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1、 Training Material forMEASUREMENTSYSTEMANALYSISContents:1)INTRODUCTION FOR MEASUREMENT SYSTEM ANALYSIS 2)GENERAL METHODS ILLUSTRATION FOR MEASUREMENT SYSTEM ANALYSIS1)VARIABLE GAGE ANALYSIS METHOD2)1)THE AVERAGE-RANGE METHOD3)2)THE ANOVA METHOD4)ATTRIBUTE GAGE ANALYSIS METHOD5)1)SHORT METHOD6)2)HYPO

2、THESIS TEST ANALYSIS7)3)SIGNAL DETECTION THEORY8)4)LONG METHOD3)ACCEPTABILITY CRITERIA4)CONCLUSION5)FOUR METHODS COMPARISONIntroduction:Basic requirements by QS-9000&TS16949 Base on QS9000&TS16949 requirements,all measurement system which were mentioned in Quality Plan should be conducted Measuremen

3、t System Analysis.MSA RequirementIntroduction: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 indica

4、tes 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 processOperationOutputInputGeneral ProcessMeasurementAnalysisValueDecisionProcess to be ManagedMeasurement ProcessMeasurement:The assignm

5、ent 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 processIntroduction:What are the variations o

6、f measurement processMeasurement(Observed)Value=Actual Value+Variance of The Measurement System2obs=2 actual+variance of the measurement system 2Introduction:Where does the variation of measurement system come from?The Five Characterizations of Measurement System:1.Location Variation:Bias;Stability;

7、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 systemIntroduction:Where does the variation of measurement system come from?The Five Characterizations of Me

8、asurement 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 i

9、s in statistical control with respect to location.StabilityIntroduction: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 operatin

10、g range of the measurement instrument.It is a systematic error component of the measurement system.LinearityIntroduction: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

11、 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.RepeatabilityIntroduction:Where does the vari

12、ation 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 characteri

13、stics of the same part.It is between-system variation,commonly referred to as A.V.-Appraiser Variation.ReproducibilityIntroduction: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

14、&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

15、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

16、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 GageAttribute GageAnalysis Techniques:Preparation before MSA1.The approach to be used should be planned.2.The number

17、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 ha

18、ve 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 Analysis1.General Gage R&R Study:The Ave

19、rage 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

20、 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

21、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 est

22、imate 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

23、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.Analysis Techniques:Variable Gage

24、Analysis10 Parts3 Appraisers3 Trials1.The Average and Range Method:2.A range control chart is created to determine if the measurement process is stable 3.and consistent.For each appraiser calculate the range of the repeated measurements 4.for the same part.Analysis Techniques:Variable Gage AnalysisR

25、ange of Repeated Measures0102030401A2A3A4A5A1B2B3B4B5B1C2C3C4C5C0.01MMMinXXRRangeMax-Analysis Techniques:Variable Gage Analysis 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

26、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.ROperatorRPartsTrialsXXOperator*Analysis Techniques:Variable Gage AnalysisRDLCLRDUCLRRRR34Operators No.o

27、fThe 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 n

28、ot 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.Analysis Techniques:Variable Gage AnalysisRepeatability-Equipment Variation(E.V.)The constant d2*is based on

29、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 pro

30、cess output tolerance or process output variation to determine a percent equipment variation(%EV).12*15.5KRdREV100*15.5)(%100*)(%mEVPROCEVLSLUSLEVTOLEVAnalysis Techniques:Variable Gage AnalysisReproducibility-Appraiser Variation(A.V.)Xdiff is the difference between the largest average reading by an

31、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).ntEVKXAVDiff222*-100*

32、15.5)(%100*)(%mAVPROCAVLSLUSLAVTOLAV-Analysis Techniques:Variable Gage AnalysisRepeatability 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 ca

33、n 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 follow

34、s:22&AVEVRR100*&/LSLUSLRRTP-Analysis Techniques:Variable Gage Analysis100*15.5&%mRRRRProcess 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,

35、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 variation3KRPVp22&PVRRTVmAnalysis Techniques:Variable Gage Analysis1.The ANOVA Method:2.A weakness with the Average-Range method of using the

36、range to determine 3.gage R&R is that it does not consider the variation introduced into a measurement 4.through the interaction between different conditions(appraiser)and the gage.5.Consequently,to account for this variation an analysis of variance method(ANOVA)6.is utilized.In addition,when the sa

37、mple size increases,use of the range to estimate 7.the variation in not very precise.Furthermore,with software packages readily 8.available,the ANOVA method is a viable choice.9.The total variation in an individual measurement equals:10.The part to part variation is estimated by p2;the operator vari

38、ation is estimated by 11.o2;the interaction effect is estimated by op2;while repeatability is estimated by r2 22222rpooptAnalysis Techniques:Variable Gage AnalysisSourceSSdFMSF*Part(P)2.).()(YYtnPSSip-11)()(pPSSPMS)()(*POMSPMSF Operator(O)2.).()(YYnpOSSjt-11)()(tOSSOMS)()(*POMSOMSF Interaction(PO)2.

39、).()(YYYYnPOSSjiij(p-1)(t-1)1)(1()()(tpPOSSPOMSMSEPOMSF)(*Repeatability2.)(ijijkYYSSEpt(n-1)1(nptSSEMSETotal2.)(YYSSTijknpt-1Part:tnSnSPMSSprop222)(Operator:pnSnSOMSSorop222)(Interaction:nSOPMSSopr22)(Repeatability:MSESr2Analysis Techniques:Variable Gage AnalysisTotal:22222ropopSSSSStThe gage R&R st

40、atistics are then calculated as follows:2222ropoSSSSmsMeasurement Error:Part:tnSnSPMSPVrop22)(15.5Operator:pnSnSOMSOVrop22)(15.5Interaction:nSOPMSIVr2)(15.5Reproducibility:22IVOVAVRepeatability:MSEEV15.5Measurement Error:22&AVEVRRTotal:22PVRRTVAnalysis Techniques:Variable Gage Analysis1.Acceptabilit

41、y Criteria:2.The gage repeatability and reproducibility:%R&R(P/P ratio:%total of total 3.variance;P/T ration:%total of tolerance):4.Less than 10%Outstanding5.10%to 20%Capable6.20%to 30%Marginally Capable7.Greater than 30%NOT CAPABLE8.For the P/P ratio and the P/T ratio,either or both approaches can

42、be taken 9.depending on the intended use of the measurement system and the desires of the 10.customer.Generally,If the measurement system is only going to be use to inspect 11.if the product meets the specs,then we should use the%R&R base on the tolerance 12.(P/T ratio).If the measurement system is

43、going to be use for process optimization13./characterization analysis,then we should use the%R&R base on total variation 14.(P/P ratio).Analysis Techniques:Variable Gage Analysis1.Acceptability Criteria:2.For a Gage deemed to be INCAPABLE for its application.The team must review 3.the design of the

44、gage to improve its intended application and its ability to 4.measure critical measurements correctly.Also,if a re-calibration is required,please5.follow caliberation steps.6.If repeatability is large compared to reproducibility,the reasons might be:7.1)the instrument needs maintenance,the gage shou

45、ld be redesigned 8.2)the location for gaging needs to be improved 9.3)there is excessive within-part variation.10.If reproducibility is large compared to repeatability,then the possible causes 11.could be:12.1)inadequate training on the gage,13.2)calibrations are not effective,14.3)a fixture may be

46、needed to help use the gage more consistently.Analysis Techniques:Variable Gage Analysis1.The Measurement Bias:2.Using a certified sample,and a control chart of repeated measurements,the bias of 3.a measurement process can be determined.Bias is the difference between the known 4.value and the averag

47、e of repeated measurement of the known sample.Bias is 5.sometimes called accuracy.XKnownBIASProcess Variation=6 Sigma RangePercent Bias=BIASProcess VariationAnalysis Techniques:Variable Gage Analysis1.Linearity:2.Linearity of a measurement process is the difference in the bias or precision values 3.

48、through the expected operating range of the gauge.To evaluate linearity,a graph paring the bias or precision to the expected operating range is created.5.A problem with linearity exists if the graph exhibits different bias or precision for 6.different expected operating ranges.7.By using the followi

49、ng procedure,linearity can be determined.8.1)Select five parts whose measurements cover the operating range of the gage.9.2)Verify the true measurements of each part.10.3)Have each part be randomly measured 12 times on the gage by one operator.11.4)Calculate the part average and the bias for each pa

50、rt.12.5)Plot the bias and the reference values.13.6)Calculate the linear regression line that best fits these points.Analysis Techniques:Variable Gage AnalysisXaYbnXXnYXXYaxxXbiasybaxyPart22)(value reference7)Calculate the goodness of fit statistic:nYYnXXnYXXYR222222)()(Analysis Techniques:Variable

51、Gage Analysis8)Determine linearity and percent linearity:Linearity=Slope x Process variation(m)%Linearity=100linearity/Process VariationThe acceptability criteria of Bias,Linearity depend on Quality Control Plan,characteristic being measured and gage speciality,suggested criteria of ESG is as follow

52、ing: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 t

53、o 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:At

54、tribute 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

55、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

56、Measurement Result table 1Analysis Techniques:Attribute Gage StudyAcceptability 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 m

57、easurement results are not whole agreement,at part 15#and 17#,appraisers decisions are not agree.so the battery length gage can not be used and must be improved and re-evaluated.Analysis Techniques:Attribute Gage Study Hypothesis Test Analysis:Short method should know the variable reference value of

58、 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 TargetIIIIIUSLLSLAnalysis Techniques:Attribute Gage Study Hypothesis test analysis depends on cross tabulatio

59、n 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 res

60、ults 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 Samples3 Appraisers3 TrialsTable 2 Filler gage measuring result Pa

61、rt 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

62、 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

63、+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

64、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

65、 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 Analysis Techniques:Attribute Gage StudyIn order to determine the level of agreement among the appraisers,we applied Cohens Kappa which is used to assess inter-rater reliability when observing or otherwise coding qualit

66、ative/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 Analysis Techniques:Attribute Gage Study 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 Cros