02training material for msa

Training Material for

MEASUREMENTSYSTEMANALYSIS

Contents :

1) INTRODUCTION FOR MEASUREMENT SYSTEM ANALYSIS

2) GENERAL METHODS ILLUSTRATION FOR MEASUREMENT SYSTEM ANALYSIS1) VARIABLE GAGE ANALYSIS METHOD 1) THE AVERAGE-RANGE METHOD 2) THE ANOVA METHOD1) ATTRIBUTE GAGE ANALYSIS METHOD 1) SHORT METHOD 2) HYPOTHESIS TEST ANALYSIS 3) SIGNAL DETECTION THEORY 4) LONG METHOD

3) ACCEPTABILITY CRITERIA4) CONCLUSION5) FOUR METHODS COMPARISON

Introduction: Basic requirements by QS-9000 & TS16949• Base on QS9000 & TS16949 requirements, all measurement system which were mentioned in Quality Plan should be conducted Measurement System Analysis.

MSA Requirement

Introduction: The category of Measurement System

• Most industrial measurement system can be divided two categories, one is variable measurement system, another is attribute measurement system. An attribute gage cannot indicate how good or how bad a part is , but only indicates that the part is accepted or rejected. The most common of these is a Go/No-go gage.

Variable GageAttribute Gage (Go/No-go Gage)

Introduction: What is a measurement process

Operation OutputInput

General Process

Measurement Analysis

Value

DecisionProcess to be Managed

Measurement Process

Measurement: The assignment of a numerical value to material things to represent the relations among them with respect to a particular process. Measurement Process: The process of assigning the numerical value to material things.

Introduction: What are the variations of measurement process

Introduction: What are the variations of measurement process

Measurement(Observed) Value = Actual Value + Variance of The Measurement System

2

σobs = 2

σ actual + σ variance of the measurement system 2

Introduction: Where does the variation of measurement system come from?• The Five Characterizations of Measurement System: 1. Location Variation: Bias; Stability; Linearity Bias is the difference between the observed average of measurements and a reference value. Bias is often referred to as accuracy. It is a systematic error component of the measurement system

Introduction: Where does the variation of measurement system come from?• The Five Characterizations of Measurement System: 1. Location Variation: Bias; Stability; Linearity Stability(Alias: Drift): Stability is the total variation in the measurements obtained with a measurement system on the same master or parts when measuring a single characteristic over an extended time period. A stable measurement process is in statistical control with respect to location.

Stability

Introduction: Where does the variation of measurement system come from?• The Five Characterizations of Measurement System: 1. Location Variation: Bias; Stability; Linearity Linearity is the difference in the bias values through the expected operating range of the measurement instrument. It is a systematic error component of the measurement system.

Linearity

Introduction: Where does the variation of measurement system come from?• The Five Characterizations of Measurement System: 2. Width Variation: Repeatability; Reproducibility; Gage R&R Repeatability is the variation in measurements obtained with one measurement instrument when used several times while measuring the identical characteristic on the same part by an appraiser. It is a Within-system variation, commonly referred to as E.V.---Equipment Variation.

Repeatability

Introduction: Where does the variation of measurement system come from?• The Five Characterizations of Measurement System: 2. Width Variation: Repeatability; Reproducibility; Gage R&R Reproducibility is the variation in the average of the measurements made by different appraisers using the same gage when measuring the identical characteristics of the same part. It is between-system variation, commonly referred to as A.V.---Appraiser Variation.

Reproducibility

Introduction: Where does the variation of measurement system come from?• The Five Characterizations of Measurement System: 2. Width Variation: Repeatability; Reproducibility; Gage R&R Gage R&R means Gage repeatability and reproducibility, which combined estimate of measurement system repeatability and reproducibility. This combined measurement error then is compared with the process output variability to compute the gage percentage R&R (%R&R). The %R&R is the basis for making a judgment of whether the measurement system is good enough to measure the process.

Analysis Techniques: • Currently there are three techniques for variable measurement system and four techniques for attribute measurement system analysis were recommended by AIAG MSA Reference Manual.

• Range Method

• Average - Range Method

• ANOVA

• Short Method

• Long Method

• Hypothesis Test Analyses

• Signal Detection Theory

• Followings are some practical examples to illustrate how to perform four methods respectively.

Variable Gage Attribute Gage

Analysis Techniques: Preparation before MSA

1. The approach to be used should be planned.2. The number of appraisers, number of sample parts, and number of repeat readings should be determined in advance.3. The appraisers should be selected form those who normally operate the instrument.4. The sample parts must be selected from the process and represent its entire operating range.5. The instrument must have a discrimination that allows at least one-tenth of the expected process variation of the characteristic to be read directly.6. The measurement procedure should be defined in advance to ensure the consistent measuring method.

Analysis Techniques: Variable Gage Analysis

1. General Gage R&R Study: The Average and Range Method

The ANOVA Method

The common step for conducting Gage R&R study:1. Verify calibration of measurement equipment to be studied.2. Obtain a sample of parts that represent the actual or expected range of process variation.3. Add a concealed mark to each identifying the units as numbers 1 through 10. It is critical that you can identify which unit is which. At the same time it is detrimental if the participants in the study can tell one unit from the other (may bias their measurement should they recall how it measured previously).4. Request 3 appraisers. Refer to these appraisers as a A, B, and C appraisers. If the measurement will be done repetitively such as in a production environment, it is preferable to use the actual appraiser that will be performing the measurement.

For extreme cases, a minimum of two appraisers can be used, but this is strongly discouraged as a less accurate estimate of measurement variation will result.5. Let appraiser A measure 10 parts in a random order while you record the data noting the concealed marking. Let appraisers B and C measure the same 10 parts Note: Do not allow the appraisers to witness each other performing the

measurement. The reason is the same as why the unit markings are concealed, TO PREVENT BIAS.6. Repeat the measurements for all three appraisers, but this time present the samples to each in a random order different from the original measurements. This is to again help reduce bias in the measurements.


……

10 Parts 3 Appraisers3 Trials

1. The Average and Range Method: A range control chart is created to determine if the measurement process is stable and consistent. For each appraiser calculate the range of the repeated measurements for the same part.


Range of Repeated Measures

0

10

20

30

40

1A 2A 3A 4A 5A 1B 2B 3B 4B 5B 1C 2C 3C 4C 5C

0.01

MM

MinXXRRange Max -


The average range for each operator is then computed.

The average of the measurements taken by an operator is calculated.

A control chart of ranges is created. The centerline represents the average range for all operators in the study, while the upper and lower control limit constants are based on the number of times each operator measured each part (trials).

Parts of No.

ROperatorR

PartsTrials

XXOperator

*


RDLCL

RDUCL

RR

R

R

3

4

Operators No.of

The centerline and control limits are graphed onto a control chart and the calculated ranges are then plotted on the control chart. The range control chart is examined to determine measurement process stability. If any of the plotted ranges fall outside the control limits the measurement process is not stable, and further analysis should not take place. However, it is common to have the particular operator re-measure the particular process output again and use that data if it is in-control.


Repeatability - Equipment Variation (E.V.)

The constant d2* is based on the number of measurements used to compute the

individual ranges(n) or trials, the number of parts in the study, and the number of different conditions under study. The constant K1 is based on the number of times a part was repeatedly measured (trials).

The equipment variation is often compared to the process output tolerance or process output variation to determine a percent equipment variation (%EV).

12

**15.5 KRd

REV

100*15.5

)(%

100*)(%

m

EVPROCEV

LSLUSL

EVTOLEV


Reproducibility - Appraiser Variation(A.V.)

Xdiff is the difference between the largest average reading by an operator and the

smallest average reading by an operator. The constant K2 is based on the number of different conditions analyzed. The appraiser variation is often compared to the process output tolerance or process output variation to determine a percent appraiser variation (%AV).

nt

EVKXAV Diff

222* -

100*15.5

)(%

100*)(%

m

AVPROCAV

LSLUSL

AVTOLAV

-


Repeatability and Reproducibility( Gage R&R)

The gage error (R&R) is compared to the process output tolerance to estimate the precision to tolerance ratio (P/T ratio). This is important to determine if the measurement system can discriminate between good and bad output.

The basic interest of studying the measurement process is to determine if the measurement system is capable of measuring a process output characteristic with its own unique variability. This is know as the Percent R&R (P/P ratio, %R&R), and calculated as follows:

22& AVEVRR

100*&

/LSLUSL

RRTP

-


100*15.5

&&%

m

RRRR

Process or Total Variation:If the process output variation (m) is not known, the total variation can be estimated using the data in the study. First the part variation is determined:

Rp is the range of the part averages, while K3 is a constant based on the number of parts in the study.The total variation (TV) is just the square root of the sum of the squares of R&R and the part variation

3KRPV p

22& PVRRTVm

Analysis Techniques: Variable Gage Analysis1. The ANOVA Method:

A weakness with the Average-Range method of using the range to determine gage R&R is that it does not consider the variation introduced into a measurement through the interaction between different conditions (appraiser) and the gage. Consequently, to account for this variation an analysis of variance method (ANOVA) is utilized. In addition, when the sample size increases, use of the range to estimate the variation in not very precise. Furthermore, with software packages readily available, the ANOVA method is a viable choice.The total variation in an individual measurement equals:

The part to part variation is estimated by p2; the operator variation is estimated by

o2; the interaction effect is estimated by op

2; while repeatability is estimated by r2

22222rpoopt

Analysis Techniques: Variable Gage AnalysisSource SS dF MS F*Part (P) 2...)..()( YYtnPSS i

p-1

1

)()(

p

PSSPMS

)(

)(*

POMS

PMSF

Operator (O) 2...)..()( YYnpOSS jt-1

1

)()(

t

OSSOMS

)(

)(*

POMS

OMSF

Interaction (PO) 2...).....()( YYYYnPOSS jiij(p-1)(t-1)

)1)(1(

)()(

tp

POSSPOMS

MSE

POMSF

)(*

Repeatability 2.)( ijijk YYSSE pt(n-1)

)1(

npt

SSEMSE

Total 2...)( YYSST ijknpt-1

Part:tn

SnSPMSSp

rop22

2 )( Operator:

pn

SnSOMSSo

rop22

2 )(

Interaction:n

SOPMSSop r

22 )(

Repeatability: MSESr 2


Total: 22222ropop SSSSSt

The gage R&R statistics are then calculated as follows:

2222ropo SSSSms Measurement Error:

Part:tn

SnSPMSPV rop

22)(15.5

Operator:

pn

SnSOMSOV

rop22)(

15.5

Interaction:n

SOPMSIV r

2)(15.5

Reproducibility: 22 IVOVAV

Repeatability: MSEEV 15.5 Measurement Error: 22& AVEVRR

Total: 22 PVRRTV

Analysis Techniques: Variable Gage Analysis1. Acceptability Criteria:The gage repeatability and reproducibility: %R&R (P/P ratio: % total of total variance; P/T ration:% total of tolerance): Less than 10% Outstanding 10% to 20% Capable 20% to 30% Marginally Capable

Greater than 30% NOT CAPABLEFor the P/P ratio and the P/T ratio, either or both approaches can be taken depending on the intended use of the measurement system and the desires of the customer. Generally, If the measurement system is only going to be use to inspect if the product meets the specs, then we should use the %R&R base on the tolerance (P/T ratio). If the measurement system is going to be use for process optimization/characterization analysis, then we should use the %R&R base on total variation (P/P ratio).

Analysis Techniques: Variable Gage Analysis1. Acceptability Criteria:For a Gage deemed to be INCAPABLE for it’s application. The team must review the design of the gage to improve it’s intended application and it’s ability to measure critical measurements correctly. Also, if a re-calibration is required, pleasefollow caliberation steps.If repeatability is large compared to reproducibility, the reasons might be: 1) the instrument needs maintenance, the gage should be redesigned 2) the location for gaging needs to be improved 3) there is excessive within-part variation. If reproducibility is large compared to repeatability, then the possible causes could be: 1) inadequate training on the gage, 2) calibrations are not effective, 3) a fixture may be needed to help use the gage more consistently.

Analysis Techniques: Variable Gage Analysis1. The Measurement Bias: Using a certified sample, and a control chart of repeated measurements, the bias of a measurement process can be determined. Bias is the difference between the known value and the average of repeated measurement of the known sample. Bias is sometimes called accuracy.

XKnownBIAS

Process Variation = 6 Sigma Range

Percent Bias = BIASProcess Variation

Analysis Techniques: Variable Gage Analysis1. Linearity: Linearity of a measurement process is the difference in the bias or precision values through the expected operating range of the gauge. To evaluate linearity, a graph comparing the bias or precision to the expected operating range is created. A problem with linearity exists if the graph exhibits different bias or precision for different expected operating ranges.By using the following procedure, linearity can be determined.1) Select five parts whose measurements cover the operating range of the gage.2) Verify the true measurements of each part.3) Have each part be randomly measured 12 times on the gage by one operator.4) Calculate the part average and the bias for each part.5) Plot the bias and the reference values. 6) Calculate the linear regression line that best fits these points.


XaYb

n

XX

n

YXXY

a

x

xXbiasy

baxy

Part

22 )(

value reference

7) Calculate the goodness of fit statistic:

n

YY

n

XX

n

YXXY

R2

22

2

2

2

)()(

Analysis Techniques: Variable Gage Analysis8) Determine linearity and percent linearity: Linearity = Slope x Process variation(m) %Linearity = 100[linearity/Process Variation]The acceptability criteria of Bias, Linearity depend on Quality Control Plan, characteristic being measured and gage speciality, suggested criteria of ESG is as following: Under 5% - acceptable 5% to 15% - may be acceptable based upon importance of application, cost of measurement device, cost of repairs, etc., Over 15% - Considered not acceptable - every effort should be made to improve the systemThe stability is determined through the use of a control chart. It is important to note that, when using control charts, one must not only watch for points that fall outside of the control limits, but also care other special cause signals such as trends and centerline hugging.Guideline for the detection of such signals can be found in many publications on SPC.

Analysis Techniques: Attribute Gage Study

• Short Method: A Short Method example for battery length go/no-go gage study: The Short method need to be conduct by selecting 20 parts which have been measured by a variable gage in advance, some of the parts are slightly below and above both specification limits. Two appraisers then measure all parts twice randomly.

Appraiser A Appraiser B

1 2 1 2 1 G G G G

2 NG NG NG NG

3 G G G G

4 G G G G

5 G G G G

6 G G G G

7 G G G G

8 G G G G

9 NG NG NG NG

10 NG NG NG NG

11 G G G G

12 G G G G

13 G G G G

14 G G G G

15 G G NG G

16 G G G G

17 NG NG G G

18 G G G G

19 G G G G

20 G G G G

Disagree

Measurement Result table 1


Acceptability criteria: If all measurement results (four per part) agree, the gage is acceptable. If the measurement results do not agree, the gage can not be accepted, it must be improved and re-evaluated.

Conclusion: Because table 1 listed measurement results are not whole agreement, at part 15# and 17#, appraiser’s decisions are not agree. so the battery length gage can not be used and must be improved and re-evaluated.


• Hypothesis Test Analysis: Short method should know the variable reference value of samples in advance. However, in some situations it is hard to realize to get all samples variable reference value. So in this case, Hypothesis test analysis shall be applied for gage study.

IIII

Target

II III

USLLSL

Analysis Techniques: Attribute Gage Study• Hypothesis test analysis depends on cross tabulation method which needs to take a random sample of 50 parts from the present process and use 3 appraisers who make 3 measurements on each part and decide if the part is acceptable or not. Appraisers measure the parts and if the part is within limits they give “1” and if not they give “0” and write those results in a table. In order to eliminate any bias produced, the labeled samples are mixed before giving to appraisers for identification in each trails. Following table 2 listed filler gage measuring results for the battery \welding gap:

……

50 Samples 3 Appraisers

3 Trials

Table 2 Filler gage measuring result Part A-1 A-2 A-3 B-1 B-2 B-3 C-1 C-2 C-3 Refer Code

1 0 0 0 0 0 0 0 0 0 0 -

2 1 1 1 1 1 1 1 1 1 1 +

3 1 1 1 1 1 1 1 1 1 1 +

4 0 0 0 0 0 0 0 0 0 0 -

5 0 0 0 0 0 0 0 0 0 0 -

6 1 0 1 0 1 1 1 0 0 1 x

7 1 1 1 1 1 1 1 0 1 1 x

8 0 0 0 0 0 0 0 0 0 0 -

9 1 1 1 1 1 1 1 1 1 1 +

10 0 0 0 0 0 0 0 0 0 0 -

11 0 0 0 0 0 0 0 0 0 0 -

12 1 1 1 1 1 1 1 1 1 1 +

13 1 1 1 1 1 1 1 1 1 1 +

14 1 1 1 1 1 1 1 1 1 1 +

15 1 1 1 1 1 1 1 1 1 1 +

16 1 1 1 1 1 1 1 1 1 1 +

17 1 1 1 1 1 1 1 1 1 1 +

18 1 1 1 1 1 1 1 1 1 1 +

19 1 1 1 1 1 1 1 1 1 1 +

20 1 1 0 1 1 1 1 0 0 1 x

21 0 0 0 0 0 0 0 0 0 0 -

22 0 0 0 0 0 0 0 0 0 0 -

23 0 0 1 0 1 0 1 1 0 0 x

24 1 1 1 1 1 1 1 1 1 1 +

25 1 1 1 1 1 1 1 1 1 1 +

26 1 1 1 1 1 1 1 1 1 1 +

27 0 0 0 0 0 0 0 0 0 0 -

28 0 0 0 0 0 0 0 0 0 0 -

29 0 0 0 0 0 1 0 0 0 0 x

30 1 1 1 1 1 1 1 1 1 1 +

31 1 1 1 1 1 1 1 1 1 1 +

32 1 1 1 1 1 1 1 1 1 1 +

33 0 0 1 0 0 1 0 1 1 0 x

34 1 1 1 1 1 1 1 1 1 1 +

35 1 1 0 1 1 1 1 0 1 1 x

36 0 0 0 0 0 0 0 0 0 0 -

37 1 1 1 1 1 1 1 1 1 1 +

38 0 0 0 0 0 0 0 0 0 0 -

39 1 1 1 1 1 1 1 1 1 1 +

40 1 1 1 1 1 1 1 1 1 1 +

Table 2 Filler gage measuring result

41 0 0 0 0 0 0 0 0 0 0 -

42 1 0 1 1 1 1 1 1 0 1 x

43 1 1 1 1 1 1 1 1 1 1 +

44 1 1 1 1 1 1 1 1 1 1 +

45 1 1 1 1 1 1 1 1 1 1 +

46 0 0 0 0 0 0 0 0 0 0 -

47 0 0 0 0 0 0 0 0 0 0 -

48 1 1 1 1 1 1 1 1 1 1 +

49 0 0 0 0 0 0 0 0 0 0 -

50 1 1 1 1 1 1 1 1 1 1 +

Table 2 Filler gage measuring result


In order to determine the level of agreement among the appraisers, we applied Cohen’s Kappa which is used to assess inter-rater reliability when observing or otherwise coding qualitative/categorical variables. It can measure the agreement between the evaluations of two raters when both are rating the same object.

Step 1. Organize the score into a contingency table. Since the variable being rated has two categories, the contingency table will be a 2*2 table: Table 3


B Total

.00 1.00

A .00 Count 53 6 59

Expected Count 21. 6 37. 4 59. 0

Count 2 89 91

1.00 Expected Count 33. 4 57. 6 91. 0

Total Count 55 95 150

Expected Count 55. 0 95. 0 150. 0

A*B Cross-Tabulation Table 3


Step 2. Compute the row totals (sum across the values on the same row) and column totals of the observed frequencies.Step 3 Compute the overall total (show in the table 3). As a computational check, be sure that the row totals and the column totals sum to the same value for the overall total, and the overall total matches the number of cases in the original data set.Step 4 Compute the total number of agreements by summing the values in the diagonal cells of the table. Σa = 53+ 89 = 142Step 5 Compute the expected frequency for the number of agreements that would have been expected by chance for each coding category.

ef = = = 21.6

Repeat the formula for other cell, we got other expected count (show in the table 3).

row total * col totaloverall total

59 * 55150

Step 6 Compute the sum of the expected frequencies of agreement by chance. Σef = 21.6+57.6 = 79.2Step 7 Compute Kappa

K = = = 0.89 Step 8 Evaluate Kappa - A general rule of thumb is that values of kappa greater than 0.75 indicate good to excellent agreement; values less than 0.4 indicate poor agreement. Repeat above step, we can got following kappa measures for the appraisers: Table 4


Σa-ΣefN-Σef

142-79.2150-79.2

Kappa A B C

A - 0. 89 0. 83 B 0. 89 - 0. 85 C 0. 83 0. 85 -

Table 4

Using the same steps to calculated the kappa measure to determine the agreement of each appraiser to the reference decision: Table 5

Total summary on Table 6:


A B C

Kappa 0. 92 0. 93 0. 85

Table 5

Source Appraiser A Appraiser B Appraiser C

Total Inspected 50 50 50# Matched 44 46 43

Mixed 6 4 795%UCI 95. 50% 97. 80% 94. 20%

Calculated Score 88% 92% 86%95%LCI 75. 70% 81% 73. 30%

Total Inspected 50# in Agreement 42

95%UCI 92. 80% Calculated Score 84%

95%LCI 73. 70%

%Score vs Attribute

Anne Ben Cathy

75

85

95

Appraiser

Per

cent

Within Appraiser

Anne Ben Cathy

75

85

95

Appraiser

Per

cent

Appraiser vs Standard

Assessment AgreementDate of study:Reported by:Name of product:Misc:

[ , ] 95.0% CI

Percent


Analysis Techniques: Attribute Gage StudyThe AIAG MSA reference manual edition 3 provides acceptability criteria for each appraisers results:

Definition:False Alarm – The number of times of which the operator (s) identify a good sample as a bad one.Miss – The number of times of which the operators identify a bad sample as a good one.

Decision Measurement System

Effectiveness Miss Rate False Alarm Rate

Acceptable for appraiser ≥ 90% ≤ 2% ≤ 5%

Marginally acceptable for the appraiser - may need improvement

≥ 80% ≤ 5% ≤ 10%

Unacceptable for the appraiser - needs improvements

<80% >5% >10%

Number of correct decisionsTotal opportunities for a decision

Effectiveness =


Number of False AlarmTotal opportunities for a decision

False Alarm Rate =

Number of False AlarmTotal opportunities for a decision

Miss Rate =

So summarizing all the information of the example with this table: Table 7

False Alarm Rate

A 88% 4% 8%B 92% 6% 2%C 86% 8% 14%

Effectiveness Miss Rate


Conclusion: The measurement system was acceptable with appraiser B, marginal with appraiser A, and unacceptable for C. So we shall determine if there is a misunderstanding with appraiser C that requires further training and then need to re-do MSA. The final decision criteria should be based on the impact to the remaining process and final customer. Generally, the measurement system is acceptable if all 3 factors are acceptable or marginal.Minitab also can perform attribute gage analysis, but it didn’t declare the acceptability criteria, so it is not recognized by QS9000 standard.

Analysis Techniques: Attribute Gage Study• Signal Detection Theory is to determine an approximation of the width of the region II area so as to calculate the measurement system GR&R.

Also used filler gage as example to perform Signal Detection approach. The tolerance is 0.45 ~0.55mm. The process needs to take a random sample of 50 parts from the practical process and use 3 appraisers who make 3 measurements on each part, and then got following table: Table 8

IIII

Target

II III

USLLSL

Part A-1 A-2 A-3 B-1 B-2 B-3 C-1 C-2 C-3 Refer Value Code

1 0 0 0 0 0 0 0 0 0 0. 57036 -

2 1 1 1 1 1 1 1 1 1 0. 566152 +

3 1 1 1 1 1 1 1 1 1 0. 502295 +

4 0 0 0 0 0 0 0 0 0 0. 437817 -

5 0 0 0 0 0 0 0 0 0 0. 576459 -

6 1 0 1 0 1 1 1 0 0 0. 544951 x

7 1 1 1 1 1 1 1 0 1 0. 465454 x

8 0 0 0 0 0 0 0 0 0 0. 566152 -

9 1 1 1 1 1 1 1 1 1 0. 476901 +

10 0 0 0 0 0 0 0 0 0 0. 589656 -

11 0 0 0 0 0 0 0 0 0 0. 429228 -

12 1 1 1 1 1 1 1 1 1 0. 509015 +

13 1 1 1 1 1 1 1 1 1 0. 515537 +

14 1 1 1 1 1 1 1 1 1 0. 488905 +

15 1 1 1 1 1 1 1 1 1 0. 542704 +

16 1 1 1 1 1 1 1 1 1 0. 517377 +

17 1 1 1 1 1 1 1 1 1 0. 531939 +

18 1 1 1 1 1 1 1 1 1 0. 519694 +

19 1 1 1 1 1 1 1 1 1 0. 484167 +

20 1 1 0 1 1 1 1 0 0 0. 465454 x

21 0 0 0 0 0 0 0 0 0 0. 561457 -

22 0 0 0 0 0 0 0 0 0 0. 427687 -

23 0 0 1 0 1 0 1 1 0 0. 545604 x

24 1 1 1 1 1 1 1 1 1 0. 520496 +

Table 8 Signal Detection Table for Filler Gage

25 1 1 1 1 1 1 1 1 1 0. 477236 +

26 1 1 1 1 1 1 1 1 1 0. 529065 +

27 0 0 0 0 0 0 0 0 0 0. 566575 -

28 0 0 0 0 0 0 0 0 0 0. 412453 -

29 0 0 0 0 0 1 0 0 0 0. 559918 x

30 1 1 1 1 1 1 1 1 1 0. 514192 +

31 1 1 1 1 1 1 1 1 1 0. 502436 +

32 1 1 1 1 1 1 1 1 1 0. 521642 +

33 0 0 1 0 0 1 0 1 1 0. 449696 x

34 1 1 1 1 1 1 1 1 1 0. 487613 +

35 1 1 0 1 1 1 1 0 1 0. 46241 x

36 0 0 0 0 0 0 0 0 0 0. 587893 -

37 1 1 1 1 1 1 1 1 1 0. 483803 +

38 0 0 0 0 0 0 0 0 0 0. 446697 -

39 1 1 1 1 1 1 1 1 1 0. 486379 +

40 1 1 1 1 1 1 1 1 1 0. 493441 +

41 0 0 0 0 0 0 0 0 0 0. 580273 -

42 1 0 1 1 1 1 1 1 0 0. 543077 x

43 1 1 1 1 1 1 1 1 1 0. 470832 +

44 1 1 1 1 1 1 1 1 1 0. 513779 +

45 1 1 1 1 1 1 1 1 1 0. 501132 +

46 0 0 0 0 0 0 0 0 0 0. 576532 -

47 0 0 0 0 0 0 0 0 0 0. 432179 -

48 1 1 1 1 1 1 1 1 1 0. 488184 +

49 0 0 0 0 0 0 0 0 0 0. 435281 -

50 1 1 1 1 1 1 1 1 1 0. 498698 +

Table 8 Signal Detection Table for Filler Gage

Analysis Techniques: Attribute Gage Study• Above table 8 shows the 50 parts measurement result, “0” standard rejected, “1” standard acceptable, code “-” standard region I, code “x” standard region II, code “+” standard region III.• And then base on the part reference value to arrange in order from Max. to Min., meanwhile to show the code: Table 9

Refer Code

0. 589656 -

0. 587893 -

0. 580273 -

0. 576532 -

0. 576459 -

0. 57036 -

0. 566575 -

0. 566152 -

0. 566152 -

0. 561457 -

0. 559918 x

0. 545604 x

0. 544951 x

0. 543077 x

Refer Code

0. 542704 +

0. 531939 +

0. 529065 +

0. 521642 +

0. 520496 +

0. 519694 +

0. 517377 +

0. 515537 +

0. 514192 +

0. 513779 +

0. 509015 +

0. 502436 +

0. 502295 +

0. 501132 +

Refer Code

0. 498698 +

0. 493441 +

0. 488905 +

0. 488184 +

0. 487613 +

0. 486379 +

0. 484167 +

0. 483803 +

0. 477236 +

0. 476901 +

0. 470832 +

0. 465454 x

0. 465454 x

0. 46241 x

Refer Code

0. 449696 x

0. 446697 -

0. 437817 -

0. 435281 -

0. 432179 -

0. 429228 -

0. 427687 -

0. 412453 -

Region III Region IRegion I

Region II Region II

Analysis Techniques: Attribute Gage Study• Next step we should find Xa value which located region I , but is the nearest to region II. Xb value which located region III, but is the nearest to region II. And then calculate the distance of region II.

dLSL = Xa,LSL - Xb,LSL = 0.446697 – 0.470832 = 0.024135 dUSL = Xa,USL - Xb,USL = 0.566152 – 0.542704 = 0.023448

0.0237910.55 – 0.45

GR&R = = = 0.023791 dUSL +dLSL

2

0.023448 +0.0241352

%GR&R = = = 0.277 = 27.7% GR&R

USL -LSL

• Conclusion: The %GR&R is larger than 10%, but less than 30%, it may be acceptable based upon importance of application, cost of measurement device, cost of repairs, etc.


• Long Method is used the concept of the Gage Performance Curve (GPC) to develop a measurement system study. It focuses on assessing the repeatability and bias of the measurement system. The purpose of developing a GPC is to determine the probability of either accepting or rejecting a part of some reference value.

• The first step of Long Method is the part selection. It is necessary to know the part reference value which was measured with variable measurement system. The approach should select 8 parts as nearly equidistant intervals as practical. The Maximum and minimum values should represent the process range. The 8 parts must be measured 20 times with the attribute gage. We use “m” to represent the measuring times, use “a” to represent the number of accepts. For the smallest (or largest) part, the value must be a=0; For the largest (or smallest) part, the value must be a=20; For the 6 other parts, the value 1≤a≤19.


……

8 Samples

1 Appraiser

20 Trials


ReferenceValue (ActualMeasurement)

(XT)

Number ofAccepts (a)

0.26 00.25 10.24 20.23 50.22 90.21 150.2 20

0.17 20

Example: We use a filler gage to measure the fitting gap between battery and hand phone which specification is 0~0.2mm. The number of accepts for each part are: Table 10

Table 10


• The second step is the acceptance probabilities calculation for each part using the binomial adjustments:

ReferenceValue (ActualMeasurement)

(XT)

Number ofAccepts (a)

Pa

0.26 0 0. 0250.25 1 0. 0750.24 2 0. 1250.23 5 0. 2750.22 9 0. 4750.21 15 0. 7250.2 20 0. 975

0.17 20 1

Table 11

P'a =

<if a + 0.5 m

a m

0.5, a≠0

>if a - 0.5 m

a m 0.5, a≠20

0.5

if a m

0.5 =

Analysis Techniques: Attribute Gage Study• The third step: Plot Gage Performance Curve with part reference value XT as X axis, and the probability of acceptance P'a as Y axis

Gage Performance Curve

00. 050. 1

0. 150. 2

0. 250. 3

0. 350. 4

0. 450. 5

0. 550. 6

0. 650. 7

0. 750. 8

0. 850. 9

0. 951

1. 05

USL

RepeatabilityPa=0.5%Pa=99.5%

Analysis Techniques: Attribute Gage Study• The fourth step: Base on Gage Performance Curve to find XT value at Pa = 0.5%

and Pa = 99.5% (using normal probability paper can get more accurate estimates).

We also can use Statistical Forecast calculation to get the XT value. XT = 0.264 at Pa = 0.5% XT = 0.184 at Pa = 99.5%

Bias = XT (at Pa = 0.5%)-USL = 0.264 – 0.2 =0.064

The repeatability is determined by finding the differences of the XT value corresponding to Pa = 99.5% and Pa = 0.05% and dividing by an adjustment factor

of 1.08. Repeatability = XT(at Pa = 0.5%) - XT(at Pa = 99.5%)

1.08

= = 0.0740.264 – 0.184

1.08


• Conclusion: Because the filler gage repeatability is 7.4% , Bias is 6.4%. Both of them are less than 10%, so the gage can be accepted to use.

Four Methods Comparison

• The four methods for attribute measurement study have respective feature. The Short method look like simple, but it need to select enough parts which are slightly below and above both specification limits, and must measure variable reference value in advance. Hypothesis Test didn’t need to measure the variable reference value, so it is feasible for manufacturing, but it need large sample size. Signal Detection method can determine an approximation of the width of the region II area so as to calculate the measurement system GR&R. Long method is used the concept of the Gage Performance Curve (GPC) to assess the repeatability and bias of the measurement system. When the importance of the measurement system need to be highly assured, the Signal Detection method and Long method would be necessary. Although the statistical calculation process for above methods is complex, now we are designing a software to be able to perform the four methods process and calculation.

02training material for msa

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