")%1 4"' 0. -%2 1(3 45" 1 -6" -1 /( ' -(7 5"

?

.?

@

A

! "#$ & ' ( ') $##& *+, -( . # ' / 0 " 1 2 +



624


Detection of Assignable Causes or Patterns

Remember Control Charts are used to monitor a process performance and to detect SpecialCauses due to assignable causes or patterns. The standardized rules of your organization may

have some of the numbers slightly differing. For example, some organizations have 7 or 8 pointsin a row on the same side of the Center Line. We will soon show you how to find what yourSigmaXL® version has for defaults for the Special Cause tests.

There are typically 8 available tests for detecting Special Cause variation. Only 4 of the 8 SpecialCause tests can only be used Range, Moving Range or Standard Deviation charts which are usedto monitor “within” variation. Note, SigmaXL® V6 does not include tests for special causes on theRange, Moving Range or Standard Deviation charts.

If you are unsure of what is meant by these specific rule definitions, do not worry. The next fewslides will specifically explain how to interpret these rules.


!"#$%"& !()%$* +#,+-)$. */.- +) & -)0 *.* 1. +#2 . + $(.% )* *+2#) 1&. -)0* .* "% /) $$.%#*3

4(. 5" &&"6 +#2 %0 &.* ) %. ) //& +-)1 &. 5"% 1"$( 7) %+)1&. ) #, 8$$% +10$. 9) $) $" , .$.-$

*/.- +) & -)0*.*3

4(.*. 5"0% %0 &.* ) %. $(. "#&: ) //& +-)1 &. $.*$* 5"% ;) #2 . <;=> ?"7 +#2 ;) #2 . <?;=> "%

@$)#,) %, 9.7 +)$+"# <@= -()%$*3

! A #. /"+#$ B"%. $()# C @$)#,) %, 9.7 +)$ +"#* 5 %"B $(. -.#$.% & +#. 3

! D / "+#$* +# ) %"6 ) & & . + $(.% +#-%.)*+#2 "% ) & & ,.-%.)*+#2 3

! EF /"+#$* +# ) %"6 ) &$.%#)$ +#2 0/ )#, ,"6 #3

! G / "+#$* +# ) %"6 "# $(. *)B . *+,. "5 $(. -.#$.% & +#.3

4(.*. %.B)+#+#2 5"0% %0 &.* )%. "#&: 5"% 7) %+)1&. ,) $) $" ,.$.-$ */.- +) & -) 0*.*3

! H "0 $ "5 C /"+#$* 2 %.)$.% $() # H @ $)# ,) %, 9.7+) $+"#* 5 %"B $(. -.#$.% & +#. "# $(.

*) B . * +, . 3

! F " 0$ "5 I / "+#$* 2 %.)$.% $() # E @ $)# ,) %, 9.7 +)$ +"# 5 %"B $(. -.# $.% & +#. "# $(.

*) B . * +, . 3

! E I / "+#$* +# ) %"6 ) & & 6 +$(+# "#. @$)# ,) %, 9.7 +)$+"# "5 .+$(.% * +,. "5 $(. -.#$.%

&+#.3

! J / "+#$* +# ) %"6 ) & & 2 %.)$.% $() # "#. @$)#,) %, 9.7+) $+"# "5 .+ $(.% * +,. "5 $(.

-.#$.% &+#.3



625


Recommended Special Cause Detection Rules

Special Cause Rule Default in SigmaXL®


! "# %&'()&)*+%*, -./ &0*10((2 3%+451+ 65#+30 7) %*%+%0 ((28 +4) &56+ 9%610((2 5:9%516 9%5(0+%5*6 07)

&57) )06%(2 ;)+)<+);= -./ 5* &0*10((2 #%((); <40 7+6 07) <5&&5* '(0<) #57 %*%+%0 ( 16) 5# ;)#)<+

'7)9)*+%5* +)<4*%>1)6=

! ?4)6) @ 71()6 07) !"#$%& &' +4) &56+ )06%(2 ;)+)<+); :2 ')765**)(=

A B *) '5%*+ &57) +40* @ -+0*;0 7; C)9%0+%5*6 #75& +4) <)*+)7 (%*)=

A D '5%*+6 %* 0 753 0(( )%+4)7 %*<7)06%*, 57 0(( ;)<7)0 6%*, =

A EF '5%*+6 %* 0 753 0(( 3%+4%* 5*) -+0*;0 7; C)9%0+%5* 5# )%+4)7 6%;) 5# +4) <)*+)7 (%*)=

! C7= -4)3407+ +40+ 357G); 3%+4 +4) H)6+)7* I()<+7%< / 5= 30 6 <7);%+); 3%+4 +4) #5((53%*, J 71()6

7)#)77); +5 06 H )6+)7* I()<+7%< K1()6=

A B *) '5%*+ &57) +40* @ -+0*;0 7; C)9%0+%5*6 #75& +4) <)*+)7 (%*)=

A ( '5%*+6 %* 0 753 5* +4) 60&) 6%;) 5# +4) <)*+)7 (%*)=

A L 51+ 5# @ '5%*+6 , 7)0+)7 +40* L -+0*;0 7; C)9%0+%5*6 #75& +4) <)*+)7 (%*) 5* +4) 60&) 6%;)=

A J 51+ 5# F '5%*+6 , 7)0+)7 +40* E -+0*;0 7; C)9%0+%5* #75& +4) <)*+)7 (%*) 5* +4) 60&) 6%;)=

! M51 &%,4+ *5+%<) +4) H )6+)7* I()<+7%< 71()6 9072 6(%,4+(2= ?4) %&'57+0*<) %6 +5 :) <5*6%6+)*+ %*

2517 57,0*%N0+%5* 0*; ;)<%;) 340+ 71()6 251 3%(( 16) +5 ;)+)<+ 6')<%0( <016)6=

! OIKM #)3 57,0*%N0 +%5*6 16) 0(( P 71()6 #57 ;)+)<+%*, 6')<%0( <016)6=

When a Belt is using SigmaXL®, the default tests can be set when running SPC on the variable or

Attribute Data. A Belt can always change which tests are selected.



626


As promised, we will now closely review the definition of the Special Cause tests. The first test isone point more than 3 sigmas from the Center Line. The 3 sigma lines are added or subtractedfrom the Center Line. The sigma estimation for the short-term variation will be shown later in this

module.

If only one point is above the upper 3 sigma line or below the lower 3 sigma line, then a SpecialCause is indicated. This does not mean you need to confirm if another point is also outside of the 3sigma lines before action is to be taken. Don’t forget the methodology of using SPC.

Special Cause Test Examples


If you want to see the SigmaXL® output on the left, execute the SigmaXL® command “Control

Charts > ‘ Tests for Special Causes’ Defaults”. Remember, your numbers may vary in the slideand those are set in the defaults as you were shown recently in this module. From now on, we willassume your rules are the same as shown in this module. If not, just adjust the conclusions.



627


Special Cause Test Examples

The third test lookingfor a Special Cause

is six points in a rowall increasing or alldecreasing. Thismeans if sixconsecutive times,the present point ishigher than theprevious point thanthe rule has beenviolated and theprocess is out of

control. The rule isalso violated if for sixconsecutive timesthe present point islower than the


This rule would also be violated if nine consecutive points are below the Center Line. The amountaway from the Center Line does not matter as long as the consecutive points are all on the sameside of the Center Line.

The second testfor detectingSpecial Causes

is nine points ina row on thesame side of theCenter Line.This literallymeans if nineconsecutivepoints are abovethe Center Line,then a SpecialCause isdetected thatwould accountfor a potentialMean shift in theprocess.

previous point on the SPC chart.

This rule obviously needs the time order when plotting on the SPC charts to be valid. Typically,these charts plot increasing time from left to right with the most recent point on the right hand sideof the chart. Do not make the mistake of seeing six points in a line indicating an out of controlcondition. Note on the example shown on the right, a straight line shows 7 points but it takes thatmany in order to have six consecutive points increasing. This rule would be violated no matter

what zone the points occur.



628


Special Cause Test Examples (cont.)

The fifth Special Causetest looks for 2 out of 3consecutive points morethan 2 sigma away fromthe Center Line on thesame side. The 2 sigmaline is obviously 2/3 ofthe distance from theCenter Line as the 3sigma line. Please noteit is not required that thepoints more than 2

sigma away be inconsecutive order, they just have to be within agroup of 3 consecutivepoints. Notice the


then the process is considered out of control or a Special Cause is indicated. This rule does notdepend on the points being in any particular zone of the chart. Also note the process is notconsidered to be out of control until after the 14th point has followed the alternating up and downpattern.

The fourth rulefor a SpecialCause indicationis fourteen points

in a rowalternating upand down. Inother words, ifthe first pointincreased fromthe last point andthe second pointdecreased fromthe first point andthe third point

increased fromthe second pointand so on forfourteen points,

example shown on the right does NOT have 2 consecutive points 2 sigma away from the CenterLine but 2 out of the 3 consecutive are more than 2 sigma away. Notice this rule is not violated ifthe 2 points that are more than 2 sigma but NOT on the same side.

Have you noticed that SigmaXL® will automatically place a number by the point that violates theSpecial Cause rule and that number tells you which of the Special Cause tests has been violated.

In this example shown on the right, the Special Cause rule was violated two times.



629


Special Cause Test Examples (cont.)

The seventh Special Causetest looks for 15 points in arow all within one sigmafrom the Center Line. Youmight think this is a goodthing and it certainly is.However, a you might wantto find the Special Cause

for this reduced variation sothe improvement can besustained in the future.


The sixth Special Causetest looks for any four out offive points more than onesigma from the Center Line

all on the same side. Onlythe 4 points that were morethan one sigma need to beon the same side. If four ofthe five consecutive pointsare more than one sigmafrom the Center Line and onthe same side, do NOTmake the wrong assumptionthat the rule would not beviolated if one of the four

points was actually morethan 2 sigma from theCenter Line.

The eighth and final testfor Special Causedetection is having eightpoints in a row all morethan one sigma from theCenter Line. The eightconsecutive points can be

any number of sigmaaway from the CenterLine. Do NOT make thewrong assumption this rulewould not be violated ifsome of the points weremore than 2 sigma awayfrom the Center Line. Ifyou reread the rule, it juststates the points must bemore than one sigma from

the Center Line.



630


SPC Center Line and Control Limit Calculations


This is a reference in case you really want to get into the nitty-gritty. The formulas shown here arethe basis for Control Charts.

!" #$%#"&' &)' *"+" ,'&'+- ./ &)' 01234 32%" # "12 56 !.1&+.# !)"+&-7 3&) &)' /.##. 7 318 9

Where:

Xbar: Average of the individuals, becomes the centerline on the Individuals chart

Xi: Individual data points

k: Number of individual data points

Ri : Moving range between individuals, generally calculated using the difference between

each successive pair of readings

MRbar: The average moving range, the centerline on the range chartUCLX: Upper control limit on individuals chart

LCLX: Lower control limit on individuals chart

UCLMR: Upper control limit on moving range

LCLMR : Lower control limit on moving range (does not apply for sample sizes below 7)

E2, D3, D4: Constants that vary according to the sample size used in obtaining the moving range

k

x

X

k

1i

i!=

=

k

R

R M

k

i

i!=

R MEXUCL2x

+=

R MEXLCL2x

"=

R MDUCL4MR

=

R MDLCL3MR

=

!'1&'+# 31' !. 1&+.# :3, 3&-

56 ; " + < $. , * % &' 2 " ; . 4 ' =

2 > < &" ;#' ./ $.1-&"1&- /.+ -%;8 +.%* - 3 ?' 1=

# !"#$ &'($ )"#*+,#'- . 56 ; " + < $. , * % &' 2 " ; . 4 ' =

2 > < &" ;#' ./ $.1-&"1&- /.+ -%;8 +.%* - 3 ?' 1=

# !"#$ &'($ )"#*+,#'- .

!" #$%#"&' &)' * " +" , '&'+- ./ &)' 0 1" + " 23 4 !.2 &+.# !)" +&- 5 6&) &)'

/.##.5 627 8

k

x

X

k

1i

i!=

=

k

R

R

k

i

i!=

R AXUCL2x

+=

R AXLCL2x

"=

R DUCL4R

=

R DLCL3R

=

!'2&'+# 62' !. 2&+.# 96, 6&-

Where:

Xi: Average of the subgroup averages, it becomes the centerline of the control chart

Xi: Average of each subgroup

k: Number of subgroups

Ri : Range of each subgroup (Maximum observation – Minimum observation)

Rbar: The average range of the subgroups, the centerline on the range chart

UCLX: Upper control limit on average chartLCLX: Lower control limit on average chart

UCLR: Upper control limit on range chart

LCLR : Lower control limit range chart

A2, D3, D4: Constants that vary according to the subgroup sample size

Where:




Ri : Range of each subgroup (Maximum observation – Minimum observation)

Rbar: The average range of the subgroups, the centerline on the range chart

UCLX: Upper control limit on average chartLCLX: Lower control limit on average chart

UCLR: Upper control limit on range chart

LCLR : Lower control limit range chart

A2, D3, D4: Constants that vary according to the subgroup sample size

4 : " + ;$ . , * % & '3 " : . < ' =

3 > ; &": #' ./ $.2-&" 2&- /.+ -%:7 +.%* - 6?' 2=

# !"#$ &'($ )"#*+,#'- . 4 : " + ;$ . , * % & '3 " : . < ' =

3 > ; &": #' ./ $.2-&" 2&- /.+ -%:7 +.%* - 6?' 2=

# !"#$ &'($ )"#*+,#'- .



631


SPC Center Line and Control Limit Calculations (cont.)


Yet another reference just in case anyone wants to do this stuff manually…have fun!!!!

!" #$%#"&' &)' * " +" , '&'+- ./ &)' 0 1" + " 23 4 ! .2&+.# !)"+&- 5 6 &) &)'

/.##. 5 627 8

Where:




si : Standard deviation of each subgroup

Sbar: The average s. d. of the subgroups, the centerline on the S chart

UCLX: Upper control limit on average chart

LCLX: Lower control limit on average chart

UCLS: Upper control limit on S chart

LCLS : Lower control limit S chart

A3, B3, B4: Constants that vary according to the subgroup sample size

Where:




si : Standard deviation of each subgroup

Sbar: The average s. d. of the subgroups, the centerline on the S chart

UCLX: Upper control limit on average chart

LCLX: Lower control limit on average chart

UCLS: Upper control limit on S chart

LCLS : Lower control limit S chart

A3, B3, B4: Constants that vary according to the subgroup sample size

k

x

X

k

1i

i!=

=

SAXUCL3x

+=

!'2&'+# 62' !. 2&+.# 96,6&-

SAXLCL3x

"=k

s

S

k

1i

i!=

=

SBUCL4S

=

SBLCL3S

=

4 : " + ;$. , *%&'3 ": . < '=

$> ; &" :#' ./ $.2-&" 2&- /.+ -%:7 +.%* - 6?' 2=

# !"#$ &'($ )"#*+,#'- . 4 : " + ;$. , *%&'3 ": . < '=

$> ; &" :#' ./ $.2-&" 2&- /.+ -%:7 +.%* - 6?' 2=

# !"#$ &'($ )"#*+,#'- .

We are now moving to the formula summaries for the Attribute SPC Charts. These formulas are fairlybasic. The upper and lower Control Limits are equidistant from the Mean % defective unless youreach a natural limit of 100 or 0%. Remember the p Chart is for tracking the proportion or %defective.

These formulas are a bit more elementary because they are for Attribute Control Charts. Recall pCharts track the proportion or % defective.

!" #$%#" &' &)' * " +" , '&'+- ./ &)' 0 !. 1&+.# !)" +&- 2 3&) &)' /.# #.2 314 5

Where:

p: Average proportion defective (0.0 – 1.0)

ni: Number inspected in each subgroup

LCLp: Lower control limit on p chart

UCLp: Upper control limit on p chart

inspecteditemsof numberTotal

itemsdefectiveof numberTotal p =

in

p p )1(3 pUCL p

!

+=

!'1&'+#31' !. 1&+.# 63,3&-

in

p p )1(3 pLCL p

!

!

=

!"#$% '(% ) *#'+*, -"."'/ 0+% 0 12#$'"*# *1

/0.3,% /"4%5 '(%6 7",, 80+6 1*+ %0$( /0.3,%9



632




The nP Chart’s formulas resemble the P Chart. This chart tracks the number of defective items in asubgroup.

The U Chart is also basic in construction and is used to monitor the number of defects per unit.

!" #$%#"&' &)' *" +" , '&'+- . / &)' 01 !.0 &+.# !)" +&- 2 3 &) &)'

/.##. 2 304 5

Where:

np: Average number defective items per subgroup


LCLnp: Lower control limit on nP chart

UCLnp: Upper control limit on nP chart

subgroupsof numberTotal

itemsdefectiveof numberTotal pn =

)1(3 pnUCL inp p pni

!+=

!'0&'+# 30' !. 0&+.# 63,3&-

p)- p(1n3 pnLCL iinp !=

!"#$% '(% ) *#'+*, -"."'/ 0 1 2 ) %#'%+ -"#% 3 +% 3 45#$'"*#

*4 /3.6,% /"7%8 '(%9 :",, ;3+9 4*+ %3$( /3.6,%<

!" #$%#"&' &)' * " +" , '&'+- ./ &)' 0 !.1 &+.# !)" +&- 2 3&) &)'

/.##. 2 314 5

Where:

u: Total number of defects divided by the total number of units inspected.


LCLu: Lower control limit on u chart.

UCLu: Upper control limit on u chart.

InspectedUnitsof numberTotal

Identifieddefectsof numberTotalu =

in

u3uUCLu +=

!'1&'+#31' !. 1&+.# 63,3&-

!"#$% '(% ) *#'+*, -"."'/ 0+% 0 12#$'"*# *1 /0.3,%

/"4%5 '(%6 7",, 80+6 1*+ %0$( /0.3,%9

in

u3uLCLu !=



633




The C Control Charts are a nice way of monitoring the number of defects in sampled subgroups.

This EWMA can be considered a smoothing monitoring system with Control Limits. This is rarelyused without computers or automated calculations. The items plotted are NOT the actualmeasurements but the weighted measurements. The exponentially weighted moving average isuseful for considering past and historical data and is most commonly used for individualmeasurements although has been used for averages of subgroups.

!" #$%#" &' &)' *" +" , '&'+- . / &)' ! !.0 &+.# !) " +&- 1 2&) &)'

/. ##.1 203 4

5 )'+ '4

c: Total number of defects divided by the total number of subgroups.

LCLc: Lower control limit on c chart.

UCLc: Upper control limit on c chart.

subgroupsof numberTotal

defectsof numberTotalc = c3cUCLc +=

!'0&'+# 20' !. 0&+.# 62, 2&-

c3cLCLc !=

!" #$%#" &' &)' *" +" , '&'+- . / &)' 01 23 !.4 &+.# !) " +&- 5 6&)

&)' /.##.5 647 8

1 )'+'8

Zt: EWMA statistic plotted on control chart at time t

Zt-1: EWMA statistic plotted on control chart at time t-1

: The weighting factor between 0 and 1 – suggest using 0.2

: Standard deviation of historical data (pooled standard deviation for subgroups

– MRbar/d2 for individual observations)

Xt: Individual data point or sample averages at time t

UCL: Upper control limit on EWMA chart

LCL: Lower control limit on EWMA chart

n: Subgroup sample size

1ttt Z! )(1X! Z#

#+= ]! )(1)[1! 2

! (

n

"3XUCL 2t

##

#

+=

!'4&'+#64' !. 4&+.# 96,6&-

]! )(1)[1! 2

! (

n

"3XLCL 2t

##

#

#=



634




The CUSUM is an even more difficult technique to handle with manual calculations. We aren’t evenshowing the math behind this rarely used chart. Following the Control Chart selection route shownearlier, we remember the CUSUM is used when historical information is as important as present data.

Note, SigmaXL® V6 does not include CUSUM.

!" #$% #"&' &)' *" +" , '&'+- ./ &)' !01 02 ! .3&+. # !)" +&- 4 5 &)

267 689 : 82 .+ .&)'+ *+.;+", - 53$' &)' $" #$% #"& 5.3- "+' '<'3

, .+' $.,* # 5$"&'= &)" 3 &)' >? 29 $)" +&- @

:'$" %-' ./ &)5- $., *#'A 5 &B ./ /.+, %#" -C 'A '$%&5.3 ./ ' 5&)'+

&) 5- .+ &)' >? 29 " +' 3 .& =.3' 4 5 &).%& " %&., " &5.3 " 3=

$.,*%&'+ "-- 5-&"3$'@

9)C "3B D.=B ;.& " #"*&.*Eh, anybody got a laptop?



635


Pre-Control Charts


The Pre-Control Charts are often used for startups with high scrap cost or low production volumesbetween setups. Pre-Control Charts are like a stoplight are the easiest type of SPC to use byoperators or staff. Remember Pre-Control Charts are to be used ONLY for outputs of a process.

Another approach to using Pre-Control Charts is to use Process Capability to set the limits whereyellow and red meet. SigmaXL® does not include Pre-Control.

!"#$%&'("&) %+,"(- !"# %&'&(" )#%*(&+# (, (-# ".#/ &0&/* (&,1 %&'&("2 3-&" &" (-# 0&)"(*14 5 6 78 /-*)( 9,! :&%% "## ".#/&0&/*(&,1 %&'&(" .%,((#4 0,) "(* (&"(&/* % .),/#""/,1(),%2 3-&" &" (-# ',"( ;* "&/ (9.# ,0 /-* )( *14 !1",.-&"(&/* (#4 !"# ,0 .),/#""/,1(),%2

!"# % &'"() <,1# ,!("&4# (-#

".#/&0&/*(&,1 %&'&("2 =&>1*%" (-#

.),/#"" &" ,!(?,0?/,1(),% *14

"-,!%4 ;# "(,..#4

RED Yellow Yellow RedGREEN

0.5 0.750.25 1.00.0

Target USLLSL

RED Yellow Yellow RedGREEN

0.5 0.750.25 1.00.0

Target USLLSL

* "+ +&, % &'" ( 2 <,1# ;#(:##1

(-# @A 7&1#" *14 (-#

".#/&0&/*(&,1 %&'&("B &14&/*(#"

/*!(&,1 *14 (-# 1##4 (, :*(/-

(-# .),/#"" /%,"#%9

- .""' % &'" ) <,1# %&#"

;#(:##1 (-# @A 7&1#"B "&>1*%" (-#

.),/#"" &" &1 /,1(),%

Process Setup and Restart with Pre-Control

! "# $ %&' %() +,-./00

! "# %&'()*+ ' ,-#./001 *)2/ .#30/.&4)2/ ,'-40 5&04 *'(( 6)47)3 47/ 8 -//3 9 #3/

! "7/ ,-#./00 07#&(: ;/ %&'()*)/: '*4/- 4##( .7'38/01 ':<&045/3401 3/6

#,/-'4#-01 5'4/-)'( .7'38/01 /4.

1-( %2-, %() 3 () -%() +,-./00

! ='5,(/ 46# .#30/.&4)2/ ,'-40 '4 ,-/:/4/-5)3/: *-/%&/3.+ > ?* /)47/- ,' -4 )0 )3 47/ -/:1 04#, ,-#:&.4)#3 '3: *)3: -/'0#3 *#- 2'-)'4)#3

> @ 7/3 #3/ ,' -4 *' ((0 )3 47/ +/((#6 9 #3/ )30,/.4 47/ #47/- ' 3:

! ?* 47/ 0/.#3: ,'-4 *'((0 )3 47/ 8-//3 9#3/ 47/3 .#34)3&/

! ?* 47/ 0/.#3: ,'-4 *'((0 )3 47/ +/((#6 9 #3/ #3 47/ 0'5/ 0):/1 5'A/ '3

':<&045/34 4# 47/ ,-#./00

! ?* 0/.#3: ,' -4 *'((0 )3 47/ +/((#6 9 #3/ #3 47/ #,,#0)4/ 0):/ #- )3 47/

-/: 9#3/1 47/ ,-#./00 )0 #&4 #* .#34-#( '3: 07#&(: ;/ 04#,,/:

> ?* ' 3+ ,' -4 *' ((0 #&40):/ 47/ 0,/.)*).'4)#3 ()5)40 #- )3 47/ -/: 9 #3/1 47/

,-#./00 )0 #&4 #* .#34-#( '3: 07#&(: ;/ 04#,,/:



636


Responding to Out of Control Indications


SPC can be actually harmful if those operating the process respond to process variation withsuboptimizing. A basic rule of SPC is if it is not out of control as indicated by the rules, then do notmake any adjustments. There are studies where an operator that responds to off centermeasurements will actually produce worse variation than a process not altered at all. Remember,being off the Center Line is NOT a sign of out of control because Common Cause variation exists.

Training is required to use and interpret the charts not to mention training for you as a Belt to properlycreate an SPC chart.

SPC is an excitingtool but we mustnot get enamoredwith it. The power

of SPC is not tofind the Center Lineand Control Limitsbut to react to outof controlindications with anout of control actionplan. SPC foreffectiveness atcontrolling andreducing long-term

variation is torespondimmediately to outof control orSpecial Causeindications.

Attribute SPC Example

SPC power is to react to the Out of Control (OOC) indicationswith an Out of Control Action Plan (OCAP).

• Requires immediate response to Special Cause.

•

No reaction while process is within limits!

OCAP

If response time is too

high, get additional

person on phone bank

VIOLATION:

Special Cause is

indicated

Observation

I n d i v i d u a l V a l u e

3128252219161310741

40

30

20

10

0

_ X=18.38

UCL=39.76

LCL=-3.01

1

Individual SPC chart for Response Time



637


Attribute SPC Example (cont.)




638




Now we must see if the next few weeks are showing Special Cause from the results. The samplesize remained at 250 and the defective checks were 61, 64, 77.

Average % defective = 20.380%UCL = 28.0%

LCL = 12.7%

No Special Causes were detected.



639




The chart has now been updated to include the new points.



640




Let’s walk through another example of using SPC within SigmaXL® but in this case it will bewith Continuous Data. Open the worksheet called “hole diameter ” and select the appropriatetype of Control Chart and calculate the Center Line and Control Limits.

Let’s try another one, this time variable…

Because of the Special Cause, the process must refer to the OCAP or Out of Control Action Planthat states what Root Causes need to be investigated and what actions are taken to get theprocess back in Control. After the corrective actions were taken, wait until the next sample is takento see if the process has changed to not show Special Cause actions. If still out of control, refer to

the OCAP and take further action to improve the process. However, DO NOT make any morechanges if the process shows back in control after the next reading. Also, even if the next readingseems higher than the Center Line don’t cause more variability. If process changes aredocumented after this project was closed, the Control Limits should be recalculated as in step 9 ofthe SPC methodology.

Special Cause OCAPActivate



641




The example has Continuous Data, subgroups and we have no interest in small changes in thissmall process output. The Xbar R Chart is selected because we are uninterested in the Xbar SChart for this example.



642






643




Note: The Mean, UCL and LCL are unchanged when SigmaXL®’s Add Data button is used.



644






645



SPC Chart Option in SigmaXL® for Levels



646



You have now completed Control Phase – Statistical Process Control.

! Describe the elements of an SPC chart and the purposes ofSPC

! Understand how SPC ranks in defect prevention

! Describe the 13 Step route or methodology of implementing a

chart

! Design subgroups if needed for SPC usage

! Determine the frequency of sampling

! Understand the Control Chart selection methodology

!

Be familiar with Control Chart parameter calculations such asUCL, LCL and the Center Line


Notes



647


Lean Six Sigma

Black Belt Training

Now we are going to continue in the Control Phase with “Six Sigma Control Plans”.

Control PhaseSix Sigma Control Plans



648


Six Sigma Control Plans

Overview

End of Control: Your Objectives

We have discussed all of the tools to improve and sustain your project success. However, you might havemany options or too many options to implement final monitoring or controls. This module will aid you indefect reduction selection.

Another objective of this module is to understand the elements of a good Control Plan needed to sustain

your gains.

The last physical resultof the Control Phase isthe Control Plan. Thismodule will discuss a

technique to selectionvarious solutions youmight want from all ofyour defect reductiontechniques foundearlier in this phase.We will also discusselements of a ControlPlan to aid you andyour organization tosustain your project’sresults.


!"# !"% & ' ()* +,)- .-' */!"# !"% & ' ()* +,)- .-' */

01213+ ()*+,)-/01213+ ()* +,)-/

41' * ()*+,) -/41' * ()*+,) -/

5 6 7 ' * 3 1 6 ( ' 8 ' 9 " -" +:5 6 7 ' * 3 1 6 ( ' 8 ' 9 " -" +:

56 7' *316 ;# 81, "&1*+/56 7' *316 ;# 81, "&1*+/

< 1-3)&1 +) ()* +,)-< 1-3)&1 +) ()* +,)-

!+'+ "/+"3' - .,)31/ / ( )*+,)-

=!.(>

!+'+ "/+ "3'- . ,)31// ()* +,)-

=!.(>

< ,' 8 ? 8 @ 5 3+")* A+1& /< ,' 8 ? 8 @ 53+ ")* A+1&/

!"#$%&"' !)#)*%&"'!"#$%&"' !)#)*%&"'

+ "'%,"# -#.' /#)0)'%1+ "'%,"# -#.' / #)0)'%1



649


Selecting Solutions

Impact Considerations

Selecting solutions comes down to a business decision. The impact, cost and timeliness of theimprovement are all important. These improvement possibilities must be balanced against thebusiness needs. A cost benefit analysis is always a good tool to use to assist in determining thepriorities.

Recall us talking about the progression of a Six Sigma project? Practical Problem – Statistical

Problem – Statistical Solution – Practical Solution. Consider the Practical Solutions from abusiness decision point of view.


!"#"$%&'( &*+,-."*"'%/ %- &*+#"*"'%0

1 2&( 34#"."# -56"$%&." ".7 #87%&-' -9 7## +-%"'%&7 # &*+,-."*"'%/

: ;*+7$% -9 "7$3 &*+,-."*"'%: < -/% %- &*+#"*"'% "7$3 &*+,-."*"'%

: =&*" %- &*+#"*"'% "7$3 &*+,-."*"'%

1 >7 #7'$" ?"/&," @&%3 A87'%&9&7 5#" ".7 #87%&-'

: B'(&'"",&'( 7#@7C/ @7'%/ %3" (-#? /%7'?7,?

: !7#"/ 7#@7C/ @7'%/ &'."'%-,C

: D,-?8$%&-' 7#@7C/ @7'%/ *-," $7+7$&%C

=3" %--# 9-, /"#"$%&'( ?"9"$% +,"."'%&-' *"%3-?/ &/ 8''"$"//7,C 9-, 68/% 7

9"@ $37'("/ %- %3" +,-$"//E

1 F7 'C +,-6"$%/ @&%3 /*7##", /$-+"/ 37." 9"@G 58% .&%7# $-'%,-#

*"%3-?/ +8% &'%- %3" +,-$"//E

Now that

s IMPACT



650


Cost Considerations

Time Considerations


The clock’s ticking…

It’s all about the cash



651


Improvement Selection Matrix

The significance rating is the relative ranking of outputs. If one output is rated a 10 and it is twice theimportance of a second output, the rating for the second output would be a 5. The improvements, usuallyimpacting the X’s, are listed and the relative impact of each item on the left is rated against its impact tothe output. The overall impact rating for one improvement is the sum of the individual impact ratingsmultiplied by their respective significant rating of the output impacted. Items on the left having moreimpacts on multiple outputs will have a higher overall impact rating. The cost and timing ratings aremultiplied against the overall impact rating.

The improvements listed with the highest overall ratings are the first to get consideration. The range ofimpact ratings can be zero to seven. An impact of zero means no impact. The cost and timing ratings are

rated zero to seven. With zero being prohibitive in the cost or timing category.


This shouldresemble the X-YMatrix. This tool is

of no use if youhave one or twoimprovementefforts to consider.The outputs listedabove in mostcases resemblethose of youroriginal X-Y Matrixbut you might haveanother business

output added.



652


Improvement Selection Matrix Project Outputs

Improvement Selection Matrix

The recommendedcost ratings from zeroto seven are here. Inmany companies,expenditures that arenot capitalized usually

are desired becausethey are smaller andare merely expensed.Your business mayhave differentstrategies or need ofcash so consider yourbusiness’ situation.

Just like when usingthe FMEA, your

ratings may vary forthe three SelectionMatrix categories.Feel free to usewhatever objectiveratings you desire.

These are somegeneral guidelineratings, customizethem to meet yourbusiness, just try tostandardize whatevercriteria you choose.


!"#$%"& %() *+,-()%"& .+/"#,0 -1 &-2" !"-3+,/4

5 6#0/ +% ,7 -1 /7+ 8 90 %,"-00 /7+ 7-"#: -(/%; %<#0

5 =%/+ /7+ #$>-"/%(,+ -1 /7+ >"-,+00 8 90 -( % 0,% ;+ -1 ? /- ?@A ? #0 (-/ B+"& #$>-"/%(/C ?@ #0 ,"#/#,%;

A D7+ *#E(#1#,%(,+ "%(F#(E0 $20/ $%/,7 &-2" 2>)%/+) GH8 .%/"#<

"%(F#(E0

Cost to Implement Ratings

7Improvement Costs are minimal with upfront and ongoing

expenses.

6Improvement Costs are low and can be expensed with no capital

authorization and recurring expenses are low.

5Improvement Costs are low and can be expensed with no capital

authorization and recurring expenses are higher.

4Medium capital priority because of relative ranking of return on

investment.

3Low capital priority because of relative ranking of return on

investment.

2High capital and ongoing expenses make a low priority for capital

investment.

1High capital and/or expenses without acceptable return on

investment.

0Significant capital and ongoing expenses without alignment with

business priorities.



653


Improvement Selection Matrix (cont.)

Example of Completed Solution Selection Matrix

These time ratings are ranked from zero to seven. You might wonder why something that wouldtake a year or more we suggest gets a zero rating suggesting the improvement not be considered.Many businesses have cycle times of products less than a year so improvements that long are illconsidered.

This is just an example of a completed Selection Matrix. Remember that a cost or time rating ofzero would eliminate the improvement from consideration by your project. Remember your ratingsof the solutions should involved your whole team to get their knowledge and understanding of finalpriorities.

Again, higher overall ratings are the improvements to be considered. Do NOT forget about thepotential to run improvements in parallel. Running projects of complexity might need the experienceof a trained project manager. Often projects need to be managed with gantt charts or timelines

showing critical milestones.


Time to Implement Ratings

7 Less than a week to get in place and workable.

6 7 - 14 days to get in place and workable.

5 2 - 8 weeks to get the improvement in place and workable.

4 2 - 3 months to get the improvement in place and workable.




0Over a year to get the improvement in place and workable. All

above times include time for approvals process.

86 7 7 4214

52 7 7 2548

63 3 6 1134

36 5 5 900

60 3 3 540

63 5 2 630

OVERALL

IMPACT

RATING

COST

RATING

TIME

RATING

OVERALL

RATING

O u

t s i d e n o i s e s d o n o t

i n t e r f e r w i t h s p e a k e r s

C o

f f e e i s h o t a n d r i c h

t a s

t i n g

P l e

n t y o f b o t t l e d w a t e r

a v a i l a b l e

F o o d c h o i c e s i n c l u d e

" h e a l t h y c h o i c e s "

Significance Rating 10 9 8 9

Potential ImprovementsImpact

Rating

Impact

Rating

Impact

Rating

Impact

Rating

1 Hotel staff monitors room 2 2 6 0

2 Mgmt visits/leaves ph # 2 0 4 0

3 Replace old coffee makers/coffee 0 7 0 0

4 Menus provided with nutrition info 0 0 0 4

5 Comp. gen. "quiet time" scheduled 6 0 0 0

6 Dietician approves menus 0 0 0 7

!"# $% &' " '( ) + ','-).%( / 0 )$.1 2 3)#3 )

!"#$%&'"'()* ,-). ).' .-/ .'$ %&'$011 $0)-(/ *.%213 4' / -&'( 5-$*) #$-%$-)67

8''# -( "-(3 ).0) 1%(/ )-"' 5$0"' 90 #-)01 -(&'*)"'()*: ')97 *.%213 .0&'#0 $011'1 '55%$)* )% ;''# 3'106* 5$%" 52$).'$ %992$$-(/ 7



654


Implementing Solutions in Your Organization

Once you’ve decideddefect reductionsolutions, you need toplan those solutions. Aplan means more thanthe proverbial back ofthe envelope solutionand should includetimelines, criticalmilestones, projectreview dates andspecific actions notedfor success in yoursolutionimplementation. Many

people use Excel or MSProject but manyoptions exist to planyour project closingwith these futuresustaining plans.

What is a Control Plan?


!"#$%"%&'(')*& ,$(&- -.*/$0 %"#.(-)1 % '.% &%%0 '*2

3 4 56(&)1 % '.% '(-7- (&0 5%-*/58%-

3 9-'(:$)-. 5%($)-')8 ')"% ;5("%- (&0 0%( 0$)&%-

3 !0%&');< (8')*&- &%8%--( 5< '* %&-/5% -/88%--

= *"#*&%&'- *; (& !"#$%"%&'(')*& ,$(& )&8$/0%2

3 > *57 :5%(70*?& -'5/8'/5%

3 !&;$/%&8% -'5('%6 < ;*5 #5)*5)')%- (&0 5%-*/58)&6

3 @)-7 "(&( 6%"%&' #$(&

3 A /0)' 5%-/$'- ;*5 8*"#$%')*& (&0 5)-7-B

A $$ -*$/')*&- "/-' :% #( 5' *; = *&'5*$ ,$(& C*8/"%&'B

!" $%&" % '(%) *+),- ."/

! # $ % &'$ ( ) (* % +, -

! ! "#$$%& ()* * + ", - %(."#/#&0 (, ($%* ( )(%- 12" *2 &#$2"#&0 3.2& $"24 4 #&0

5"2.%(( 2" 5"2-).$ 6+" #+$ #2&

! 72.)* %&$ + 4 428 #&0 $%+ * $2 12"* + 4 4, - 2.)* %&$ + 4 4 .2&$"24 * %$92 -(

)(%- $2 * %%$ 5"2:%.$ 0 2+ 4

! ; #6 # &0 -2 . )*% &$ $2 /% )5- + $% - +( &% 8 * % + ()" % *% &$ (, ($% *( + &-

. 2&$" 2 4 *% $92- ( + " % + -- % - 1 2" . 2&$# &)2)( # *5" 26 % *% &$

! < 1$%& )( %- $2 ."%+ $% .2&.#(% 25%"+ $2" #&(5 %.$#2& (9 %%$

! = < > + "%5 4+ .%* %&$ 21 #&12"* + $#2& .2& $+ #&%- #& -%$+ # 4%- 25 %"+ $#&0 ?

* + #&$%&+ &.%? 2" -% (#0 & #&( $").$#2&(

! @AA@= >BC; 52 "$#2& 21 1 #&+ 4 5" 2:%.$ "%5 2"$

" D #&+ 4 5"2 :%.$( + "% 2"0 + &#E+ $#2&+ 4 4, - %5%& -%& $

! B & 1 2" *+4 2" 1 2" *+4

" D #4%- + ( 5+ "$ 21 5"2 :%.$ $"+ .F #&0 * %.9+ &#(* 12" 2"0 + &#E + $#2&

! >"+.F /%&%1#$(

! G%1%"%&.% 12" )&() ($+ #&%- "%()4$(

We have a plan don’t we?



655


WHO Should Create a Control Plan

WHY Do We Need a Control Plan?


!"# %#&' ()*+,-. )- %"# /*)0#1%2222

3 4 56 4 7 (") "&8 & *)9# ,- :#;,-,-. < #=#1>%,-. )* 1"&-.,-. %"#/*)1#88?

@ 388)1,& %#8

@ !#1"-,1&9 7=/#*%8

@ A>/#*B,8)*8

@ C& -&.#*8

@ A ,%# C& -&.#*

@ D>'&- E#8)>*1#8 !" $%$ %&''e did it

Going for the distance, not the sprint



656


Control Plan Information

Control Plan Elements

Control Plans useall of theinformation fromthe previousphases of yourproject and thedefect preventionmethods selected.Control Plans maynot be excitingbecause you arenot doing anythingnew to the processbut stabilizing theprocess in the

future with thisdocument.


The five elementsof a Control Planinclude thedocumentation,

monitoring,response, trainingand aligningsystems andstructures.

!"# %#& ' ( #)#*+, - %"# .+/ %0+* 1*& / 23 4%5* 56 5/7 & * * & )& 5 *& 2*#

5/8+0' & %5+/ 80+' %"# 8+**+9 5/7 :

! ;#-4* %- 80+' %"# <#&-40# &/( = /& *36# 1"& -#-

! >#--+/- *#&0/#( 8 0+' - 5'5 *&0 , 0+(4?%- & /( , 0+?#--#-

! !#&' @- A /+9 *#(7 # + 8 %"# , 0+?#--

! B#-57 / C<D= -

! B#-57 / 0#) 5#9 -

! B#8#?% 10#)#/%5+/ <#%"+(- -#*#?%#(

=*57 /5/7

E 3 - %# ' -

F E%04?%40#-

B+?4' # /%& % 5 +/

1 * & /

B+?4' # /%& % 5 +/

1 * & /

<+/5%+0 5/71 * & /

<+/5%+0 5/71 * & /

;# - ,+/- # 1 * & /;# - ,+/- # 1 * & /

!0& 5/5/71 * & /



657


Training Plan


! "# $ ! "% & #() % *+, % &+#*- (./ 0+(. &(% +*+*) 1

! "#$%& ()*+ ,-&. /0 -#& ()*1$2&)&3-%

4 5&$*6& 7#$ +1& (32$62&. (3 -#& *1$,&%%()*+,-&. /0 -#& ()*1$2&)&3-

4 5&$*6& 7#$ %8**$1- -#& *1$,&%% ()*+,-&. /0

-#& ()*1$2&)&3-

! "#$%& ()*+ ,-&. /0 -#& 9 $3-1$6 56+3

4 51$,&%% $73&1%: )+3+; &1%

4 5&$*6& 7#$ %8**$1- -#& *1$,&%%&% (32$62&. (3 -#& 9 $3-1$6 56+3

4 5&$*6& 7#$ 7(66 )+<& ,#+3;&% -$ -#& *1$,&%% (3 -#& =8-81&

2(% +*+*)

34% *

2(% +*+*)

34% *

! "# % &'' (#) * '+,+ ,"+ ,-. &/&/0 1

! "##$%&' ($ (*'&+&+,

- ./$ 01'++&+,2 %$3$140#$+( '+% $5$67(&4+ &8 '

*$804+8&9&1&(: 4; (/$ 0*4<$6( ($'#

- .:0&6'11: 84#$ 4; (/$ (*'&+&+, &8 64+%76($% 9:

(/$ 0*4<$6( ($'#

! = 7'1&;&$% (*'&+$*8

- .:0&6'11: 4>+$% 9: ' (*'&+&+, %$0'*(#$+( 4* 0*46$88 4>+$*- ./48$ >/4 '*$ *$804+8&91$ ;4* 64+%76(&+, (/$ 4+?,4&+,

(*'&+&+, #78( 9$ &%$+(&;&$%

@0$6&;&6 (*'&+&+, #'($*&'18 +$$% %$3$140&+,A

! B4>$*B4&+(2 C + (/$ D49 6/$6E1&8(2 F5$*6&8$82 $(6A

2-.&/&/0

3 ' . /

2-.&/&/0

3 ' . /

! "#$ &'(( )*+'$'$, -# ./$01.)#02

! "+) '3 )"# )'4#('$# )/ )*+'$ #5#*6/$#

/$ )"# $#& 7*/.#338#392

! "+) &'(( )*',, #* /$,/'$, )*+'$'$,2

: ; #& #47(/6## /*'#$)+)'/$2

: <#=*#3"#* )*+'$'$,2

: >+*) /= )"# *#37/$3# 7(+ $ &"#$ 4/$')/*'$, 3"/&3

7#*=/*4+$.# 0#,*+0'$,2

!"# $% $% &

'(# %

!"# $% $% &

'(# %



658


Training Plan (cont.)


!"# $%$%& ()# % * +,)$%-

Training Module

Who Will Create

Modules

Schedule for

Training Modules

Completion

Who Will be

Trained

Schedule for

Training Trainer(s)

Integration into

Ongoing New

Employee

Training

Final Location of

Employee

Manuals

!"#$%$%&

( ) # %

!"#$%$%&

( ) # %

Documentation Plan

!"#$%&'()(*"' *, '&#&,,)-. (" &',$-& (/)( 0/)(

/), 1&&' 2&)-'&3 4-"% (/& 5-"6&#( *, ,/)-&3 )'3

*',(*($(*"')2*7 &38

9 :,&3 (" ) *3 *%52&%&'()(*"' "4 ,"2$(*"',

9 :,&3 4"- "';<"*'< (-)*'*'<

=/*, *, "4(&' (/& )#($)2 >*')2 ?&5"-( ,"%& "-<)'*7 )(*"', $,&@

!" #$% &' ()(*"' % $,( -& . &/ ( #$00&'( (" -& $,& 1$2

DocumentationDocumentation

PlanPlan!"#$%&'()(*"'

, -)'

!"#$%&'()(*"'

, -)'



659


Documentation Plan (cont.)


!"#$% "' (# )*+,-.#. )* "/# 0'+-$#*"1")'* 2,1*3

! 24'+#%% .'+-$#*"1")'*

" 56 .1 "#. 24' +#%% 716 %89 ,': +/14"%

" 24'+#.-4#% ;<= 2>% ?

" @7AB

! C'*"4', 2,1* . '+-$#*"1")'*

" D41 )* )*E $ 1 *-1 ,%

"

7'*)"'4)*E 6,1 *F6 4'+#%% $ 1 *1 E #$ #*" +/1 4"%G 4#6' 4"%G% ' 6 %

" H#%6'*%# 6 ,1*F@7AB

" < I %"#$% 1 *. %"4-+"-4#%FJ'( .#%+4 )6")'*%G 6#49'4$1 *+#

$ 1 *1 E #$#* " '( J#+")K#%

0'+ -$#*" 1 " )'*

2 , 1 *

0'+ -$#*" 1 " )'*

2 , 1 *

! ""#$ % #%$ '(")* %"#+# ,# -. /*' 0*123 (%-4 -#*% 5,4 %6 ! "#$%&'$()(*(+, .+ (/%*#/#'+.+(&'

0 1*.23 1#*+ #'$45#$ .** 6&24/#'+$ .5# 2455#'+

.+ 7.'6 &88

0 1*.23 1#*+ #'$45#$ +7#5# ($ . %5&2#$$ +& /&6(8,

6&24/#'+.+(&' .$ +7# %5&2#$$ 27.'9#$ (' %*.2#

0 1*.23 1#*+ #'$45#$ +7#5# ($ . %5&2#$$ (' %*.2# +& 5#:(#;

6&24/#'+.+(&' &' 5#94*.5 ).$($ 8&5 2455#'2,< .2245.2,

! "#$%&'$()(*(+, 8&5 &'9 &('9 %5&2#$$ =&59.'(> .+(&'. **, ). $#6?0 @*.' /4$+ &4+*('# ;7& ($ 5#$%&'$()*# 8&5 /.3('9

4%6. +#$< /&6(8(2. +(&'$ +& 6&24/#'+.+(&' .$ +7#, &2245

0 @*.' /4$+ &4+*('# ;7& ($ 5#$%&'$()*# +& 5#:(#; 6&24/#'+$A

#'$45('9 2455#'2,< .2245.2, &8 6&24/#'+.+(&'

Documentation

Plan

Documentation

Plan



660


Documentation Plan (cont.)


!"#$% &'()(*"' ,-) ' . $(- *'& !"#$%&'( ) ( *"'

, - ) '

!"#$%&'( ) ( *"'

, - ) '

Document ItemsNecessary

ImmediateResponsibility

Update/ModificationResponsibility

ReviewResponsibility

Monitoring Plan



661


Monitoring Plan (cont.)


Knowledge Retention Tests -

–

When to Sample:

•

After training

• Regular intervals

•

Random intervals (often in auditing sense)

–

How to Sample

– How to Measure

Monitoring

Plan

I knew I should have

paid more attention

Statistical Process Control:

–

Control Charts

• Posted in area where data collected

•

Plot data points real time

– Act on Out of Control Response with guidelines from

the Out of Control Action Plan (OCAP).

– Record actions taken to achieve in-control results.

• Notes impacting performance on chart should be

encouraged

– Establishing new limits

•

Based on signals that process performance has changed

Monitoring

Plan



662


Response Plan


!"#$ &' ( ) *+( , ,--. ,- /'+ 0-* ,1+ "- 2&,-*&2) 3.( 2

! $ . .-4 ' 5*- 6+'' 7( 2( ) +* ( 28 ,1-'+ &29-.9+8 &2 ,1+ 5 *-6+'',- '++ ,1+ +2,&*+ 5*-6+'' ( 28 1 -4 +9+*: -2+ 6-2,* &;/,+' ,- (8+0+6, 0*++ 5*-8/6,<'+*9&6+=

! 3*-9 &8+' ,1+ 7 +( 2' ,- > ++5 ,1+ 8-6/7 +2, 6/**+2,?*+( ''+''&2) @3A ' ( ' ,1+ 5*-6+'' 61( 2) +'

#

Process

Function

(Step)

Potential

Failure Modes

(process

defects)

Potential

Failure Effects

(Y's)

S

E

V

C

l

a

s

Potential

Causes of

Failure (X's)

O

C

C

Current

Process

Controls

D

E

T

R

P

N

Recommend

Actions

Responsible

Person &

Target Date

Taken

Actions

S

E

V

O

C

C

D

E

T

R

P

N

1

2

3

4

5

6

"-2&,-*&2)

3 .( 2

"-2&,-*&2)

3 .( 2

Monitoring Plan

Check Lists/Matrices

– Key items to check

–

Decision criteria; decision road map

– Multi-variable tables

Monitoring

Plan

Visual Management

– Alerts or signals to trigger action.

•

Empty bins being returned to when need stock

replenished

•

Red/yellow/green reports to signal process

performance

–

Can be audible also.

–

5S is necessary for Visual Management



663


Response Plan


! " # $ % & # " ( )* & # ! "#$%&'( *+",(--.(-/ $" 0"%%"1 12('

$2(+( &- 3 4(0(,$ "+ 5 #$ "0 6 "'$+"% 0+"7 7"'&$"+&'8 9 : 5 #$ "0 ,"'$+"% *"&'$ "' 6 "'$+"% 6 23+$

: ; "' +3'4"7 <(23 =&"+ 1&$2&' 6 "'$+"% >&7&$- &'6 "'$+"% 6 23+$

: 6 "'4&$&"'? =3+&3 <%( *+"=(' $" *+"4#,( 4(0(,$- *+(-('$ &' *+",(--

: 6 2(,@ -2(($ 03 &%#+(

: A #$"73$&"' 03&%#+(

B(-*"'-( $" *""+ *+",(-- +(-#%$- 3+( 3 7#-$ &' $+3&'&'8C

!"#$ %&# " ( )*&# *+" ),- ,&. /% 012 "&3# 1 $/ *3"/ 4 ,35

&"4 ,&6%+2 *3,%& * # ,3 7"0%2 "# *- *, )*7 )" 8

! " # $ % & # " ( ) * &! " # $ % & # " ( ) * &

! " # $ " % & % '( " * + & ( $ " % ( & , - . % /

! "#$ &'())$'* +,' - '$*.,/*$

0 1 #-& -'$ &#$ +-(23'$ 4,5$* &, 6#$67 +,'8

0 9*3-22: 4,/(&,' &#$ #()#$*& '(*7 ;<* (/ &#$ .',6$**

! "#$ '$6,44$/5$5 '$*.,/*$ +,' &#$ +-(23'$ 4,5$

! "#$ '$*.,/*(=(2(&($* +,' '$*.,/5(/) &, &#$ +-(23'$ 4,5$

! >,634$/&-&(,/ ,+ ?$*.,/*$ @2-/ =$(/) +,22,A$5 (/ - +-( 23'$ 4,5$

! >$&-(2$5 (/+,'4-&(,/ ,/ &#$ 6,/5(&(,/* *3'',3/5(/) &#$ +-(23'$

4,5$

+ & ($" %(& , - .%+ & ($" %(& , - .%



664


Response Plan – Abnormality Report


! !"#$ % &"' ') *+,"-#$# %)-

. /"- 0$ % &+1" , )'"2)**+13

! 4 1 )5 % ' " $ , "#/ )' 0)1)- 67 )%-7 *)-#%-+) +2% , 8 1 )5", "- # 3

! 9"%-0)1*"*),,%#,"-# #)

"&%,%-$#%-7 '"0"*#23

! : %#2 . % #/ ;<= > ? ? ? 2#$-' $ 1' )0/$5%-7 $ @A9 )1 @)11"*# %5"A*#%)- 9"B+"2#3

! C"#/)' #) *)& &"*# 01"B+ "-*D ) 0

*)11"*#%5" $ *#%)-23

Process

Metric

Signal

Situation Code

Detailed Situation

Date

Code of Cause

Corrective Action

Who To Be Involved

What To Be Done

Date for completion of analysis

Date for implementation of permanent prevention

C u r r e n t S i t u a t i o n

I

n v e s t i g a t i o n o f C a u s e

R o o t C a u s e A n a l y s i s

9"28)-2" 4 &$-9"28)-2" 4 &$-

Aligning Systems and Structures

!"#$%&# ()* #$+,-$,+%# (+% $.% /(#0# 12+ (33240)5

6%263% $2 -.()5% $.%0+ /%.(702+# 6%+&()%)$3"8

9 :%+12+&()-% 52( 3#; 2/<%-$07%#

9 :230-0%#; 6+2-%*,+%#

9 =2/ *%#-+06$02)#

9 >)-%)$07% -2&6%)#($02)

9 >)-%)$07% 6+25 +(&#? -2)$%#$#? %$-

!"#$# & $# '()* + &) , -"( $.+ .#$/ -.$&.#*0#-

1( $ & '0* ) / # ) . ( 1 -2 -.# / - & ) , - .$3 4.3 $# - 5

!"#$ %#%$

'()*+,)

- '*./0*/.+)

!"#$ %#%$

'()*+,)

- '*./0*/.+)



665


Aligning Systems and Structures (cont.)


Project Sign Off

! " #$ &'( )* +#,-.&#+#/$- $0,$ () /)$ ,1'2/ 3'$0

(#-'&#( 4#0,5')&-

! " #$ &'( )* +.1$'61# +#,-.&#- *)& $0# -,+#

(#-'&#( 4#0,5')&-

! 7+61#+#/$ +#,-.&#- $0,$ ,1'2 / 3'$0 (#-'&#( 4#0,5')&- 8.&&#/$19 /)$

+)$'5,$#( 49 '/8#/$'5#-

! : 0,/2# +,/,2 #+#/$ +.-$ 8)/-'(#& 9).& 6&)8#-- 80,/2 #- ,/( 0)3$0# 6&)8#-- 3'11 &#-6)/(;

! < &# $0# 0).&19 '/8#/$'5#- 0.&$'/2 9).& 80,/8# )* -.88#--;

!"#$ %#%$

' ( ) *+, )

- ' *./0*/.+)

!"#$ %#%$

' ( ) *+, )

- ' *./0*/.+)

!"#$ &"$'() $( * ##+," *--".$*/-" (0 1 (/$,(2 32*/ 4#

'*54/6 #+.",54#(,# */) &*/*6"&"/$ 0(, $'" *,"*

4/5(25")7

8 9""$4/6 0(, * #+&&*,: ,".(,$

8 ;."-404- -'* /6"# $( $'" .,(-"## '46 '246 '$")

8 </0(,&*$4(/ ='"," 1 (/$,(2 32*/ 4# 042")

!"#$ %#%$

' ( )* + , )

- ' *./0*/.+)

!"#$ %#%$

' ( )* + , )

- ' *./0*/.+)

123 *45*6) 5 72%*.2" 8"5%9ow that s a Control Plan



666



You have now completed Control Phase – Six Sigma Control Plans.

! Identify all 5 phases of the Six Sigma methodology

!

Identify at least 3 tools from each phase

!

Show progress on your ongoing project


Now for the last few questions to ask if you have been progressing on a real world project whiletaking this learning. First, has your project made success in the primary metric withoutcompromising your secondary metrics? Second, have you been faithfully updating your metriccharts and keeping your process owner and project champion updated on your team’s activities. Ifnot, then start NOW.

Remember a basic change management idea you learned in the Define Phase. If you getinvolvement of team members who work in the process and keep the project champion and processowner updated as to results, then you have the greatest chance of success.

Notes



667


Lean Six Sigma

Black Belt Training

Control PhaseWrap Up and Action Items



668



Control Phase Overview—The Goal

Organizational Change

! " ##$%& ($)%*+),-,.,&/

! 0*+,&*(,+1

! 2$)%*+3,+1

! 04+41,+1

! 56-(4#,+1 #74+1$ 8 #*+&,+9*9) .$4(+,+1

! :74(,+1 -$)& %(4#&,#$)

! ;*&$+&,4 . <*( 7*(,= *+&4. ($%.,#4 &,*+ *( $>%4 +),*+ *< ($)9.&)

!"#$!"#$ & & ' (" ) * + ' (" ) *+ , , -. /$* ' +0#*11 $" 1 " +0 (* -.-. /$* ' +0#*11 $" 1 " +0 (* -.

2 32 45 67 67 8 ' +0 9*#/ 1: ##*1 1 " #$-*; *< =2 32 45 67 67 8 ' +0 9*#/ 1: ##*1 1 " #$-*; *< =

•

Assess the final Process Capability.

• Revisit Lean with an eye for sustaining the project.

• Evaluate methods for Defect Prevention.

• Explore various methods to monitor process using SPC.

•

Implement a Control Plan.

ooooaaallllll

The goal of the Control Phase is to:



669


Control Phase—The Roadblocks

DMAIC Roadmap


!""# %"& '() *"')+',-. &"-/0."1#2 -+/ *.-+ '" -//&)22 '()3

0)%"&) '()4 0)1"3) *&"0.)325

6 !-1# "% *&"7)1' 2,8+ "%%

6 9)-3 3)30)&2 -&) +"' ,+:".:)/ ,+ ; "+'&". <.-+ /)2,8+

6 =- +-8)3)+' /")2 +"' (-:) #+">.)/8) "+ 3"+,'"&,+8 -+/

&)-1',+8 +))/2

6 ?,+- +1,- . 0)+)%,'2 -&) +"' '&-1#)/ -+/ ,+')8 &-')/ ,+'"

0@2,+)22

6 !-1# "% 0@4 ,+ "% *&"1)22 "*)&-'"&2 "& 2'-%%

!"#$%&'( *+,-.#/ 0+#1

022#22 3 %1-&.&%(4 5 161 -&.&%(4 1$" 7#1 28+#/#$% 3(2%#/2

!"#$%&'( 1$" *+&,+&%&9# 0.. : ;2

*+,<#=>&26+,<# !/61?% :;2 @1<# A $ *+,-.#/

!"#$%&'(4 *+&,+&%&9#4 3#.#?% 3,.8%&,$2 5,$%+,. ,+ B.&/&$1%# :;2 5 182&$C *+,-.#/2

!/6.#/#$%3 ,.8%&,$2 %, 5 ,$%+,. ,+ B.&/&$1%# :;2 5 182&$C *+,-.#/2

!/6.#/#$% 5 ,$%+,. *.1$ %, B$28+# *+,-.#/ >,#2$; % D#%8+$

E#+&'( F&$1$?&1. !/61?%

>#%#+/&$# 066+,6+&1%# *+,G#?% F,?82

B2%&/1%# 5A *H

B2%1-.&2I J#1/

5 I 1 / 6 & , $ =

* + , ? # 2 2 A K $ # +

> # ' & $ #

7 # 1 2 8 + #

0 $ 1 . ( 9 #

! / 6 + ,

< #

5 , $ % + , .

!"#$%&'( *+,-.#/ 0+#1

022#22 3 %1-&.&%(4 5 161 -&.&%(4 1$" 7#1 28+#/#$% 3(2%#/2

!"#$%&'( 1$" *+&,+&%&9# 0.. : ;2

*+,<#=>&26+,<# !/61?% :;2 @1<# A $ *+,-.#/

!"#$%&'(4 *+&,+&%&9#4 3#.#?% 3,.8%&,$2 5,$%+,. ,+ B.&/&$1%# :;2 5 182&$C *+,-.#/2

!/6.#/#$%3 ,.8%&,$2 %, 5 ,$%+,. ,+ B.&/&$1%# :;2 5 182&$C *+,-.#/2

!/6.#/#$% 5 ,$%+,. *.1$ %, B$28+# *+,-.#/ >,#2$; % D#%8+$

E#+&'( F&$1$?&1. !/61?%

>#%#+/&$# 066+,6+&1%# *+,G#?% F,?82

B2%&/1%# 5A *H

B2%1-.&2I J#1/

5 I 1 / 6 & , $ =

* + , ? # 2 2 A K $ # +

> # ' & $ #

7 # 1 2 8 + #

0 $ 1 . ( 9 #

! / 6 + ,

< #

5 , $ % + , .



670


Control Phase

Control Phase Checklist


!"#$%&'"'() +','-)'.

/'&',%# 0$12(2(3 4,1(

!"#,'"'() 0$12(2(3 4,1(

/'&',%# /%-5"'()1)2%( 4,1(

!"#,'"'() /%-5"'()1)2%( 4,1(

/'&',%# 6%(2)%$2(3 4,1(

!"#,'"'() 6%(2)%$2(3 4,1 (

7 % )% 8 '9) 4$%:'-)

/'&',%# ;'<#%(<' 4,1(

!"#,'"'() ;'<#%(<' 4,1(

/'&',%# 4,1( )% =,23( +><)'"< 1(. +)$5-)5$'<

=,23 ( + ><)'"< 1 (. + )$5-)5$'<

?'$2@> A2(1(-21, !"#1-)

!"#$%&'"'() +','-)'.

/'&',%# 0$12(2(3 4,1(

!"#,'"'() 0$12(2(3 4,1(

/'&',%# /%-5"'()1)2%( 4,1(

!"#,'"'() /%-5"'()1)2%( 4,1(

/'&',%# 6%(2)%$2(3 4,1(

!"#,'"'() 6%(2)%$2(3 4,1 (

7 % )% 8 '9) 4$%:'-)

/'&',%# ;'<#%(<' 4,1(

!"#,'"'() ;'<#%(<' 4,1(

/'&',%# 4,1( )% =,23( +><)'"< 1(. +)$5-)5$'<

=,23 ( + ><)'"< 1 (. + )$5-)5$'<

?'$2@> A2(1(-21, !"#1-)

Control Questions

Step One: Process Enhancement And ControlResults

• How do the results of the improvement(s) match the requirements of the businesscase and improvement goals?

• What are the vital few X’s?• How will you control or redesign these X’s?• Is there a process control plan in place?• Has the control plan been handed off to the process owner?

Step Two: Capability Analysis for X and YProcess Capability

• How are you monitoring the Y’s?

Step Three: Standardization And Continuous Improvement• How are you going to ensure that this problem does not return?•

Is the learning transferable across the business?• What is the action plan for spreading the best practice?• Is there a project documentation file?• How is this referenced in process procedures and product drawings?• What is the mechanism to ensure this is not reinvented in the future?

Step Four: Document what you have learned• Is there an updated FMEA?• Is the control plan fully documented and implemented?• What are the financial implications?• Are there any spin-off projects?• What lessons have you learned?

General Questions• Are there any issues/barriers preventing the completion of the project?• Do the Champion, the Belt and Finance all agree that this project is complete?



671


Planning for Action

Summary


!"#$ &'()"*+ *($+'(, &,#$

-$(.,"/0" 12#'3$0 4"+.""$ 4513$"11"1 #$/ /36313($1

-$(.,"/0" +'#$17"' 4"+.""$ 8",+9 :; 9 #$/ +"#< <"<4"'1

=<&,"<"$+#+3($ &,#$ 7(' "77"*+36" &'(*"/5'"1

>31+#?" &'((73$0 &,#$ 7(' 3$&5+1 (' (5+&5+1

@ 2#'+ # &,# $ +( # **( <&,312 +2" /"13'"/ 1+#+" (7 +2" *5,+5'"

@ ($+'(, &,# $ 7(' 3$&5+1

@ ($+'(, &,# $ 7(' (5+&5+

:'3('3+3A" '31?1 (7 (5+&5+ 7#3,5'"

B3$#,3A" -"C =$&5+ D#'3#4,"1 E-:=DF +( <""+ 0(#,

:'(*"11 <#& (7 3<&'(6"/ &'(*"11

=<&,"<"$+ *2#$0" #*'(11 &'()"*+ +"#<

@ #,*5,#+" 4"$"73+1 7(' 4'"#?+2'(502

G"1+ 6#,3/#+3($ &,#$ 7(' # 1&"*373* +3<"

! " ## ! $ & " '# ! $# ! ( &# ! "# ! ) '

!"#$ &'()"*+ *($+'(, &,#$

-$(.,"/0" 12#'3$0 4"+.""$ 4513$"11"1 #$/ /36313($1

-$(.,"/0" +'#$17"' 4"+.""$ 8",+9 :; 9 #$/ +"#< <"<4"'1

=<&,"<"$+#+3($ &,#$ 7(' "77"*+36" &'(*"/5'"1

>31+#?" &'((73$0 &,#$ 7(' 3$&5+1 (' (5+&5+1

@ 2#'+ # &,# $ +( # **( <&,312 +2" /"13'"/ 1+#+" (7 +2" *5,+5'"

@ ($+'(, &,# $ 7(' 3$&5+1

@ ($+'(, &,# $ 7(' (5+&5+

:'3('3+3A" '31?1 (7 (5+&5+ 7#3,5'"

B3$#,3A" -"C =$&5+ D#'3#4,"1 E-:=DF +( <""+ 0(#,

:'(*"11 <#& (7 3<&'(6"/ &'(*"11

=<&,"<"$+ *2#$0" #*'(11 &'()"*+ +"#<

@ #,*5,#+" 4"$"73+1 7(' 4'"#?+2'(502

G"1+ 6#,3/#+3($ &,#$ 7(' # 1&"*373* +3<"

! " ## ! $ & " '# ! $# ! ( &# ! "# ! ) '

H"&"#+ 1#<" &'(*"11 7(' 1"*($/#'C <"+'3*1

I2( . 3<&'(6"<"$+ 3$ H:J +2'(502 #*+3($ 3+"<1

@ (<&,"+" H:J #11"11<"$+ .3+2 '"631"/ 7'"K5"$*C # $/ *($+'(,1

B3$#,3A" &'(4,"< 1(,63$0 1+'#+"0C

=/"$+37C #* +5#, 6"'151 #&&# '"$+ @ &?

L1+#4,3 12 *($+3$5(51 (' #++'345+" <"+'3*1 7(' @ &?

H"&"#+ 1#<" &'(*"11 7(' 1"*($/#'C <"+'3*1

I2( . 3<&'(6"<"$+ 3$ H:J +2'(502 #*+3($ 3+"<1

@ (<&,"+" H:J #11"11<"$+ .3+2 '"631"/ 7'"K5"$*C # $/ *($+'(,1

B3$#,3A" &'(4,"< 1(,63$0 1+'#+"0C

=/"$+37C #* +5#, 6"'151 #&&# '"$+ @ &?

L1+#4,3 12 *($+3$5(51 (' #++'345+" <"+'3*1 7(' @ &?

!" "$%& '(%)" * +(, &$(,-./

! "#$% # '(%#) *+,%)-.#+,/+0 12 .3% -4%'/2/' ,%(/$%)#5(%- .1 '164(%.%

71*) 4)18%'.9

! "#$% -.#).%, .1 ,%$%(14 # 4)18%'. 4(#+ .1 6%%. .3% ,%(/$%)#5(%-9

! "# $% /,%+./2/%, :#7- .1 ,%# ( :/.3 41.%+./# ( )1#,5(1';-9

! <% )%#,7 .1 #44(7 .3% = /> = /0 6# 6%.31, 1+ 71*) ? @AB 4)18%'.9



673


Glossary

Affinity Diagram - A technique for organizing individual pieces of information into groups or broader categories.

ANOVA - Analysis of Variance – A statistical test for identifying significant differences between process orsystem treatments or conditions. It is done by comparing the variances around the means of the conditionsbeing compared.

Attribute Data - Data which on one of a set of discrete values such as pass or fail, yes or no.

Average - Also called the mean, it is the arithmetic average of all of the sample values. It is calculated by addingall of the sample values together and dividing by the number of elements (n) in the sample.

Bar Chart - A graphical method which depicts how data fall into different categories.

Black Belt - An individual who receives approximately four weeks training in DMAIC, analytical problem solving,and change management methods. A Black Belt is a full time six sigma team leader solving problems under thedirection of a Champion.

Breakthrough Improvement - A rate of improvement at or near 70% over baseline performance of the as-isprocess characteristic.

Capability - A comparison of the required operation width of a process or system to its actual performancewidth. Expressed as a percentage (yield), a defect rate (dpm, dpmo,), an index (Cp, Cpk, Pp, Ppk), or as asigma score (Z).

Cause and Effect Diagram - Fishbone Diagram - A pictorial diagram in the shape of a fishbone showing allpossible variables that could affect a given process output measure.

Central Tendency - A measure of the point about which a group of values is clustered; two measures of centraltendency are the mean, and the median.

Champion - A Champion recognizes, defines, assigns and supports the successful completion of six sigmaprojects; they are accountable for the results of the project and the business roadmap to achieve six sigmawithin their span of control.

Characteristic - A process input or output which can be measured and monitored.

Common Causes of Variation - Those sources of variability in a process which are truly random, i.e., inherentin the process itself.

Complexity -The level of difficulty to build, solve or understand something based on the number of inputs,interactions and uncertainty involved.

Control Chart - The most powerful tool of statistical process control. It consists of a run chart, together withstatistically determined upper and lower control limits and a centerline.

Control Limits - Upper and lower bounds in a control chart that are determined by the process itself. They canbe used to detect special or common causes of variation. They are usually set at ±3 standard deviations fromthe central tendency.

Correlation Coefficient - A measure of the linear relationship between two variables.

Cost of Poor Quality (COPQ) - The costs associated with any activity that is not doing the right thing right thefirst time. It is the financial qualification any waste that is not integral to the product or service which yourcompany provides.



674


Glossary

CP - A capability measure defined as the ratio of the specification width to short-term process performancewidth.

CPk -. An adjusted short-term capability index that reduces the capability score in proportion to the offset of theprocess center from the specification target.

Critical to Quality (CTQ) - Any characteristic that is critical to the perceived quality of the product, process orsystem. See Significant Y.

Critical X - An input to a process or system that exerts a significant influence on any one or all of the keyoutputs of a process.

Customer - Anyone who uses or consumes a product or service, whether internal or external to the providingorganization or provider.

Cycle Time - The total amount of elapsed time expended from the time a task, product or service is starteduntil it is completed.

Defect - An output of a process that does not meet a defined specification, requirement or desire such as time,length, color, finish, quantity, temperature etc.

Defective - A unit of product or service that contains at least one defect .

Deployment (Six Sigma) - The planning, launch, training and implementation management of a six sigmainitiative within a company.

Design of Experiments (DOE) - Generally, it is the discipline of using an efficient, structured, and provenapproach to interrogating a process or system for the purpose of maximizing the gain in process or systemknowledge.

Design for Six Sigma (DFSS) - The use of six sigma thinking, tools and methods applied to the design ofproducts and services to improve the initial release performance, ongoing reliability, and life-cycle cost.

DMAIC - The acronym for core phases of the six sigma methodology used to solve process and businessproblems through data and analytical methods. See define, measure, analyze, improve and control.

DPMO - Defects per million opportunities – The total number of defects observed divided by the total numberof opportunities, expressed in parts per million. Sometimes called Defects per Million (DPM).

DPU - Defects per unit - The total number of defects detected in some number of units divided by the totalnumber of those units.

Entitlement - The best demonstrated performance for an existing configuration of a process or system. It is an

empirical demonstration of what level of improvement can potentially be reached.

Epsilon ! - Greek symbol used to represent residual error.

Experimental Design - See Design of Experiments.

Failure Mode and Effects Analysis (FMEA) - A procedure used to identify, assess, and mitigate risksassociated with potential product, system, or process failure modes.

Finance Representative - An individual who provides an independent evaluation of a six sigma project interms of hard and/or soft savings. They are a project support resource to both Champions and ProjectLeaders.



675


Glossary

Fishbone Diagram - See cause and effect diagram.

Flowchart - A graphic model of the flow of activities, material, and/or information that occurs during a process.

Gage R&R - Quantitative assessment of how much variation (repeatability and reproducibility) is in a measurementsystem compared to the total variation of the process or system.

Green Belt - An individual who receives approximately two weeks of training in DMAIC, analytical problem solving,and change management methods. A Green Belt is a part time six sigma position that applies six sigma to theirlocal area, doing smaller-scoped projects and providing support to Black Belt projects.

Hidden Factory or Operation - Corrective and non-value-added work required to produce a unit of output that isgenerally not recognized as an unnecessary generator of waste in form of resources, materials and cost.

Histogram - A bar chart that depicts the frequencies (by the height of the plotted bars) of numerical ormeasurement categories.

Implementation Team - A cross-functional executive team representing various areas of the company . Its charter

is to drive the implementation of six sigma by defining and documenting practices, methods and operating policies.

Input - A resource consumed, utilized, or added to a process or system. Synonymous with X, characteristic, andinput variable.

Input-Process-Output (IPO) Diagram - A visual representation of a process or system where inputs arerepresented by input arrows to a box (representing the process or system) and outputs are shown using arrowsemanating out of the box.

lshikawa Diagram - See cause and effect diagram and fishbone diagram.

Least Squares - A method of curve-fitting that defines the best fit as the one that minimizes the sum of the squareddeviations of the data points from the fitted curve.

Long-term Variation - The observed variation of an input or output characteristic which has had the opportunity toexperience the majority of the variation effects that influence it.

Lower Control Limit (LCL) - for control charts: the limit above which the subgroup statistics must remain for theprocess to be in control. Typically, 3 standard deviations below the central tendency.

Lower Specification Limit (LSL) - The lowest value of a characteristic which is acceptable.

Master Black Belt - An individual who has received training beyond a Black Belt. The technical, go-to expertregarding technical and project issues in six sigma. Master Black Belts teach and mentor other six sigma Belts,their projects and support Champions.

Mean - See average.

Measurement - The act of obtaining knowledge about an event or characteristic through measured quantificationor assignment to categories.

Measurement Accuracy - For a repeated measurement, it is a comparison of the average of the measurementscompare to some known standard.

Measurement Precision - For a repeated measurement, it is the amount of variation that exists in the measuredvalues.



676


Glossary

Measurement Systems Analysis (MSA) - An assessment of the accuracy and precision of a method of obtainingmeasurements. See also Gage R&R.

Median - The middle value of a data set when the values are arranged in either ascending or descending order.

Metric - A measure that is considered to be a key indicator of performance. It should be linked to goals orobjectives and carefully monitored.

Natural Tolerances of a Process - See Control Limits.

Nominal Group Technique - A structured method that a team can use to generate and rank a list of ideas or items. Non-Value Added (NVA) - Any activity performed in producing a product or delivering a service that does not addvalue, where value is defined as changing the form, fit or function of the product or service and is something forwhich the customer is willing to pay.

Normal Distribution - The distribution characterized by the smooth, bell- shaped curve. Synonymous with

Gaussian Distribution.

Objective Statement - A succinct statement of the goals, timing and expectations of a six sigma improvementproject.

Opportunities - The number of characteristics, parameters or features of a product or service that can be classifiedas acceptable or unacceptable.

Out of Control - A process is said to be out of control if it exhibits variations larger than its control limits or shows apattern of variation.

Output - A resource or item or characteristic that is the product of a process or system. See also Y, CTQ.

Pareto Chart - A bar chart for attribute (or categorical) data categories are presented in descending order offrequency.

Pareto Principle - The general principle originally proposed by Vilfredo Pareto (1848-1923) that the majority ofinfluence on an outcome is exerted by a minority of input factors.

Poka-Yoke - A translation of a Japanese term meaning to mistake-proof.

Probability - The likelihood of an event or circumstance occurring.

Problem Statement - A succinct statement of a business situation which is used to bound and describe theproblem the six sigma project is attempting to solve.

Process - A set of activities and material and/or information flow which transforms a set of inputs into outputs forthe purpose of producing a product, providing a service or performing a task.

Process Characterization - The act of thoroughly understanding a process, including the specific relationship(s)between its outputs and the inputs, and its performance and capability.

Process Certification - Establishing documented evidence that a process will consistently produce requiredoutcome or meet required specifications.

Process Flow Diagram - See flowchart.



677


Glossary

Process Member - A individual who performs activities within a process to deliver a process output, a productor a service to a customer.

Process Owner - Process Owners have responsibility for process performance and resources. They providesupport, resources and functional expertise to six sigma projects. They are accountable for implementing

developed six sigma solutions into their process.

Quality Function Deployment (QFD) - A systematic process used to integrate customer requirements intoevery aspect of the design and delivery of products and services.

Range - A measure of the variability in a data set. It is the difference between the largest and smallest valuesin a data set.

Regression Analysis - A statistical technique for determining the mathematical relation between a measuredquantity and the variables it depends on. Includes Simple and Multiple Linear Regression.

Repeatability (of a Measurement) - The extent to which repeated measurements of a particular object with aparticular instrument produce the same value. See also Gage R&R.

Reproducibility (of a Measurement) - The extent to which repeated measurements of a particular object witha particular individual produce the same value. See also Gage R&R.

Rework - Activity required to correct defects produced by a process.

Risk Priority Number (RPN) - In Failure Mode Effects Analysis -- the aggregate score of a failure modeincluding its severity, frequency of occurrence, and ability to be detected.

Rolled Throughput Yield (RTY) - The probability of a unit going through all process steps or systemcharacteristics with zero defects.

R.U.M.B.A. - An acronym used to describe a method to determine the validity of customer requirements. Itstands for Reasonable, Understandable, Measurable, Believable, and Achievable.

Run Chart - A basic graphical tool that charts a characteristic’s performance over time.

Scatter Plot - A chart in which one variable is plotted against another to determine the relationship, if any,between the two.

Screening Experiment - A type of experiment to identify the subset of significant factors from among a largegroup of potential factors.

Short Term Variation - The amount of variation observed in a characteristic which has not had the opportunityto experience all the sources of variation from the inputs acting on it.

Sigma Score (Z) - A commonly used measure of process capability that represents the number of short-termstandard deviations between the center of a process and the closest specification limit. Sometimes referred toas sigma level, or simply Sigma.

Significant Y - An output of a process that exerts a significant influence on the success of the process or thecustomer.

Six Sigma Leader - An individual that leads the implementation of Six Sigma, coordinating all of the necessaryactivities, assures optimal results are obtained and keeps everyone informed of progress made.



678


Glossary

Six Sigma Project - A well defined effort that states a business problem in quantifiable terms and with knownimprovement expectations.

Six Sigma (System) - A proven set of analytical tools, project management techniques, reporting methods andmanagement techniques combined to form a powerful problem solving and business improvement methodology.

Special Cause Variation - Those non-random causes of variation that can be detected by the use of control chartsand good process documentation.

Specification Limits - The bounds of acceptable performance for a characteristic.

Stability (of a Process) - A process is said to be stable if it shows no recognizable pattern of change and nospecial causes of variation are present.

Standard Deviation - One of the most common measures of variability in a data set or in a population. It is thesquare root of the variance.

Statistical Problem - A problem that is addressed with facts and data analysis methods.

Statistical Process Control (SPC) - The use of basic graphical and statistical methods for measuring, analyzing,and controlling the variation of a process for the purpose of continuously improving the process. A process is said tobe in a state of statistical control when it exhibits only random variation.

Statistical Solution - A data driven solution with known confidence/risk levels, as opposed to a qualitative, “I think”solution.

Supplier - An individual or entity responsible for providing an input to a process in the form of resources orinformation.

Trend - A gradual, systematic change over time or some other variable.

TSSW - Thinking the six sigma way – A mental model for improvement which perceives outcomes through a causeand effect relationship combined with six sigma concepts to solve everyday and business problems.

Two-Level Design - An experiment where all factors are set at one of two levels, denoted as low and high (-1 and +1).

Upper Control Limit (UCL) for Control Charts - The upper limit below which a process statistic must remain to bein control. Typically this value is 3 standard deviations above the central tendency.

Upper Specification Limit (USL) - The highest value of a characteristic which is acceptable.

Variability - A generic term that refers to the property of a characteristic, process or system to take on differentvalues when it is repeated.

Variables - Quantities which are subject to change or variability.

Variable Data - Data which is continuous, which can be meaningfully subdivided, i.e. can have decimalsubdivisions.

Variance - A specifically defined mathematical measure of variability in a data set or population. It is the square ofthe standard deviation.

Variation - See variability.



679

Glossary

VOB - Voice of the business – Represents the needs of the business and the key stakeholders of the business.It is usually items such as profitability, revenue, growth, market share, etc.

VOC - Voice of the customer – Represents the expressed and non-expressed needs, wants and desires of therecipient of a process output, a product or a service. Its is usually expressed as specifications, requirements orexpectations.

VOP - Voice of the process – Represents the performance and capability of a process to achieve bothbusiness and customer needs. It is usually expressed in some form of an efficiency and/or effectivenessmetric.

Waste - Waste represents material, effort and time that does not add value in the eyes of key stakeholders(Customers, Employees, Investors).

X - An input characteristic to a process or system. In six sigma it is usually used in the expression of Y=f(X),where the output (Y) is a function of the inputs (X).

Y - An output characteristic of a process. In six sigma it is usually used in the expression of Y=f(X), where the

output (Y) is a function of the inputs (X).

Yellow Belt - An individual who receives approximately one week of training in problem solving and processoptimization methods. Yellow Belts participate in Process Management activates, participate on Green andBlack Belt projects and apply concepts to their work area and their job.

Z Score – See Sigma Score.

ECareers BB EL Manual XL PDF

Documents

Transcript of ECareers BB EL Manual XL PDF