1 © Visteon Corporation GB-Mod #8 Rev 3.6 10/03 Measure Phase GB Mod #8.

1© Visteon Corporation GB-Mod #8 Rev 3.6 10/03

Measure Phase

GB Mod #8


Continuous Improvement Road Map

Improve

Control

• Define CTQ• Determine Current State

• Determine Key Input / Output Variables

• Perform MSA• Calculate initial process

capabilities

Measure

• Verify Effects of Key inputs with DOE’s

• Determine Optimum Settings

• Update Control Plan• Verify Improvements

Analyze• Evaluate Existing Control Plan• Using statistical methods to determine potential key inputs• Prioritize key input variables

N

Define


Measurement Phase

• Plan the Project • Identify Key Input and Output Variables

(KPIVs & KPOVs)• Confirm Measurement Systems• Determine Initial Process Capabilities


Measure - Toolbox

• Process Mapping• MSA / GR&R• Capability Analysis

Cpk (Continuous) DPMO (Attribute)


Section Objectives

• Gain an understanding of the different data types Variable Attribute

• Capable of mapping a process showing process inputs and outputs

• Understand the basics behind measurement system error

• Understand the concepts behind capability metrics


Process Mapping


Suppliers Business CustomersBlock DiagramsSparse detail

Input-OutputDiagrams

Detailed …

...Increasingly detailed through

decomposition

ProcessFlowchartingGreat detail

Process Mapping – Levels of detail


Detailed Process Mapping

• A tool which provides a structured approach to creating the Y=f(x) relationship.

• Utilizes structured 7 step method.• It’s a Team Effort - One person does not

know all the process In a plant project:

Manufacturing Engineers Line Operators Line Supervisors Maintenance Technicians


Detailed Process Mapping

• Inputs to Detailed Mapping: Brainstorming Walking the floor Operator Manuals Engineering Specifications Operator Experience PEMME (People, Equipment, Methods, Material,

Environment)


Detailed Process Mapping - Step 1

1) Define the scope of the process the team needs to focus on. The scope of the process needs to be at an actionable level. Are all the steps below documented at an actionable level?

Prepare Reactor Oxidize Stabilize Finish

Charge melted wax Put in set points Put in set points Check nozzle typeBring to reaction temp Sample hourly Slowly reduce press Put in set points

Monitor acid number Monitor temp Monitor appearance

DPU = 0.05 DPU = 0.02 DPU = 0.01 DPU = 0.11CT = 45 sec CT = 30 sec CT = 5 sec CT = 21 secCOPQ = ? COPQ = ? COPQ = ? COPQ = ?



2) Document all tasks or operations needed in the production of a “good” product or service (include; defect data, cycle time, costs, etc. at each step if available). Additionally, all inspection, rework, transportation steps should be identified.











3) Document each task or operation above as value add or non value add. Value add: Is recognized by the customer Changes the product Is required by law, regulation, the contract, or for

health, safety, & environmental considerations

NVAVA VA NVA


4) List both internal and external Y's at each process step.

Internal Y’s are outputs that are critical for the next operation.

External Y’s are outputs identified as critical by the customer.


Output

Prep timePrepare Reactor Acid number

ViscosityCharge melted wax Reactor temp

Bring to reaction temp Temp profileHT coeff

Oxid timeOxidize Acid number

ColorPut in set points ViscositySample hourly Reactor temp

Monitor acid number Temp profile

Offgas flowOffgas compHT coeffResp time

Output

Stab timeStabilize Acid number

ColorPut in set points Viscosity

Slowly reduce press Reactor temp

Monitor temp Temp profileOffgas flowOffgas compHT coeff

Finish timeFinish Acid number

ColorCheck nozzle type ViscosityPut in set points Drop Point

Monitor appearance HardnessPellet appearance

1

2

3

4


Identifying the ‘Y’s• What condition do we want to see the product in

when it leaves this process step?• What critical dimensions need to be satisfied

before moving to the next step?• What critical characteristics or features must be

satisfied?• Are these important for the next process step

(internal customer) or are they critical for the external customer?




5) List both internal and external X's at each process step.External inputs are critical characteristics identified from raw material.

Internal inputs are variables within the process itself.

Input

Agit speedTemperaturePressureAir flow% O2 in air

Air temp

Belt speedBelt tempFlow rateNozzle typeHole sizeRoom tempAgit speedTank temp

Output



Slowly reduce press Reactor tempMonitor temp Temp profile

Off gas flowOff gas compHT coeff


ColorCheck nozzle type Viscosity

Put in set points Drop PointMonitor appearance Hardness

Pellet appear

Output

Prep timePrepare ReactorAcid numberViscosityCharge melted waxReactor tempBring to reaction tempTemp profileHT coeff




Offgas flow

Input

Wax gradeAmt waxCharge rateAgit speedRxn tempPressureAir flow% O2 in air

ViscosityWax temp

AN targetAgit speed *Temperature *Pressure *Air flow *% O2 in air

Air tempAir humidity Offgas comp

HT coeffResp time


Identifying the ‘X’s• What inputs/factors/variables in this process step

may have an effect on the Y’s identified?• What factors may prevent from successfully

achieving the Y’s identified?• Use the brainstorming techniques and the

PEMME categories to fully explore the range of potential inputs.




6) Classify all X's as one or more of the following:- Controllable (C): these are inputs that you can adjust or

control while the process is running (i.e...., speed, feed rate, temperature, pressure, etc)

- Standard Operating Procedures (SOP): common sense items that one should execute because it makes sense. The goal here is to ensure that we document the true procedure (i.e...., cleaning, safety, loading of components, setup, etc)

- Noise (N): things you cannot control due to cost or difficulty (ambient temperature or humidity, operator training).



Input Type Output

Agit speed Contr Stab time

Temperature ContrStabilize

Acid number

Pressure Contr Color

Air flow ContrPut in set points

Viscosity

% O2 in air NoiseSlowly reduce press

Reactor temp

Air temp ContrMonitor temp

Temp profile

Off gas flow

Off gas comp

HT coeff

Belt speed Contr Finish time

Belt temp ContrFinish

Acid number

Flow rate Contr Color

Nozzle type ContrCheck nozzle type

Viscosity

Hole size ContrPut in set points

Drop Point

Room temp NoiseMonitor appearance

Hardness

Agit speed Contr Pellet appear

Tank temp Contr

Input Type Output

Wax grade ContrPrep timeAmt wax Contr Prepare ReactorAcid numberCharge rate ContrViscosityAgit speed Contr Charge melted waxReactor tempRxn temp Contr Bring to reaction tempTemp profilePressure ContrHT coeffAir flow Contr

% O2 in air Noise

Viscosity Noise

Wax temp Noise

AN target Contr Oxid time

Agit speed * Contr Oxidize Acid number

Temperature * Contr Color

Pressure * Contr Put in set points Viscosity

Air flow * Contr Sample hourly Reactor temp

% O2 in air Noise Monitor acid number Temp profile

Air temp Contr Offgas flow

Air humidity Noise Offgas comp

HT coeff

Resp time



7) Identify where you currently are collecting data and also identify where you may need to collect data. These areas can be called Tally Points

Tally Point 1 Tally Point 2

Output

Prep timePrepare ReactorAcid numberViscosityCharge melted waxReactor tempBring to reaction tempTemp profileHT coeff




Offgas flow

Input

Wax gradeAmt waxCharge rateAgit speedRxn tempPressureAir flow% O2 in air

ViscosityWax temp

AN targetAgit speed *Temperature *Pressure *Air flow *% O2 in air

Air tempAir humidity Offgas comp

HT coeffResp time

Input

Agit speedTemperaturePressureAir flow% O2 in air

Air temp

Belt speedBelt tempFlow rateNozzle typeHole sizeRoom tempAgit speedTank temp

Output



Slowly reduce press Reactor tempMonitor temp Temp profile

Off gas flowOff gas compHT coeff


ColorCheck nozzle type Viscosity

Put in set points Drop PointMonitor appearance Hardness

Pellet appear


Process Map Example – CAB Brazing

InputControllable or

Noise?M'ment System

Spec Process OutputM'ment System

Spec

Belt speed through fluxer C Tachometer As per condensor 2-tier.

Nozzle diameter (blockages) C

Flowrate? Back

pressure? Diameter?

Dependent on measurement system.

Correct external flux application (quantity)

None None

Flow rate of aqueous flux C Flow meter TBDUniform distribution of aqueous flux

Visual No dry segments

on core

Nozzle alignment/orientation CAngle,

spacing measurement

Current setting? Minimum flux on internal fin Visual No flux inside core

Flux purity C Visual No foreign bodies. Correct belt position Visual TBDCore position (across width) C Tape-measure TBDPresence of flux covers C Visual All headers covered.Flux Concentration in solution C By weight Target?

Belt speed through furnace C Tachometer As per condensor 2-tier.Sufficient clad flow (no leakers)

Leak test <3cc/min

Loading density (mass loading) C Count models Definition required. OK Silicon diffusion/erosion Lab check ?

Temperature profile (Set points) C Thermocouple As per control plan. No underbrazeInternal braze

check?

Oxygen levels N None <400 PPM No oxidation VisualNo core

discolouration

Nitrogen levels (flow rate) C Flow meterCurrent setting (paint

mark)Dimensional conformance to spec

Vernier As per drawing

Nitrogen purity C ? ? Good internal braze Visual>70% per tube &

no bridgingHumidity - Dew point N None <400 PPM No discolouration Visual ?

Core position (across width) C Tape-measure TBD No damage VisualAcceptance Standards

Adequate external fin adhesion

Visual >70% per tube??

Flux Application

Furnace


Exercise


Example!

• Pick an actual process from within the plant• Create a Process Map for that Process

This can be a manufacturing or transactional process

For ExampleFloat Bracket CuttingVinyl LayupBilling ProcessWork order creation


Yet another Example!

• Break up into your catapult teams. • Create a process map of the launching

activities• Be sure to identify the key inputs and outputs• Be prepared to report back to the class.


Expanding the Detailed Process Map

InputMeas. Sys.

Spec TypeMajor Step

Sub-Step OutputMeas. Sys.

Spec.Cp/ Cpk

X's Process Steps Y's

• Measurement System How this input or output is measured?

• Specification USL, Target, LSL

• Type Controllable, Noise, SOP, Material

Notice how much information you have about the process in a very simple format!


Example of Detailed Map

Input Meas. Sys. Spec Type Major Step Sub-Step OutputMeas. Sys.

Spec.Cp/ Cpk

Prepare Production

BatchTank Temp

Thermocoup 300-310 Cont Set Tank

TempSoftening

PointLab Test

118 125 1.6/1.2

Agit. RPM

Tachometer 275-300 Cont Agitate ViscosityLab Test

55 75 1.0/0.6

PenetrationLab Test

15 20 1.2/.8

KPIV's Process Steps KPOV's

This can be created easily in Excel


Uses for the Detailed Process Map

• You must have an accurate map which represents the actual process. It provides critical input to: Input to Cause and Effects Matrix Input to initial assessment of factors (x’s). Input to evaluation of process outputs. Foundation for the Measure Phase

• The detailed process map should be updated as suspected factors are eliminated and as new factors come to light during the project.


Next Steps

Detailed Process Map

Cause and Effects Matrix

1 2 3 4 5 6 7 8 9 10 11

Process Step Process Inputs Hea

vies

in

Pro

duct

Ligh

ts in

P

rodu

ct

Moi

stur

e in

P

rodu

ct

Aci

dity

in

Pro

duct

Low

Cap

acity

Fr

om U

nit

Exc

essi

ve

Dow

ntim

e

Mat

eria

l Lo

sses

Cor

rosi

on o

f E

quip

men

t

Poo

r Rea

ctor

P

erfo

rman

ce

Total

139 Day Tanks Analysis 10 10 9 9 3359 Reactor Cat./HF Ratio 5 8 7 1577 Reactor Rxr Temperature 6 5 4 7 149

73 Lights Removal Condenser Leak 4 8 2 4 1 14874 Lights Removal Reboiler Leak 4 8 2 4 1 148

131 Purification Low Stages 8 8 144144 Final Storage Containers 3 2 6 6 140100 Neutralization pH Value 6 6 3 13816 Catalyst Stripper Pluggage 3 6 5 3 137

111 Drying Decomposition 2 6 3 2 2 13439 Drier Water Carryover 4 6 5 1 13234 Drier Molecular Sieve 3 3 2 7 2 125

OUTPUTS

INP

UT

S

Input Type Output

Agit speed Contr Stab timeTemperature Contr Stabilize Acid numberPressure Contr ColorAir flow Contr Put in setpoints Viscosity% O2 in air Noise Slowly reduce press Reactor temp

Air temp Contr Monitor temp Temp profileOffgas flowOffgas compHT coeff

Belt speed Contr Finish timeBelt temp Contr Finish Acid numberFlow rate Contr ColorNozzle type SOP Check nozzle type ViscosityHole size Contr Put in setpoints Drop PointRoom temp Noise Monitor appearance HardnessAgit speed Contr Pellet appearTank temp Contr

Input Type Output

Wax grade SOP Prep timeAmt wax Contr Prepare Reactor Acid numberCharge rate Contr ViscosityAgit speed Contr Charge melted wax Reactor tempRxn temp Contr Bring to reaction temp Temp profilePressure Contr HT coeffAir flow Contr% O2 in air Noise

Viscosity NoiseWax temp Noise

AN target SOP Oxid timeAgit speed * Contr Oxidize Acid numberTemperature * Contr ColorPressure * Contr Put in setpoints ViscosityAir flow * Contr Sample hourly Reactor temp% O2 in air Noise Monitor acid number Temp profile

Air temp Contr Offgas flowAir humidity Noise Offgas comp

HT coeffResp time


Types of Data


What do you want to know?

Information Sources:

• Words (A to Z)

• Pictorial

• Verbal

• Numeric (0-9)

1) What do you want to know?

2) How do you want to see what it is thatyou need to know?

3) What type of tool will generate what itis that you need to see?

4) What type of data is required of theselected tool ?

5) Where can you get the required typeof data?

CriticalQuestions

Plan

Execute

“Data does not provide information – You have to torture data for it to give information. And the instrument of torture is statistics”. Dr. Mikel Harry.

Grouping Measurement

Discrete Continuous

Nominal Ordinal

Interval Ratio


Discrete Vs. Continuous Data

FAIL PASS

Electrical Circuit

DISCRETE

NO-GO GO

QTY UNIT DESCRIPTION TOTAL

1 $10.00 $10.00

3 $1.50 $4.50

10 $10.00 $10.00

2 $5.00 $10.00

SHIPPING ORDER

ERROR

$

TEMPERATURE

Thermometer

Time

CONTINUOUS

Caliper

$


Example

• Breakout into your groups• Create a list of various types of data that is

collected in your areas and categorize it accordingly (Continuous or Discrete)

• Be prepared to present your findings to the class


Continuous

Discrete $ $

SparseInformation

Rich WithInformation

The Advantage of Continuous Data

• To obtain the same level of understanding regarding a process


Nominal: unrelated categories which represent membership or non-membership.

Ordinal: ordered categories with no information about distance between categories.

Interval: ordered categories with equal distance between categories, but no absolute zero point.

Ratio: ordered categories with equal distance between categories with an absolute zero point.

• Discrete data (usually)• Grouping / sorting’• Yes / no, pass / fail• Arithmetic not possible

• Discrete data• Ranking• Seldom used• Very little arithmetic possible

• Continuous data• Most common scale• Use arithmetic with caution

• Continuous data• Proportional relationship• Most forms of arithmetic apply

• Categories• Labels

• 1st, 2nd, 3rd

• Relative height• Alphabetic order• 1<2<3<4

• Temperature scales• Dial indicator

• Velocity = distance/time• Ruler

Categories of scale Description Examples

Categories of Scales


Equipment Application

Environment Materials

Poor paintadhesion

Application form

Select one from each group

Nationality

Marital status

Occupation

List of Field Reps

Access to a digital camera

Without access to a digital camera

Fred W.

Bill S.

John D.

Sam C.

Bob T.

Jim C.

Joe W.

Diane A.

Nominal Scale• Nominal scales of measure are used to classify elements into categories without

considering any specific property.

• Examples of nominal scales include “causes” on fish bone diagrams, yes / no, pass / fail, etc.


Example 1: Pareto Chart - Paint Adhesion Test

Rel

ativ

e S

ize

Pre

para

tion

Ordinal Scale

Prim

erT

ype

Pai

ntT

ype

App

licat

ion

Hum

idity

Ope

rato

r

Order ofimportance

Example 2: Customer Survey

Question: How would yourate our service?

Excellent

Very Good

Good

Fair

Poor

Ordinal Scale

• Ordinal scales of measure are used to order or rank nominal (pass / fail) data based on a specific property.

• Examples of ordinal scales include relative height, Pareto charts, customer satisfaction surveys, etc.


Types of Questions for Questionnaires

• Strongly agree

• Somewhat agree

• Neither agree or disagree

• Somewhat disagree

• Strongly disagree

• Somewhat less than expected

• Much less than expected

• One of the best of all

• Better than most

• About the same as most

• Worse than many

• One of the worst of all

• Much better than expected

• Somewhat better than expected

• As expected

Likert Scale (Ordinal)

• Example Rating Scale Ranges Five-point school grading system (A B C D E) Seven-point numerical rating (1 2 3 4 5 6 7) Verbal scale (excellent, good, average, fair, poor)


Interval and Ratio Scale

Examples of interval scale:(no absolute zero)

1. Displaced Scale

50

40

30

20

10

0

3. Relative Velocity

Examples of Ratio Scale(absolute zero)

1. Ruler

100908070605040302010

02. Position Vs Timeat Constant Speed

3. Weight As a Function of Number of Bricks

0

0.10

0.20

2. Dial Gage

Gageblock

• Interval scales of measure are used to express numerical information on a scale with equal distance between categories, but no absolute zero. a dial gage sitting on top of a gage block, comparison of differences, etc.

• Ratio scales of measure are used to express numerical information on a scale with equal distance between categories, but with an absolute zero in the range of measurement. a tape measure, ruler, position Vs time at constant speed, etc.


Discrete (Attribute) Continuous (Variable)

Continuous

(Variable)

Discrete

(Attribute)

Outputs

Inp

uts

Chi-square Analysis of Variance

Discriminate Analysis

Logistic regression

Correlation

Multiple Regression

Selecting Statistical Techniques

• There are statistical techniques to cover all combinations of data types.

These are some of the statistical techniques that you will use to drive Process Improvement


Example

• Break back into your small groups• Brainstorm ways to transform the discrete

data you identified into continuous data• Be prepared to present your findings to the

group


Measurement Systems Evaluation


Variable Gage R&R

• The ideal measurement system will produce “true” measurements every time it is used (Zero Bias, Zero Variance).

• The study of measurement systems will provide information as to the % of variation in your process data which comes from error in the measurement.

• It is also a great tool for comparing two or more measurement devices or two or more operators against one another.

• MSA should be used as part of the criteria required to accept and release a new piece of measurement equipment to manufacturing.

• It should be the basis for evaluating a measurement system which is suspect of being deficient.


Long-term

Process Variation

Short-term

Process Variation

Variation

w/in sample

Actual Process Variation

Repeatability Calibration Stability Linearity

Variation due

to instrument

Variation due

to operators

Measurement Variation

Observed Process Variation

To address actual process variability, the variation due to the measurement system must first be

identified and separated from that of the process

To address actual process variability, the variation due to the measurement system must first be

identified and separated from that of the process

Possible Sources of Process Variation


Possible Sources of Process Variation

We will look at “repeatability” and “reproducibility” since these are the primary contributors to measurement errorWe will look at “repeatability” and “reproducibility” since these are the primary contributors to measurement error

Long-term

Process Variation

Short-term

Process Variation

Variation

w/in sample

Actual Process Variation

Stability Linearity

Variation due

Measurement Variation

Observed Process Variation

Repeatability

Variation due

to operatorsto instrument

Calibration


AveragesAverages

VariabilityVariability

222measurementproducttotal +=

total product measurement

Measurement System Bias -Determined through “Calibration Study”

Measurement System Variability - Determined through “R&R Study”

AccuracyAccuracy

PrecisionPrecision

Precision Vs. Accuracy


Basic Model

Observed variability = product variability + measurement variability

Measurement System Bias: assessed via the “calibration program”:

(accuracy)

Measurement System Variability: assessed via the “variable R&R study”:

(precision)

Observed value = master value + measurement offsetmeasurement systemproducttotal

True values

Measured values

measurement offset

2

22measurement system producttotal

True values

Measured values


'Measurement Variation'

Humidity

Cleanliness

Vibration

Line Voltage Variation

Temperature Fluctuation

Operator Technique

Standard Procedures

Sufficient Work Time

Maintenance Standard

Calibration Frequency

Operator Training

Ease of Data Entry

Algorithm Instabilty

Electrical Instability

Wear

Mechanical instability

Tool

Environment

Work Methods

Sources of Measurement Variation


Knowledge to be obtained

• How big is the measurement error?• What are the sources of measurement error?• Is the tool stable over time?• Is the tool capable for this study?• How do we improve the measurement

system?


Product Variability

(Actual variability)

Product Variability

(Actual variability)

MeasurementVariability

MeasurementVariability

Total Variability(Observed variability)

Total Variability(Observed variability)

2

22Measurement systemproducttotal +=

2 2 2 2total product repeatability reproducibility= + +

Sources of Variation


Terminology

• Accuracy related terms True value Bias

• Precision related terms Repeatability Reproducibility

• Linearity• Discrimination• Stability (over time)• Correlation


Accuracy

• Accuracy - Extent to which the average of the measurements deviate from the true value True value

Theoretically correct valueNIST standards

BiasDistance between average value of all measurements

and true valueAmount tool is consistently off targetSystematic error or offset


Master Value(Reference Standard)

AverageValue

Accuracy

• Accuracy: The difference between the observed average value of measurements and the master value. The master value is an accepted, traceable reference standard (e.g., NIST).

Measurement systemproducttotal +=


Instrument 2Instrument 1


AverageValue

Accuracy

• Bias: average of measurements are different by a fixed amount, effects include: Operator bias - different operators get detectably different

averages for the same measurements on the same part Machine bias - different machines get detectably different

averages for the same measurements on the same parts


Precision

• Total variation in the measurement system• Measure of natural variation of repeated

measurements• Terms: Random error, spread, test / retest

error• Repeatability and Reproducibility

2 2 2 2total product repeatability reproducibility


Precision

• Repeatability: The inherent variability of the measurement device• Variation that occurs when repeated measurements are made of the

same variable under similar conditions Same part Same operator Same set-up Same units Same environmental conditions Short-term

• Estimated by the pooled (average) standard deviation of the distribution of repeated measurements

• Repeatability is usually less than the total variation of the measurement system



Master Value

Good Repeatability Poor Repeatability


Precision

• Repeatability: the variation between successive measurements of the same part, same characteristic, by the same person using the same instrument. Also known as test - retest error; used as an estimate of short-term measurement variation.



Precision

• Reproducibility: The variation that results when different conditions are used to make the same measurements Different operators Different set-ups Different test units Different environmental conditions Long-term measurement variation

• Estimated by the standard deviation of the averages of measurements from different measurement conditions


Inspector A

Master Value

Inspector B

Inspector C

Inspector A

Inspector B

Inspector C

Precision

• Reproducibility: The difference in the average of the measurements made by different persons using the same or different instrument when measuring the identical characteristic on the same part


Example: Accuracy Vs. Precision

• Suppose we have a reference material with a ‘true’ hardness of 5.0.

• Method 1 gives the following readings:3.8, 4.4, 4.2, 4.0

• Method 2 gives the following readings:6.5, 4.0, 3.2, 6.3

• Which method is more accurate?• Which method is more precise?• Which method do you prefer? Why?• Report out by groups (flip charts)


O

Accuracy

Gage 1: Linearity is an issue here

Measurement Units

Accuracy

Gage 2: Linearity is NOT an issue here

Measurement Units

Linearity

• Linearity: A measure of the difference in Accuracy or Precision over the range of instrument capability.

O

Y axis is deviation from master reading. When gage agrees with master, plotted point will be on 0. X axis is full range of product values that gage is to be used over.


1 2 3 4 5

Good Discrimination

1 2 3 4 5

Poor Discrimination

Discrimination

• The number of decimal places that can be measured by the system. Increments of measure should be at least one-tenth of the width of the product specification or process variation.


Stability

• The distribution of measurements remains constant and predictable over time for both mean and standard deviation

• No drifts, sudden shifts, cycles, etc...• Evaluated using a trend chart• Ensured through a regular calibration and

R&R program



Time 2

Time 1

Stability

• Evaluation of the difference in accuracy or precision over time.


Method 1

Correlation Example:

OffsetMeth

od

2


No Offset

Method 1

Meth

od

2


No Correlation

Method 1

Meth

od

2

Correlation

• A measure of linear association between two variables, e.g. two different measurement methods or two different laboratories.


• Measurement System Variance: Primary output of analytical Gage R&R To determine whether the measurement system is “good”

or “bad” for a certain application, you need to compare the measurement variation to the product/process variation

• Comparing with Tolerance: Precision-to-Tolerance Ratio (P/T)

• Comparing with Product/Process Variation (P/TV): % Repeatability and Reproducibility (%R&R) Signal-to-Noise Ratio (S/N) Discrimination Index

MS

MS

222rpdrptMS

Measurement System Metrics


P/T and P/TV

“P to TV” is used to qualify a measurement system as capable of measuring to the total observed process variation:

“P to T” is used to qualify a measurement system as capable of measuring to a given product specification:

2 2 2 2total product repeatability reproducibility= + +

2 *15.5 Measurement system (MS)=SystemMeasurement of Precision

True values

Measured values

Note: 99% of the curve will be

within 5.15 ’s.

total

MS

total

MSTVP

*15.5

*15.5

*15.5

*15.5/

2

2

==

LSLUSLLSLUSLTP MSMS

-=

-=

*15.5*15.5/

2

LSL USL

Question: When will P/TV and P/T be the same?


• Precision to Tolerance Ratio

• Addresses what percent of the Tolerance is taken up by measurement error.

• Best case: < 10% Acceptable: < 30%• Includes both repeatability and reproducibility

P TTolerance

MS/. *

=515

Tolerance = USL - LSL

Measurement Capability Index


• %R&R

• Addresses what percent of the Total Variation is taken up by measurement error.

• Best case: <10% Acceptable: <30% If the R&R is less than 30% of the total sigma, the effect

is less than five percent If less than 10% of the total sigma, the effect is less than

1%• Includes both repeatability and reproducibility

Usually expressed as percent

Usually expressed as percent% &R R MS

Total

= ´ 100

Measurement Capability Index


Uses of P/T and P/TV (%R&R)

• The P/T ratio is the most common estimate of measurement system precision. This estimate may be appropriate for evaluating how well the

measurement system can perform with respect to the spec. Specifications, however, may be too tight or too loose. Generally, the P/T ratio is a good estimate when the

measurement system is only used to classify production samples. Even then, if process capability (Cpk) is not adequate, the P/T ratio may give you a false sense of security.

The P/TV (%R&R) is the best measure for the Black Belt/Green Belt.

This estimates how well the measurement system performs with respect to the overall process variation.

%R&R is the best estimate when performing process improvement studies. Care must be taken to use samples representing full process range.


The Method - Calculating %R&R

Step 1: Collect 10 samples that represent the full range of long-term process variation. In addition, identify the operators who use this instrument daily.

Step 2: Calibrate the gage or verify the last calibration date is valid.Step 3: Setup the Minitab data collection sheet for the R&R study.

Column headings: Part ID, Operator, Trial, Measurement(s)Calc > Make Patterned Data > Simple Set of Numbers (for each input)

Step 4: Ask the first operator to measure all the samples once in random order. Blind sampling, in which the operator does not know the identity of each part should be used to reduce human bias.

Step 5: Have the second operator measure all the samples once in random order and continue until all operators have measured the samples once (this is trial 1).

Step 6: Repeat steps 4 & 5 for the required number of trials.Step 7: Enter the data and tolerance information into Minitab.

Stat > Quality Tools > Gage R&R StudyStat > Quality Tools > Gage Run Chart

Step 8: Analyze the results by assessing the quality of the measurement system based on the guidelines on the following page. Determine follow-up actions.


The Daimler-Chrysler Corporation, Ford Motor Corporation and General Motor Corporation guidelines for acceptable gage variation (based on standard deviation) as compared to total variation are given as a percent of Tolerance (% Tolerance). They are:

• Ideal 10% or less• Acceptable 10-20%• Marginal 20-30% (depends on the application)

To arrive at % Gage R&R as a percent of Tolerance, MINITAB’s ANOVA method:1. Calculates the variance component of the Gage R&R term2. Takes the square root of the variance component to get the estimated standard

deviation for the Gage R&R term.3. Multiplies 5.15 times stddev and divides by the tolerance.MiniTab presents this value at the top of an output column in the session window titled: % Tolerance.A drawback to this method of calculating percentages is that the percentages in these columns will never sum to 100%. In order to look at the true percent of variation each term is contributing to the overall variation estimate, it may be easier to look at the column titled % Contribution.

Gage R&R Study - What is Acceptable?

Copyright Minitab Inc. 1998. All rights reserved. Rel 12 (Ver 1: Rev 1)


When the calculations for variation are based upon variance components, it is assumed you are comparing the variation due to the measuring system to the overall variation in the study. Because variance components are ()2, the values on page 37 (10, 20, and 30 percent) would also have to be squared (.12, .22, .32). So when you look at this column consider the rules below instead:

• Ideal 1% or less

• Acceptable 1-4%

• Marginal 4-9% (depends on the application)

While variance components are not the units used in the measurement systems reference manual, the advantage to using variance components is that the percentages will sum to 100%. The disadvantage is that you cannot compare these values to tolerance.

Gage R&R Study - What is Acceptable?

Copyright Minitab Inc. 1998. All rights reserved. Rel 12 (Ver 1: Rev 1) Minitab 12 TrainingMeasurement System Analysis


Handling Poor Gage Capability:

• If a dominant source of variation is repeatability (equipment), you need to replace, repair, or otherwise adjust the equipment.

• If, in consultation with the equipment vendor or upon searches of industry literature, you find that the gage technology that you are using is “state-of-the-art” and it is performing to its specifications, you should still fix the gage. One temporary solution to this problem is to use signal averaging (see next page).

• If a dominant source of variation is operator (reproducibility), you must address this via training and definition of the standard operating procedure. You should look for differences between operators to give you some indication as to whether it is a training, skill, and/or procedure problem.

• Evaluate the specifications. Are they reasonable?• If the gage capability is marginal (as high as 30% of study variation)

and the process is operating at a high capability (Ppk greater than 2), then the gage is probably not hindering you and you can continue to use it.


• Note: If you want to decrease your gage error take advantage of the standard error square root of the sample.

• The signal averaging technique uses:

n

1

• n = the number of repeat measures taken on the same part

• the measurement = the average of “n” readings

• Example: a gage error of 50% can be cut in half if your point estimate is an average of 4 repeat measurements

2/14

1 • This technique should be used as a short term approach to

perform a study, but you must fix the gage.

xxxx

x xx

Distributionof Means

xxxxx

xxx

xx

x

Distributionof Individuals

Controlling Repeatability:


Measurement System Evaluation Questions

• Written inspection / measurement procedure?• Detailed process map developed?• Specific measuring system and set-up defined?• Trained or Certified Operators?• Instrument calibration performed in a timely manner?• Tracking Accuracy?• Tracking %R&R?• Tracking Bias?• Tracking Linearity?• Tracking Discrimination?• Correlation with supplier or customer where appropriate?


Measurement System Analysis Questions

• Have you picked the right measurement system? Is this measurement system associated with either critical inputs or outputs?

• What do the precision, accuracy, tolerance, P/T ratio, %R&R and trend chart look like?

• What are the sources of variation and what is the measurement error?

• What needs to be done to improve this system?• Have we informed the right people of our results?• Who owns this measurement system?• Who owns trouble shooting?• Does this system have a control plan in place?• What’s the calibration frequency? Is that frequent enough?• Do identical systems match?


Exercise!

• Break up into your catapult teams

• Using the provided data sheet, perform a Measurement system analysis on determining the length of throwing a catapult projectile

• Enter the data into either Minitab or Measurement Assurance software to get a final GR&R


Attribute Terminology

• Attribute Data: Qualitative (go / no go) data that can be tallied for recording and analysis.

• Attribute Measurement System: A measurement system that compares each part to a standard and accepts the part if this standard is met.

• Screen: 100% evaluation of product using inspection techniques (an attribute measurement system).

• Screen Effectiveness: The ability of the attribute measurement system to properly discriminate good from bad.

• Customer Bias: Operator has a tendency to hold back good product.

• Producer Bias: Operator has a tendency to pass defective product.


Purpose of Attribute R&R

• To assess your inspection or workmanship standards against your customer’s requirements

• To determine if inspectors across all shifts, all machines, etc… use the same criteria to determine “good” from “bad”

• To quantify the ability of inspectors to accurately repeat their inspection decisions

• To identify how well these inspectors are conforming to a “known master” which includes: how often operators decide to ship truly defective product how often operators do not ship truly acceptable product

• Discover areas where: training is needed procedures are lacking standards are not defined


Attribute R&R -- The Method

Step 1 - Select a minimum of 30 parts from the process.– 50% of the parts in your study should have defects– 50% of the parts should be defect free– If possible select border line (or marginal) good and bad samples

Step 2 - Identify the Inspectors who should be qualified.Step 3 - Have each inspector, independently and in random order, assess

these parts and determine whether or not they pass or fail.Step 4 - Enter the data into the Inspection.xls spreadsheet to report the

effectiveness of the attribute measurement system. Step 5 - Document the results. Implement appropriate actions to fix the

inspection process if necessary.Step 6 - Re-run the study to verify the fix.Note: A 30 piece sample will yield an estimate of inspector efficiency and

capability which has a fair amount of uncertainty. Typically a larger sample is not needed because the inspection process is obviously ineffective. The spreadsheet can handle up to 100 samples.


% APPRAISER SCORE (1) -> 100.00% 78.57% 100.00%

% SCORE VS. ATTRIBUTE (2) -> 78.57% 64.29% 71.43%

SCREEN % EFFECTIVE SCORE (3) -> 57.14%

SCREEN % EFFECTIVE SCORE vs. ATTRIBUTE (4) -> 42.86%

SCORING REPORTDATE: 3/10/96

Attribute Legend5 (used in computations) NAME: Allied Employee1 pass PRODUCT: 3313 Spark Plug All operators

2 fail BUSINESS: F&SP agree within and All Operators

between each agree with

Other standard

Known Population Y/N Y/NSample # Attribute Try #1 Try #2 Try #1 Try #2 Try #1 Try #2 Agree Agree

1 pass pass pass pass pass fail fail N N2 pass pass pass pass pass fail fail N N3 fail fail fail fail pass fail fail N N4 fail fail fail fail fail fail fail Y Y5 fail fail fail pass fail fail fail N N6 pass pass pass pass pass pass pass Y Y7 pass fail fail fail fail fail fail Y N8 pass pass pass pass pass pass pass Y Y9 fail pass pass pass pass pass pass Y N

10 fail pass pass fail fail fail fail N N11 pass pass pass pass pass pass pass Y Y12 pass pass pass pass pass pass pass Y Y13 fail fail fail fail fail fail fail Y Y14 fail fail fail pass fail fail fail N N

Operator #1 Operator #2 Operator #3

Example:


% APPRAISER SCORE(1) -> 100.00% 78.57% 100.00%

% SCORE VS. ATTRIBUTE(2) -> 78.57% 64.29% 71.43%

SCREEN % EFFECTIVE SCORE(3) -> 57.14%

SCREEN % EFFECTIVE SCORE vs. ATTRIBUTE (4) -> 42.86%

Example:

(1) If % Appraiser Score is less than 100% training needs to occur, focus on specific areas

(2) % Score Vs. Attribute is an error against a known population as deemed by experts

(3) 100% is the target for Screen % Effectiveness Score(4) Screen % Effective Vs. Attribute is an error against a

known population as deemed by the experts. 100% is the target

(5) Attribute legend allows excel to use a macro to count the number of occurrences of the legend text


Capability AnalysisFor

Continuous Data


The Need for Capability

• Can appropriately quantify the nature of the problem the team will attack as one of the following: For quantitative data (variable output, Y):

Are the specifications correct for the parameter (Y) of interest (process or performance output variable)?

Is the location of the central tendency of the parameter (Y) centered within the appropriate specifications?

Is the process variation in the parameter greater than allowed by the specifications?

For discrete qualitative events (attribute output,Y): Is the measurement system effecting our ability to assess true

process capability? What is the allowable, internal and external, escaping defect

rate?• Assessing capability allows the organization to predict its true quality

levels for all its goods and services• This guides us to the initial estimate of a product or process sigma level


Process Performance Metrics

CONTINUOUS

DATA

SHORT-

TERMCP CPK

PP PPK

DPO

DPU

PPM

YRT

DPMO

TYPE OF DATA HISTORY

OF DATA

TYPE OF METRIC

ONE

UNIVERSAL

METRIC

DISCRETE

DATA

LONG-

TERM

LONG-

TERM

DATA

Sigma

Scale


Continuous MeasuresProcess Capability

Target UpperSpecLimit

LowerSpecLimit

If the product is producedinside the spec limits

it’s OK

Actual variation fromfrom the process

Process Capability compares the actual variation to the requirements for variable data


Process Capability

Target UpperSpecLimit

LowerSpecLimit

Process Capability = Limits

Actual Variation


Situations

TargetUpperSpecLimit

LowerSpecLimit

Off Target& Capable


LowerSpecLimit

On Target& Capable


LowerSpecLimit

On Target& Not Capable


LowerSpecLimit

Off Target& Not Capable


Classic Process Capability

• To fully understand the capability of a product/process we need measure on/off target, the spread in both the short and long term

Capabilitypotential

Off Target

Short Term Long Term

Cp

PpkCpk

Pp


Short Term (Potential) Process Capability Cp

LowerSpec

UpperSpecTarget

Mean

Out ofSpecification

Out ofSpecification

Measures how well theactual variation

fits the specification

To calculate Cp we see how well the process variation

fits the specification Actual processvariation with mean and

standard deviation


LowerSpec

UpperSpecTarget

Mean USL - LSL

6st

Cp =

USL = Upper Spec LimitLSL = Lower Spec Limitst = Short term Process standard deviation

This tells us howgood the process

could be

Short Term (Potential) Process Capability Cp


If Cp = Cpk QUESTION

Sigma Level = 3Cp

Target USLLSL

Cp = 1 Sigma level = 3

33

Target USLLSL

66Cp = 2 Sigma level = 6

Cp = 1.33 Sigma level = 4

Target USLLSL

44


Example

1.60 1.90Target

S Dev = 0.08

Cp =?


Example

1.60 1.90Target

S Dev = 0.08

Cp =?

USL-LSL6st


Example

1.60 1.90Target

S Dev = 0.08

Cp =?

1.9-1.66* 0.08

=0.625


Short Term (Actual) Process Capability

LowerSpec

UpperSpecTarget

Mean

Out ofSpecification

USL -

- LSL

3st

3st

Process Capability Cpk

Cpk= Min of

This tells us in the short-term how well the process

is centred


Long Term (Overall) Process Capability

LowerSpec

UpperSpecTarget

Mean

Out ofSpecification

Out ofSpecification

USL - LSL

6lt

Process Capability Pp

Pp =

USL = Upper Spec LimitLSL = Lower Spec Limitlt = Long term Process standard deviation

This tells us in the long-term how good the process could be


Long Term (Overall) Process Capability

LowerSpec

UpperSpecTarget

Mean

Out ofSpecification

Process Capability Ppk

USL -

- LSL

3lt

3lt

Ppk= Min of

This tells us what the CUSTOMER

experiences in the long - term

Zlt = 3Ppk

For six sigma

Zlt = 4.5 = 3Ppk

Ppk = 1.5


Summary: Variable Data PerformanceP

roce

ss R

espo

nse

Time

Short-Term Measure Cp/Cpk

Long-Term Measure Pp/Ppk

What the Customer

SeesCustomer target


Short and Long Term Capability

LSL USLT LSL USLT

SHORT TERM LONG TERM

B

C

D

Cp

A

CpkPp Ppk

2.0 2.0

2.0

2.0 2.0

1.5 2.0 1.5

2.0 varies 1.0 1.0

2.0 varies 1.0 0.5


Process Width

Design Width

LSL

T

- 3

Short -Term Capability Indices

termshortp

LSLUSLC

*6

termshortUSLpk

XUSLC

*3

)()(

termshortLSLpk

LSLXC

*3

)()(

) , ( min )()( LSLpkUSLpkpk CCC

USL

+ 3

Long -Term Capability Indices

termlong

USLpk XUSL

P

*3

)()(

termlongp

LSLUSLP

*6

termlongLSLpk

LSLXP

*3

)()(

) , ( min )()( LSLpkUSLpkpk PPP

Cp, Cpk, Pp, Ppk Formulas


The Method – Collecting Capability Data (Short Term Capability)

Step 1: Ensure the gauge produces a good R&R % StudyStep 2: Ensure the machine is in a stable condition, by

measuring the first parts off following complete tool change

Step 3: when you are confident on stability measure the next 50 consecutive parts on the required dimension

Step 4: Collect data on checklist and observe/record any special cause interference. If interference causes a shift in measured values, stop exercise and start over again when the cause has been rectified.

Step 5: Take data to gauge room / Black belt for statistical analysis of normality and capability.


Capability - Caution !

94.0894.0794.0694.0594.0494.03

USLLSL

Process Capability Analysis for Diameter of

PPM Total

PPM > USL

PPM < LSL

PPM Total

PPM > USL

PPM < LSL

PPM Total

PPM > USL

PPM < LSL

Ppk

PPL

PPU

Pp

Cpm

Cpk

CPL

CPU

Cp

StDev (Overall)

StDev (Within)

Sample N

Mean

LSL

Target

USL

2221.83

2061.99

159.84

199.72

195.40

4.31

0.00

0.00

0.00

0.96

1.20

0.96

1.08

*

1.18

1.48

1.18

1.33

0.0071127

0.0057534

70

94.0556

94.0300

*

94.0760

Exp. "Overall" PerformanceExp. "Within" PerformanceObserved PerformanceOverall Capability

Potential (Within) Capability

Process Data

Within

Overall


Six Sigma Capability

3 - Sigma

6 - Sigma

And/Or


Capability AnalysisFor

Discrete Data


Six Sigma PerformanceDiscrete Data

• With discrete data often there are no upper and lower specification limits!

• We are often dealing with defects (pass/fail), proportion defective, yields etc

• In such cases 6-Sigma performance is concerned with Defect Per Unit (DPU) Defect Per Opportunity (DPO) Defects Per Million Opportunities (DPMO) First Pass or Final Yield (YFT)

Rolled throughput Yield (YRT)

Sigma Level


Defects Per Unit (DPU)

Defects Per Unit (DPU) = Number of observed defects

Number of Units

A defect is any variation of a required characteristic whichis far enough removed from its target so as to cause

customer dissatisfaction

A unit can be:

•A component•A sub-assembly•A piece of paperwork•A line of software•A purchase order•etc


DPU and Complexity

• DPU is a powerful measure but it does not take into account the complexity of the unit:

• For example a manual soldering process is known to create 2 defects per every 100 joints (each component requires 2 joints) A PCB with 100 components would have a DPU of 4 A PCB with 1000 components would have a DPU of 40

• The complexity issue can be overcome by considering the part count. In some situations this is acceptable, but what about a piece of paperwork, the complexity does not depend on part count

• To include complexity the idea of a defect opportunity can be used


Defects Per Million Opportunities (DPMO)

• They key measure in Six Sigma is the idea of Defects Per Million Opportunities (DPMO)

• Its power lies in that it is universal benchmark• We count Defect opportunities: any measurable

chance a defect could occur

DPMO = defects per unit x 1,000,000

Number of opportunities

for error in one unit

• DPMO is related to sigma level


Components of DPMO

• Opportunity - anything we can measure or test Active: An opportunity for a defect which is actively

tested or checked Passive: An opportunity that may exist, but is not

actively being looked for or tested

• Defect - any non-conformance Active: one that was previously identified Passive: One that has not been found yet and

may never be found

• Unit - the number units (part, systems components etc)


Calculating DPMO

• Count the observed level of defects. (Occasions when customer requirements are not met.)

• Determine the number of opportunities for defects to occur within the process. The defect opportunity must be important to the

stakeholder / customer. Don’t artificially hike the number of opportunities

When calculating DPMO after improvement actions, use the same number of opportunities as before the changes.

• From the two figures calculate the DPMO (number of defects per million defect opportunities).

• When calculating DPMO we should have at least 5 defects


DPMO to Sigma

• From the Six Sigma “theory” based on the Normal distribution we know that in the long term a process with a Sigma Level of 6 will produce 3.4 defects in every million

• We can use this to have a consistent measure for discrete data situations through the idea of DPMO

• Six Sigma performance = 3.4 DPMO• Tables exist to convert DPMO into sigma levels


DPMO to Sigma Level Table

• The DPMO table assumes long term data are used to estimate the yield By definition we use short-term sigma level is used for

making comparisons

Sigma level

hundredths

tenths 0.00 0.01 0.02 0.03 0.04 0.05 1.5 500,000 496,000 492,000 488,000 484,000 480,100 1.6 460,200 456,200 452,200 448,300 444,300 440,400 1.7 420,700 416,800 412,900 409,000 405,200 401,300 1.8 382,100 378,300 374,500 370,700 366,900 363,200 1.9 344,600 340,900 337,200 333,600 330,000 326,400 2.0 308,500 305,000 301,500 298,100 294,600 291,200 2.1 274,300 270,900 267,800 264,300 261,100 257,800

Sigmalevel

DPMO


Calculating Process Sigma

• Number of units processed N = __________• Total number of defects made

(include defects made and later fixed) D = __________• Number of defect opportunities

per unit m = __________• Calculate # defects per million

opportunities DPMO = 1,000,000 x (

= 1,000,000 x

= __________• Look up process sigma in sigma conversion table Sigma = __________

200

57

1

DN x m

)

( )

( ) ( )

57200 1

285,000

2.05


When starting a 6-Sigma project we need to know

where we are!!! We use the above to BASELINE

the process

6 3.4

5 233

4 6,210

3 66,807

2 308,537

99.9997

99.977

99.379

93.32

69.20

2.0

1.667

1.333

1.0

0.67

1.5

1.167

0.833

0.5

0.17

Process performance is measured by any of the below

(Defects Per Million

Opportunities)Yield %Yield % (Short term

Process Capability)

CCpp(Z) (Long termProcess

Capability)PPpkpkDPMODPMO

1 © Visteon Corporation GB-Mod #8 Rev 3.6 10/03 Measure Phase GB Mod #8.

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