Download - NG BB 25 Measurement System Analysis - Attribute

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National GuardBlack Belt Training

Module 25

Measurement System Analysis (MSA)

Attribute Data

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CPI Roadmap – Measure

Note: Activities and tools vary by project. Lists provided here are not necessarily all-inclusive.

TOOLS

•Process Mapping

•Process Cycle Efficiency/TOC

•Little’s Law

•Operational Definitions

•Data Collection Plan

•Statistical Sampling

•Measurement System Analysis

•TPM

•Generic Pull

•Setup Reduction

•Control Charts

•Histograms

•Constraint Identification

•Process Capability

ACTIVITIES• Map Current Process / Go & See

• Identify Key Input, Process, Output Metrics

• Develop Operational Definitions

• Develop Data Collection Plan

• Validate Measurement System

• Collect Baseline Data

• Identify Performance Gaps

• Estimate Financial/Operational Benefits

• Determine Process Stability/Capability

• Complete Measure Tollgate

1.Validate the

Problem

4. Determine Root

Cause

3. Set Improvement

Targets

5. Develop Counter-

Measures

6. See Counter-MeasuresThrough

2. IdentifyPerformance

Gaps

7. Confirm Results

& Process

8. StandardizeSuccessfulProcesses

Define Measure Analyze ControlImprove

8-STEP PROCESS

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3Measurement System Analysis - Attribute

Learning Objective

Understand how to conduct and interpret a measurement system analysis with Attribute Data

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Attribute Measurement Systems

Most physical measurement systems use measurement devices that provide continuous data

For continuous data Measurement System Analysis we can use control charts or Gage R&R methods

Attribute/ordinal measurement systems utilize accept/reject criteria or ratings (such as 1 - 5) to determine if an acceptable level of quality has been attained

Kappa and Kendall techniques can be used to evaluate these Attribute and Ordinal Measurement Systems

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Are You Really Stuck With Attribute Data?

Many inspection or checking processes have the ability to collect continuous data, but decide to use attribute data to simplify the task for the person taking and recording the data

Examples:

On-time Delivery can be recorded in 2 ways:

a) in hours late or

b) whether the delivery was on-time or late

Many functional tests will evaluate a product on a continuous scale (temperature, pressure drop, voltage drop, dimensional, hardness, etc) and record the results as pass/fail

Strive to get continuous data!

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Attribute and Ordinal Measurements

Attribute and Ordinal measurements often rely on subjective classifications or ratings

Examples include:

Rating different features of a service as either good or bad, or on a scale from 1 to 5 with 5 being best

Rating different aspects of employee performance as excellent, satisfactory, needs improvement

Rating wine on a) aroma, b) taste, and c) after taste

Should we evaluate these measurement systems before using them to make decisions on our CPI project?

What are the consequences of not evaluating them?

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MSA – Attribute Data

What methodologies are appropriate to assess Attribute Measurement Systems?

Attribute Systems – Kappa technique which treat all misclassifications equally

Ordinal Systems – Kendall‟s technique which considers the rank of the misclassification

For example, if we are judging an advertising service on a scale from 1 to 5 and Inspector A rates the service a „1‟ while Inspector B rates it a „5.‟ That is a greater misclassification than Inspector A rating it a „4‟ while Inspector B rates it a „5.‟

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Data Scales Nominal: Contains numbers that have no basis on which to arrange

in any order or to make any assumptions about the quantitative difference between them. These numbers are just names or labels. For example:

In an organization: Dept. 1 (Accounting), Dept. 2 (Customer Service), Dept. 3 ( Human Resources)

In an insurance co.: Business Line 1, Line 2, Line 3

Modes of transport: Mode 1 (air), Mode 2 (truck), Mode 3 (sea)

Ordinal: Contains numbers that can be ranked in some natural sequence. This scale, however, cannot make an inference about the degree of difference between the numbers. Examples:

On service performance: excellent, very good, good, fair, poor

Salsa taste test: mild, hot, very hot, makes me suffer

Customer survey: strongly agree, agree, disagree, strongly disagree

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Kappa Techniques

Kappa is appropriate for non-quantitative systems such as:

Good or bad

Go/No Go

Differentiating noises (hiss, clank, thump)

Pass/fail

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Kappa Techniques

Kappa for Attribute Data:

Treats all misclassifications equally

Does not assume that the ratings are equally distributed across the possible range

Requires that the units be independent and that the persons doing the judging or rating make their classifications independently

Requires that the assessment categories be mutually exclusive

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Operational Definitions

There are some quality characteristics that are either difficult or very time consuming to define

To assess classification consistency, several units must be classified by more than one rater or judge

If there is substantial agreement among the raters, there is the possibility, although no guarantee, that the ratings are accurate

If there is poor agreement among the raters, the usefulness of the rating is very limited

Poor attribute measurement systems can almost always be traced to poor operational definitions

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Consequences?

What are the important concerns?

What are the risks if agreement within and between raters is not good?

Are bad items escaping to the next operation in the process or to the external customer?

Are good items being reprocessed unnecessarily?

What is the standard for assessment?

How is agreement measured?

What is the Operational Definition for assessment?

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What Is Kappa? “K”

P observed

Proportion of units on which both Judges agree = proportion both Judges agree are good + proportion both Judges agree are bad

P chance (expected)

Proportion of agreements expected by chance = (proportion Judge A says good * proportion Judge B says good) + (proportion Judge A says bad * proportion B says bad)

Note: equation applies to a two category analysis, e.g., good or bad

chance

chanceobserved

P

PPK

1

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Kappa

For perfect agreement, P observed = 1 and K=1

As a rule of thumb, if Kappa is lower than 0.7, the measurement system is not adequate

If Kappa is 0.9 or above, the measurement system is considered excellent

The lower limit for Kappa can range from 0 to -1

For P observed = P chance (expected), then K=0

Therefore, a Kappa of 0 indicates that the agreement is the same as would be expected by random chance

chance

chanceobserved

P

PPK

1

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Attribute MSA Guidelines

When selecting items for the study consider the following:

If you only have two categories, good and bad, you should have a minimum of 20 good and 20 bad

As a maximum, have 50 good and 50 bad

Try to keep approximately 50% good and 50% bad

Have a variety of degrees of good and bad

If only good items are chosen for the study, what might happen to P-chance (expected)?

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Attribute MSA Guidelines (Cont.)

If you have more than two categories, with one of the categories being good and the other categories being different error modes, you should have approximately 50% of the items being good and a minimum of 10% of the items in each of the error modes

You might combine some of the error modes as “other”

The categories should be mutually exclusive or, if not, they should also be combined

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Within Rater/Repeatability Considerations

Have each rater evaluate the same item at least twice

Calculate a Kappa for each rater by creating separate Kappa tables, one for each rater

If a Kappa measurement for a particular rater is small, that rater does not repeat well within self

If the rater does not repeat well within self, then they will not repeat well with the other raters and this will hide how good or bad the others repeat between themselves

Calculate a between-rater Kappa by creating a Kappa table from the first judgment of each rater

Between-rater Kappa will be made as pairwise comparisons (A to B, B to C, A to C)

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Example: Data Set = Attribute Ordinal.mtw

An educational testing organization is training five new appraisers for the written portion of the twelfth-grade standardized essay test

The appraisers‟ ability to rate essays consistent with the standards needs to be assessed

Each appraiser rated fifteen essays on a five-point scale (-2, -1, 0, 1, 2)

The organization also rated the essays and supplied the “official score”

Each essay was rated twice and the data captured in the file Attribute Ordinal.mtw

Open the file and evaluate the appraisers' performance

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Minitab and Attribute Measurement Systems

Stat>Quality Tools>Attribute Agreement Analysis

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Minitab Dialog Box

1. Double click on theappropriate variable to place it in the required dialog box:

Attribute = Rating

Samples = SampleAppraisers = Appraiser

2. Click on OK

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Within Appraiser Percent

This output represents the percent agreement and the 95% confidence interval around that percentage

Appraiser

Pe

rce

nt

SimpsonMontgomeryHolmesHayesDuncan

100

80

60

40

20

0

95.0% C I

Percent

Date of study:

Reported by:

Name of product:

Misc:

Assessment Agreement

Within Appraisers

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Within Appraiser Session Window Output

This output is the same information contained in the graph with the addition of a Between-Appraiser assessment

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Let’s Do It Again


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Introducing a Known Standard

If you have a known standard (the real answer)for the items being inspected,let Minitab know what column that information is in.

1. Double click on theappropriate variable to place it in the required dialog box

3. Click on OK

2.

(same as before)

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Appraiser vs. Standard

Appraiser

Pe

rce

nt

Simps

on

Mon

tgom

ery

Holmes

Hayes

Dunc

an

100

90

80

70

60

50

40

30

95.0% C I

Percent

Appraiser

Pe

rce

nt

Simps

on

Mon

tgom

ery

Holmes

Hayes

Dunc

an

100

90

80

70

60

50

40

30

95.0% C I

Percent

Date of study:

Reported by:

Name of product:

Misc:

Assessment Agreement

Within Appraisers Appraiser vs Standard

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Within Appraiser

In addition to the Within-Appraiser graphic, Minitab will give percentages

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Each Appraiser vs. Standard

Some appraisers will repeat their own ratings well but may not match the standard well (look at Duncan)

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More Session Window Output

The session window will give percentage data as to how all the appraisers did when judged against the standard

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Kappa and Minitab

Minitab will calculate a Kappa for each (within) appraiser for each category

Note: This is only a part of the total data set for illustration

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Kappa vs. Standard

Minitab will also calculate a Kappa statistic for eachappraiser as compared to the standard

Note: This is only a part of the total data set for illustration

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Kappa and Minitab

Minitab will not provide a Kappa between a specific pair of appraisers, but will provide an overall Kappa between all appraisers for each possible category of response

How might this output help us improve our measurement system?

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What If My Data Is Ordinal?


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Ordinal Data

If your data is Ordinal, you must also check this box

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What Is Kendall’s

Kendall‟s coefficient can be thought of as an R-squared value, it is the correlation between the responses treating the data as attribute as compared to ordinal.

The lower the number gets, the more severe the misclassifications were.

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Kendall’s

Kendall‟s coefficient can be thought of as an R-squared value, it is the correlation between the responses treating the data as attribute as

compared to ordinal. The lower the number gets, the more severe the misclassifications were.

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Kendall’s (Cont.)

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Exercise: Seeing Stars

Divide into teams of two

One person will be the rater and one the recorder

Have each rater inspect each start and determine if it is Good or Bad (Kappa)

Record the results in Minitab

Mix up the stars and repeat with same rater 2 more times

Compare results to other raters and to the known standard

Take 30 minutes to complete the exercise and be prepared to review your findings with the class

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Takeaways

How to set-up/conduct an MSA

Use attribute data only if the measurement can not be converted to continuous data

Operational definitions are extremely important

Attribute measurement systems require a great deal of maintenance

Kappa is an easy method to test how repeatable and reproducible a subjective measurement system is

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What other comments or questions

do you have?

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References

Cohen, J., “A Coefficient of Agreement for Nominal Scales,” Educational and Psychological Measurement, Vol. 20, pp. 37-46, 1960

Futrell, D., “When Quality Is a Matter of Taste, Use Reliability Indexes,” Quality Progress, May 1995

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APPENDIX – A Practical Example of Kappa

Evaluating the Measurement System for Determining Civilian Awards


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Kappa Example #1

The Chief of Staff (COS) of the 1st Infantry Division is preparing for the redeployment of 3 brigade combat teams supporting Operation Iraqi Freedom.

The Secretary of General Staff (SGS) informs the COS that awards for civilian personnel (Department of the Army Civilians and military dependents) who provided volunteer support prior to and during the deployment is always a “significant emotional issue.” There are hundreds of submissions for awards.

A board of senior Army personnel decides who receives an award. The measurement system the board uses to determine who receives an award is a major concern due to differences in board member to board member differences as well as within board member differences.

The COS directs the SGS (a certified Army Black Belt) to conduct a measurement system study using historical data to “level set” the board members. Kappa for each board member as well as Kappa between board members must be calculated.

The COS‟ guidance is to retrain and/or replace board members until the measurement system is not a concern.

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Consider the Following Data

• The Lean Six Sigma Pocket Toolbook, p.100-103 outlines the procedures for calculating Kappa. Kappa is MSA for attribute data.

• The SGS‟ study involves two categories for recommendations, “Award” and “No Award”.

• We select 40 candidate packets from historical data and ensure that 20 are definitely for “Award” and 20 are for “No Award”.

• Board Member 1 and 2 evaluate each candidate‟s packet. The results are shown in the tables on the following slides.

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Contingency Table for Board Member 1

Populate Each Cell with the Evaluation Data

Board Member 1 – 1st : shows the results of Board Member 1’s 1st recommendations. The 1st board member recommended an “Award” or “No Award” for each of the 40 candidates on the first review of the files.

Board Member 1 – 2nd : shows the results of Board Member 1’s 2nd recommendations. The 1st

board member recommended an “Award” or “No Award” for each of the 40 candidates on the second review of the files.

Contingency Table: Counts Board Member 1 - 1st

No Award

3

318 22

19

15 18

22

Award No Award

Award

Bo

ard

Me

mb

er

1-

2n

d

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Contingency Table: Cell 1

The first cell represents the number oftimes Board Member 1 recommended a candidate should receive an “Award” in both the first and second evaluation.

Bo

ard

Me

mb

er

1-

2n

d

Contingency Table:Counts

Board Member 1 - 1st

No Award

3

318 22

19

15 18

22

Award No Award

Award

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The second cell represents the number of times Board Member 1 recommended a candidate as “No Award” the first time and “Award” the second evaluation.



No Award

3

318 22

19

15 18

22

Award No Award

Award

Bo

ard

Me

mb

er

1-

2n

d

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The third cell represents the number of times Board Member 1 recommended “Award” on the first evaluation and “No Award” on the second evaluation.



No Award

3

318 22

19

15 18

22

Award No Award

Award

Bo

ard

Me

mb

er

1-

2n

d

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The fourth cell represents the number of times Board Member 1 recommended “No Award” on the first evaluation and “No Award” on the second evaluation.



No Award

3

318 22

19

15 18

22

Award No Award

Award

Bo

ard

Me

mb

er

1-

2n

d

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Contingency Table: Sum of Row and Columns

The numbers on the margins are the totals of the rows and columns of data. The sum in both instances is 40, the total number of candidate packets reviewed.



No Award

3

318 22

19

15 18

22

Award No Award

Award

Bo

ard

Me

mb

er

1-

2n

d

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Contingency Table – Counts & Proportions

Board Member 1 Proportions: The lower table is the data in the upper table

represented as a percentage of the total.

Represents 18/40

0.550.45 0.55

0.45

Contingency Table:Proportions No Award

Bo

ard

Me

mb

er

1-

2n

d Award 0.375 0.075

No Award 0.075 0.475

Board Member 1 - 1stAward



No Award

3

318 22

19

15 18

22

Award No Award

Award

Bo

ard

Me

mb

er

1-

2n

d

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Contingency Table – Sum of Percentages

The sum percentages from the rows and columns. The sums must equal 1.0

0.550.45 0.55

0.45

Contingency Table:Proportions No Award

Bo

ard

Me

mb

er

1-

2n

d Award 0.375 0.075

No Award 0.075 0.475


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chance

chanceobserved

P

PPK

1

The verbiage for defining Kappa will vary slightly depending on whether we are defining a Within-Rater Kappa or Between-Rater Kappa

Calculating Kappa

Pobserved

Proportion of candidates for which both Board Members agree = proportion both Board Members agree are “Award” + proportion both Board Members agree are “No Award”.

Pchance

Proportion of agreements expected by chance = (proportion Board Member 1 says “Award” * proportion Board Member 2 says “Award”)+ (proportion Board Member 1 says “No Award” * proportion Member 2 says ”No Award”)

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Pobserved is the sum of the probabilities on the diagonal:P observed =(0.375 + 0.475) = 0.850

Pchance is the probabilities for each classification multiplied and then summed:Pchance =(0.450*0.450) + (0.550*0.550) = 0.505

Then KBoard Member 1=(0.850 - 0.505)/(1 - 0.505)=0.697

Kappa for Board Member 1 is sufficiently close to 0.700 that we conclude that Board Member 1

exhibits repeatability.

Calculate Kappa for Board Member 1

0.550.45 0.55

0.45

Contingency Table:Proportions

No Award

Bo

ard

Me

mb

er

1-

2n

d Award 0.375 0.075

No Award 0.075 0.475


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K Board Member 2 = ?

Calculate Kappa for Board Member 2B

oar

dM

emb

er

2-

2n

d Award

No Award

Contingency Table:Proportion


Award No Award

Bo

ard

Mem

be

r 2

-2

nd Award

No Award



Award No Award

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Kappa Between Board Members

To calculate a Kappa for between Board Members, we will use a similar procedure.

We calculate Kappa for the first recommendations of the pair of the Board Members.

NOTE: If there is a Board Member who has poor Within-Board Member repeatability (less than 85%), there is no need to calculate a Between-Board Member rating.

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Kappa – Board Member 1 to Board Member 2

Number of times both board members agreed the candidate should receive an “Award.”(using their first evaluation)


Board Member 1 - 1stAward No Award

No Award 4 17 21

Bo

ard

Me

mb

er

2-

1st

Award 14 5 19

18 22

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Number of times Board Member 1 recommended “No Award” and Board Member 2 recommended “Award”. (using their first evaluation)

Contingency Table:Counts Board Member 1 - 1st

Award No Award

No Award 4 17 21

Bo

ard

Me

mb

er

2-

1st

Award 14 5 19

18 22

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Board Member 1 to Board Member 2 Kappa

Number of times Board Member 1 recommended “Award” and Board Member 2 recommended “No Award” (using their first measurement)



No Award 4 17 21

Bo

ard

Me

mb

er

2-

1st

Award 14 5 19

18 22

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Between Board Member Kappa

Number of times both Board Members agreed the candidate was “No Award” (using their first measurement)



No Award 4 17 21

Bo

ard

Me

mb

er

2-

1st

Award 14 5 19

18 22

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Calculate Between-Board Member Kappa:

The lower table represents the data in the top with each cell being represented as a percentage of the total.



Award No Award

No Award 4 17 21

Bo

ard

Me

mb

er

2-

1st

Award 14 5 19

0.450 0.550

18 22


Award No Award

Award 0.35 0.125 0.48

No Award 0.100 0.425 0.53

Bo

ard

Me

mb

er

2-

1st


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chance

chanceobserved

P

PPK

1

The verbiage for defining Kappa will vary slightly depending on whether we are defining a Within-Board Member Kappa or Between-Board Member Kappa

Remember How to Calculate Kappa?

Pobserved

Proportion of items on which both Board Members agree = proportion both Board Members agree “Award” + proportion both Board Members agree are “No Award”.

Pchance

Proportion of agreements expected by chance = (proportion Board Member 1 recommends “Award” * proportion Board Member 2 says “No Award”) + (proportion Board Member 1 says No Award” * proportion Board Member 2 says “No Award”)

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Pobserved is the sum of the probabilities on the diagonal:Pobserved =(0.350 + 0.425) = 0.775

Pchance is the probability for each classification multiplied and then summed:Pchance =(0.480*0.450) + (0.530*0.550) = 0.503

Then Kboard Member 1 / 2=(0.775 - 0.503)/(1 - 0.503)=0.548

The Board Members evaluate candidate packets differently too often. The SGS will retrain each Board Member before dismissing a Board Member and finding a replacement.

Calculate Kappa for Board Member 1 to Board Member 2

0.450 0.550



Award No Award

Bo

ard

Me

mb

er

2-

1st

Award 0.35 0.125 0.48

No Award 0.100 0.425 0.53

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Improvement Ideas

How might we improve this measurement system?

Additional training

Physical standards/samples

Rater certification (and periodic re-certification) process

Better operational definitions

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Kappa Conclusions

Is the current measurement system adequate?

Where would you focus your improvement efforts?

What rater would you want to conduct any training that needs to be done?

Class Challenge: After exposure to Minitab in the following slides, input the data from previous example into Minitab. As homework, perform the analysis and compare the computer output and simplicity with the manual calculations performed in the previous slides.Hint: You will need to stack columns.

Download - NG BB 25 Measurement System Analysis - Attribute

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