Assessing Capability

8/7/2019 Assessing Capability

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Assessing Capability

Joel Smith

Commercial Sales

Minitab, Inc.


2/79

Schedule

Learn about the tools

Two continuous examples

Assessment of cookout locations

In class example

One binomial example

One count example (if time permits)


3/79

Brain Warmer

The Monty Hall Show


4/79

Brain Warmer

Pick Shown Should

1 2/3 Stay

2 3 Move

3 2 Move

Pick Shown Should

1 3 Move

2 1/3 Stay

3 2 Move

Pick Shown Should

1 2 Move

2 1 Move

3 1/2 Stay


5/79

What is Capability?

Assess quality

Quantify ability to meet specifications

Distinguish short- and long-term


6/79

Data Types

Continuous

Length

Time

Temperature

Binary

Yes/No, Pass/Fail

How many heads in X coin flips

Count

Defects/part

Orders in a day


7/79


Determine specifications

Verify Measurement System

Gage R&R, Attribute Gage R&R

Collect data

Look at the data

Histogram, Boxplot

Determine distribution of data

Probability Plot

Evaluate stability Control Charts

Capability

Capability Analysis


8/79


Determine specifications

Avoid this topic here

Verify Measurement System

Error types Ability to measure accurately

Collect data

Short-term and long-term

Subgrouping

Randomize collection of data


9/79


Look at the data

Always!

Determine distribution of data

Most data is not normal Good fit is critical

Some data have natural distribution

Evaluate stability Unstable process is unpredictive

Use distribution to quantify capability

Capability quantified using several statistics


10/79

Two Examples

I want to plan a 4th of July cookout

Where should I have it?

What factors should I consider?

How likely is each location to satisfy my requirements?

We make high-strength cord used to secure

parachutes

How long is each cord?

How likely is each cord to be within my specs?


11/79

Two Examples

4th of July Cookout is in slides

My locations:

State College, PA

Pasadena, CA

My factors

Temperature

Precipitation

Cord will be done here

Evaluate Length


12/79

Cookout: State College, PA

What is the capability of State College to produce goodweather on July 4th?

Average Temperature should be between 65 and 85

Precipitation should be


13/79


To assess capability:

If necessary, verify measurement system

Collect data

Look at the data

Evaluate stability using a Control Chart

Determine the distribution

Perform a Capability Analysis


14/79

Measurement System Analysis (MSA)

Do prior to collecting and analyzing data

Two types:

Continuous (Length, Time, Temperature, etc.)

Attribute (Yes/No, Poor/Fair/Good, etc.)

Establishes how much variability is coming from parts

versus operators


15/79

Measurement System Analysis (MSA)

In God we trust;

All others bring

data


16/79

Cord: MSA in Class

To test whether our Measurement System is sufficient: 3 Operators (volunteers?)

6 Parts

2 Measurements per part per operator

Randomize!

We will do Attribute Gage R&R later


17/79

Cord: MSA in Class

(Do MSA now)


18/79


For our weather data, no MSA will be done

Data has already been collected

Next steps:

Look at the data





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Look at the data:

85807570656055

Median

Mean

71.070.570.069.569.068.568.0

1st Quart ile 66.000

Median 70.000

3rd Quart ile 74.000

M aximum 85.000

68.579 71.196

68.000 71.221

5.089 6.965

A -Squared 0.20

P-Value 0.870

Mean 69.888

StDev 5.881

V ariance 34.582Skewness 0.0962166

Kurtosis -0.0008702

N 80

M inimum 55.000

A nderson-Darling Normality Test

95% C onfidence Interv al for Mean

95% C onfidence Interval for Median

95% C onfidence Interval for StDev95 % C onfidence Intervals

Summary for TAVE (F)


20/79


Data appearsnormal

Symmetry

Mean ~ Median

85807570656055

M

d

M

71.070.570.069.569.068.568.0

1s t Q ua rtile 66.000

Median 70.000

3rd Q uartile 74.000Maximum 85.000

68.579 71.196

68.000 71. 1

5.089 6.965

A -Squared 0. 0

P-V alue 0.870

Mean 69.888

StDev 5.881

Variance 34.582

S ke wness 0.0962166

K urto sis -0.0008702

N 80

M inimum 55.000


95% Confidence Interval for Mean

95% Confidence Interval for Median

95% Confidence Interval for StDev

95 %

o

c

vas

S a

o TA

! ( " )


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Evaluate Stability using a Control Chart:

736557494133251791

90

80

70

60

50

Observation

Individu

alValue

_

X=69.89

UC L=88.79

LCL=50.99

736557494133251791

20

15

10

5

0

Observation

M

ovingRange

__MR=7.11

UC L=23.22

LCL=0

I-MR Chart of TAVE (F)


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Random, stable

No out of control

Location/Spread

736557494133251791

90

80

70

60

50

Observati # $

%

&

'

ivi

'

(

al

)

al

(

e

_X=69.89

UC L=88.79

LCL=50.99

736557494133251791

20

15

10

5

0

Observati # $

M

0

vi

&

1

2

ange

__MR=7.11

UC L=23.22

LCL=0

I-M3

4

5art ofT

6 7

8(F)


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Determine Distribution

What is the Normal distribution?

Other distributions:

Weibull

Largest/smallest extreme value

Exponential


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Use a Probability Plot to Determine Distribution:

9080706050

99.9

99

95

90

80

7060504030

20

10

5

1

0.1

TAVE (F)

Percent

Mean 69.89

StDev 5.881

N 80AD 0.204

P-Value 0.870

Probability Plot of TAVE (F)Normal


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Use a Probability Plot to Determine Distribution

Fat Pencil test

Squinty Eye test

Anderson-Darling

P-value9080706050

99.9

99

95

90

80

70

60

50

40

30

20

10

5

1

0.1

TAVE (F9

P

@

rc

@

A

B

M C D E 69.89

StDC

F

5.881

N 80

AD 0.204

P-V D G H C 0.870

PrI

Pabili

Q

R

PlI

Q

of TAVE (FS

NT

U

mV

W


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Finally, perform Capability Analysis Specs: 65 to 85 degrees

Key assumptions:

Data is from a stable process Data is well-fit by distribution

We will learn:

Characteristics of data Likelihood of bad parts

Short-term vs. Long-term performance


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Finally, perform Capability Analysis

85807570656055

LSL USL

LSL 65

Target *

USL 85Sample Mean 69.8875

Sample N 80

StDev (Within) 6.16079

StDev (O verall) 5.8993

Process Data

C p 0.54

CPL 0.26

CPU 0.82

Cpk 0.26

Pp 0.57

PPL 0.28

PPU 0.85

Ppk 0.28

Cpm *

O v erall Capability

Potential (Within) Capability

PPM < LSL 187500.00

PPM > USL 0.00

PPM Total 187500.00

O bserved Performance

PP M < LSL 213794.53

PPM > USL 7083.23

PPM Total 220877.75

Exp. Within Performance

PPM < LSL 203696.86

PPM > USL 5207.36

PPM Total 208904.23

Exp. Overall Performance

Within

Overall

Process Capability of TAVE (F)


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85807570656055

LSL USL

LSL 65

Target *


Sample N 80



Process Data

C p 0.54

CPL 0.26

CPU 0.82

Cpk 0.26

Pp 0.57

PPL 0.28

PPU 0.85

Ppk 0.28

Cpm *



PPM < LSL 187500.00

PPM > USL 0.00

PPM Total 187500.00


PP M < LSL 213794.53

PPM > USL 7083.23

PPM Total 220877.75


PPM < LSL 203696.86

PPM > USL 5207.36

PPM Total 208904.23


Within

Overall


Characteristicsof Data


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85807570656055

LSL USL

LSL 65

Target *


Sample N 80



Process Data

C p 0.54

CPL 0.26

CPU 0.82

Cpk 0.26

Pp 0.57

PPL 0.28

PPU 0.85

Ppk 0.28

Cpm *



PPM < LSL 187500.00

PPM > USL 0.00

PPM Total 187500.00


PP M < LSL 213794.53

PPM > USL 7083.23

PPM Total 220877.75


PPM < LSL 203696.86

PPM > USL 5207.36

PPM Total 208904.23


Within

Overall


Likelihood of

bad parts


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85807570656055

LSL USL

LSL 65

Target *


Sample N 80



Process Data

C p 0.54

CPL 0.26

CPU 0.82

Cpk 0.26

Pp 0.57

PPL 0.28

PPU 0.85

Ppk 0.28

Cpm *



PPM < LSL 187500.00

PPM > USL 0.00

PPM Total 187500.00


PP M < LSL 213794.53

PPM > USL 7083.23

PPM Total 220877.75


PPM < LSL 203696.86

PPM > USL 5207.36

PPM Total 208904.23


Within

Overall


Short-term vs.

Long-term


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Now lets take a look at Precipitation

Recall we want


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Look at the data:

0.80.60.40.2-0.0

Median

Mean

0.1500.1250.1000.0750.0500.0250.000

1st Q uartile 0.00000

Median 0.00000

3rd Q uartile 0.07750

Maximum 0.82000

0.06261 0.15789

0.00000 0.02000

0.18528 0.25357

A-Squared 15.00

P-Va lue < 0.005

M ean 0.11025

S tD ev 0.21408

Variance 0.04583Skewness 2.05593

Kurtosis 2.95297

N 80

Minimum 0.00000





Summary for PRCP (in)


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Data appearsskewed

No symmetry

Mean Median

0.80.60.40.2-0.0

M X Y ia

M X a

0.1500.1250.1000.0750.0500.0250.000

1st Q a a b til c 0.00000

Mc d

iae

0.00000

3rd Q a artil c 0.07750

M af

im a m 0.82000

0 .0 62 61 0 .1 57 89

0 .0 00 00 0 .0 20 00

0 .1 85 28 0 .2 53 57

A -g h a

ared 15.00

P -i

a l a e < 0.005

M ea e 0.11025

S tD ev 0.21408

V aria e ce 0.04583

S k e w n e ss 2 .0 55 9 3

Kurtosis 2.95297

N 80

M inim um 0.00000

A nderson-D arling N orma lityp

est

95% C onfiden ce q nterv al forM ean

95% C onfiden ce q nterv a l forM ed ian

95% C onfiden ce q nterv al forS t D e v

9 5% C o rs

t u v r c v w rx

v ry

al s

ary for P

CP(in)


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736557494133251791

0.8

0.6

0.4

0.2

0.0

Observation

IndividualValue

_X=0.1103

UCL=0.2675

LB=0

736557494133251791

0.8

0.6

0.4

0.2

0.0

Observation

M

ovingRange

__MR=0.0591

UCL=0.1932

LCL=0

1

1

1

1

11

1

1

1

1

1

1

1

11

11

11

11

11

1

11

11

11

11

1

1

11

I-MR Chart of PRCP (in)


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STOP!


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Assumptions are not met

No stability = No capability

At this point:

Special causes

Other factors


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Is State College a good location?

Temperature

Average temperature stable year-to-year

Normal distribution 79% chance of good

Precipitation

Precipitation is unstable

Cannot determine capability


39/79

Cookout: Pasadena, CA

How about Pasadena?

Evaluate same criteria

Temperature (65 to 85)

Precipitation (


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Look at the data:

848076726864

Median

Mean

74.073.573.072.572.071.571.0

1st Quartile 70.000

M edian 72.000


Maximum 86.000

71.982 74.043

71.000 73.000

3.949 5.427

A -S quared 1.78

P -V alue < 0.005

Mean 73.013

StDev 4.571

Va riance 20.896Skewness 0.857208

Kurtosis 0.462320

N 78

M inimum 64.000





Summary for TAVE (F)


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Data appearspartly skewed

Some Asymmetry

Mean Median

848076726864

Medi n

Me n

74.073.573.072.572.071.571.0

1st

u

rtile 70.000

Medi n 72.0003rd u rtile 76.000

M ximum 86.000

71.982 74.043

71.000 73.000

3.949 5.427

-Squ r d 1.78

-V lue 0.005

Me n 73.013

S t v 4.571

V

rinc

0.896

Sk wne ss 0.857208

urtosis 0.462320

N 78

Minimum 64.000

nd

rson-

rling Normlity Test

95% C onfid nc nt rva l for Mean

95% C onfid nc nt rva l for Median

95% C onfid nc nt rv al forS t v95% Confid nc n rv l

Summj

rk

for TAVE(F)


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Cord: Look at data

First we need to collect data

Need a good distribution fit

Generally 25-50 points

Use Histogram


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736557494133251791

84

78

72

66

60

Observation

Individ

ualValue

_X=73.01

UC L=86.03

LCL=59.99

736557494133251791

20

15

10

5

0

Observation

M

ovingRange

__MR=4.90

UC L=16.00

LCL=0

1

I-MR Chart of TAVE (F)


44/79



Mostly stable

One out of control

Can we proceed?

736557494133251791

84

78

72

66

60

Observation

Indiv

idua

lValue

_X

l 73m 01

n o L= 6m 03

LCL=59 m 99

736557494133251791

20

15

10

5

0

Observation

M

oving

a

nge

__M

=4

m90

n oL=16

m00

LCL=0

1

I MR

art o

AV Fz


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Cord: Evaluate Stability

(Evaluate stability using Control Chart)


46/79

Out of Control Points

Many out of control points: Unstable process

Special causes

Other factors

Very few out of control:

Look for special cause

Only if legitimate, remove


47/79


Use a Probability Plot to Determine Distribution:

90858075706560

99.9

99

95

90

80

7060504030

20

105

1

0.1

TAVE (F)

Percent

Mean 73.01

StDev 4.571

N 78

AD 1.782

P-Value


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Use Probability Plots to Determine Distribution:

90807060

99.9

99

90

50

10

1

0.1

TA VE (F)

Perc

ent

806040

99.9

90

50

10

1

0.1

TA VE (F)

Perc

ent

100908070

99.9

99

90

50

10

0.1

TA VE (F)

Percent

100101

99.9

99

90

50

10

1

0.1

TA VE (F) - Threshold

Percent

Largest Extreme V alue

A D = 0.544

P-V alue = 0.174

3-Parameter Loglogistic

A D = 0.556

P-V alue = *

Goodness of Fit Test

Normal

A D = 1.782

P-V alue < 0.005

Weibull

A D = 3.491

P-V alue < 0.010

Probability Plot for TAVE (F)

Normal - 95% C I Weibull - 95% C I

Largest Extreme Value - 95% CI 3-Parameter Loglogistic - 95% CI


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Use a Probability Plot to Determine Distribution

Fat Pencil test

Squinty Eye test

Anderson-Darling

P-value

10090807060

99.9

99

9897

95

90

80

70605040302010

10.1

TAVE (F)

Pe

{

ce

|

t

Loc 70.94

Scale 3.628

N 78

AD 0.544

P-Value 0.174

P}obab

~ ~ty P

ot ofTAVE(F)

Largest Extreme Value - 95% CI


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Cord: Determine Distribution

(Determine distribution using Probability Plot)


51/79


Finally, perform Capability Analysis Specs: 65 to 85 degrees

Key assumptions:

Data is from a stable processData is well-fit by distribution

We will learn:

Characteristics of data

Likelihood of bad parts

Long-term performance only


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88848076726864

LSL USL

LSL 65

Target *USL 85

Sample Mean 73.0128

S ample N 78

Location 70.9361

Scale 3.62756

Process Data

Pp 0.65

P PL 0.89P PU 0.56

P pk 0.56

O verall C apability

PPM < LSL 12820.51

PPM > USL 12820.51

PPM Total 25641.03


PPM < LSL 5877.92

PPM > USL 20500.38

PPM Total 26378.30

Exp. Ov erall Performance

Process Capability of TAVE (F)Calculations Based on Largest Extreme Value Distribution Model


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88848076726864

LSL USL

LSL 65

Target *USL 85

Sample Mean 73.0128

S ample N 78

Location 70.9361

Scale 3.62756

Process Data

Pp 0.65

P PL 0.89P PU 0.56

P pk 0.56


PPM < LSL 12820.51

PPM > USL 12820.51

PPM Total 25641.03


PPM < LSL 5877.92

PPM > USL 20500.38

PPM Total 26378.30





Characteristics

of Data


54/79

88848076726864

LSL USL

LSL 65

Target *USL 85

Sample Mean 73.0128

S ample N 78

Location 70.9361

Scale 3.62756

Process Data

Pp 0.65

P PL 0.89P PU 0.56

P pk 0.56


PPM < LSL 12820.51

PPM > USL 12820.51

PPM Total 25641.03


PPM < LSL 5877.92

PPM > USL 20500.38

PPM Total 26378.30





Likelihood of

bad parts


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88848076726864

LSL USL

LSL 65

Target *USL 85

Sample Mean 73.0128

S ample N 78

Location 70.9361

Scale 3.62756

Process Data

Pp 0.65

P PL 0.89P PU 0.56

P pk 0.56


PPM < LSL 12820.51

PPM > USL 12820.51

PPM Total 25641.03


PPM < LSL 5877.92

PPM > USL 20500.38

PPM Total 26378.30





Long-term only


56/79

Cord: Capability Analysis

(Perform Capability Analysis now)


57/79


How about Precipitation?

Evaluate same criteria

Precipitation (


58/79


Look at the data:

0.060.050.040.030.020.010.00

Median

Mean

0.00200.00150.00100.00050.0000-0.0005-0.0010

1st Quartile 0.000000

Median 0 .000000


Maximum 0.060000

-0.000763 0.002301

0.000000 0.000000

0.005869 0.008066

A -Squared 29.19

P -V alue < 0.005

M ean 0.000769

S tD ev 0.006794

Variance 0.000046

Skewness 8 .8318

Kurtosis 78.0000

N 78

Minimum 0.000000





Summary for PRCP (in)


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Unusual data

Nearly all values

equal or nearly

equal

Mean Median

0060

050

040

030

020

010

00

Medi n

Me n

0 00200 00150 00100 00050 0000-0 0005-0 0010

1st u rtile 0 000000

Medi n 0 000000

3rd

u

rtile 0

000000M imum 0 060000

-0 0 007 63 0 002301

0 000000 0 000000

0005869 0

008066

A-Squ red 29 19

P-Value 0 005

Mean 0 000769

S t ev 0 006794

V arian e 0 000046

Skew ness 88318

Kurt sis 78 0000

N 78

M inimum 0 000000

A nderson-Darling Normality

est

95% C onfiden e Interval for Mean

95% C onfiden e Interval for Median

95% C onfiden

e Interval for StDev95% on idence Intervals

Summary

or PRCP in)


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736557494133251791

0.060

0.045

0.030

0.015

0.000

Observation

Individ

ualValue

_X=0.00077UC L=0.00491

LCL=-0.00338

736557494133251791

0.060

0.045

0.030

0.015

0.000

Observation

M

ovingRang

e

__MR=0.00156UC L=0.00509LCL=0

1

11

I-MR Chart of PRCP (in)


61/79



Mostly stable?

One out of control

Can we proceed?

736557494133251791

0.060

0.045

0.030

0.015

0.000

Obs

rvaion

IndividualValu

_X=0.00077UC L=0.00491

LC L=-0.00338

736557494133251791

0.060

0.045

0.030

0.015

0.000

Obs

rvaion

M

ovin

Ran

__MR=0.00156UC L=0.00509LC L=0

1

11

I-MR Char

of PRCP (in)


62/79

Out of Control Points

Many out of control points: Unstable process

Special causes

Other factors

Very few out of control:

Look for special cause

Only if legitimate, remove


63/79


Our process is out of control:

Binary process?

Can evaluate capability for binary (later)

Not enough data


64/79


STOP!


65/79


Is Pasadena a good location?

Temperature

Average temperature stable year-to-year

Non-normal distribution 97.4% chance of good

Precipitation

Precipitation is unstable

Cannot determine capability


66/79

Cookout Comparison

Which city is better

Temperature

State College = 79%

Pasadena = 97.4%

Precipitation

Precipitation is unstable for both

Relative rate is much lower in Pasadena


67/79

Cookout Comparison

A quick graph:

City

TMAX (F)TAVE (F)TMIN (F)

State CollegePasadenaState CollegePasadenaState CollegePasadena

110

100

90

80

70

60

50

40

Data

Boxplot of TMIN (F), TAVE (F), TMAX (F)


68/79

Pill Quality Example

We work for a pharma company, and pill quality iscritical

Need to evaluate our capability

Remember:

Verify measurement system

Collect data

Look at the data Evaluate stability using a Control Chart




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Pill Quality Example

Now to collect our data

Everyone open your pill bottle

Without ingesting the medication: Count the number of pills

Count how many are defective


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72/79

Circuit Board Example

We work for an electronics company, and circuit boardquality is critical

Need to evaluate our capability

Remember:

Verify measurement system

Collect data

Look at the data





73/79


Perform Gage R&R Approximated as continuous

Our criteria:

How many burn marks are on the board

We will use

3 operators

6 parts

2 runs per part


74/79


Now everyone please take on circuit board

Again without ingesting, record:

How many burn marks there are

Destructive test


75/79

Recap

Verify Measurement System Error types

Ability to measure accurately

Continuous versus Attribute

Tools

Gage R&R

Attribute Gage R&R


76/79

Recap

Collect data Short-term and long-term

Subgrouping

Randomize collection of data

Look at the data

Histograms

Boxplots

Other graphs


77/79

Recap

Determine distribution of data Most data is not normal

Good fit is critical

Some data have natural distribution

Probability Plots

Evaluate stability

Unstable process is unpredictive

Control Charts


78/79

Recap

Perform capability analysis Capability quantified using several statistics

Capability Analysis

Consider data type

Continuous

Binary

Count


79/79

The EndJoel Smith

Commercial Sales

Minitab, Inc.

Assessing Capability

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Transcript of Assessing Capability