MeasurementSystemAnalysisModuleContentMeasurementSystemAnalysisforAttributesComponentsofGageVariationEffectofMeasurementVariabilityAssessingMeasurementVariability2MeasurementSystemAnalysisforAttributesIntherealworld,noteverycharacteristicismeasurable.Insuchcases,aunitisjudgedtobegoodorbadbasedonwhetheritisdefectfreee.g.visualinspectionwhetheritservesitsfunctionalpurposee.g.functionaltesting3WarmUpExerciseTask:Youhave60secondstodocumentthenumberoftimesthe6thletterofthealphabetappearsinthefollowingtext.TheNecessityofTrainingFarmHandsforFirstClassFarmsintheFatherlyHandlingofFarmLiveStockisForemostintheEyesofFarmOwners.SincetheForefathersoftheFarmOwnersTrainedtheFarmHandsforFirstClassFarmsintheFatherlyHandlingofFarmLiveStock,theFarmOwnersFeeltheyshouldcarryonwiththeFamilyTraditionofTrainingFarmHandsofFirstClassFarmersintheFatherlyHandlingofFarmLiveStockBecausetheyBelieveitistheBasisofGoodFundamentalFarmManagement.4AttributeTerminologyAttributeData:Qualitative(go/nogo)datathatcanbetalliedforrecordingandanalysis.AttributeMeasurementSystem:Ameasurementsystemthatcompareseachparttoastandardandacceptsthepartifthisstandardismet.Screen:100%evaluationofproductusinginspectiontechniques(anattributemeasurementsystem).ScreenEffectiveness:Theabilityoftheattributemeasurementsystemtoproperlydiscriminategoodfrombad.CustomerBias:Operatorhasatendencytoholdbackgoodproduct.ProducerBias:Operatorhasatendencytopassdefectiveproduct.5AttributeR&R-Method1)Selectaminimumof30partsfromtheprocess.50%ofthepartsinyourstudyshouldhavedefects50%ofthepartsshouldbedefectfreeIfpossibleselectborderline(ormarginal)goodandbadsamples2)Identifytheinspectors,whoshouldbequalifiedandexperienced.3)Haveeachinspector,independentlyandinrandomorder,assessthesepartsanddeterminewhetherornottheypassorfail.4)EnterthedataintotheAttributeR&R.xlsspreadsheettoreporttheeffectivenessoftheattributemeasurementsystem.5)Documenttheresults.Implementappropriateactionstofixtheinspectionprocessifnecessary.6)Re-runthestudytoverifythefix.Note:A30piecesamplewillyieldanestimateofinspectorefficiencyandcapabilitywhichhasafairamountofuncertainty.Typicallyalargersampleisnotneededbecausetheinspectionprocessisobviouslyineffective.Thespreadsheetcanhandleupto100samples.6AttributeR&R-Method7AttributeR&R-ScoringForeachsample–operatorcombinationAppraiserScore=1 ifTrial1=Trial2 AppraiserScore=0 ifotherwiseTheappraiserscorereflectstheconsistencyofanoperatorinassessingthesampleunit.AttributeScore=1 ifTrial1=Trial2=Attribute AttributeScore=0 ifotherwiseTheattributescorereflectstheconsistencyofanoperator’sassessmentofthesampleunitagainstthetrueattributeofthesampleunit.8AttributeR&R-Scoring9AttributeR&R-ScoringOverallScreeningEffectivenessOverallAppraiserScore=1ifallappraiserscores=1 OverallAppraiserScore=0ifotherwiseOverallAttributeScore=1 ifallattributescores=1 OverallAttributeScore=0 ifotherwise10AttributeR&R-Scoring11NotesonAttributeR&R(1)If%AppraiserScoreislessthan100%trainingneedstooccur.Focusonspecificareas.(2)%Scorevs.Attributeisanerroragainstaknownpopulationasdeemedbyexperts.(3)100%isthetargetforScreen%EffectivenessScore.(4)Screen%Effectivevs.Attributeisanerroragainstaknownpopulation.100%isthetarget.(5)Attributelegendallowsexceltouseamacrotocountthenumberofoccurrencesofthelegendtext.12VariableGR&RStudyofyourmeasurementsystemwillrevealtherelativeamountofvariationinyourdatathatresultsfrommeasurementsystemerror.Itisalsoagreattoolforcomparingtwoormoremeasurementdevicesortwoormoreoperators.MSAshouldbeusedaspartofthecriteriaforacceptinganewpieceofmeasurementequipmenttomanufacturing.Itshouldbethebasisforevaluatingameasurementsystemwhichissuspectofbeingdeficient.Itshouldbepartoftheperiodicmaintenanceprogram.13TypesofVariations14GageVariation-BiasBiasisthedifferencebetweentheaverageofasetofmeasuredvaluesandthetruevalueofthecharacteristicbeingmeasured.x–BiasTrueValueObservedValue15ExampleAnengineerchosefive“goldenunits”thatrepresentedtheexpectedrangeofmeasurements.Twelverandommeasurementsweremadeoneachpart.Meanvalueofthefivestandardis6mmandhistoricalprocessvariationwasfoundtobe12mm.DatacanbefoundintheMeasurementSystemAnalysis.MTWfile.Meanofthesixtymeasurements x =5.9467mmMeanvalueofthefivestandards =6mm Bias =x–=5.9467–6 =–0.0533mm =0.444%ofprocessvariation16GageVariation-LinearityLinearityisthedifferenceinbiasthroughouttheexpectedrangeofmeasurements.1217GageVariation-LinearityLinearitymaybeobtainedviathefollowingprocedure:a) Foreachcase,computetheError(ei),i.e.measuredvalue–truevalueb) Foreachpart,computetheMeanError(ei),i.e.ieinc) DeterminetheslopeforbestfitlineofMeanError

vs

TrueValue

d) Linearity=|Slope|×ProcessVariation18ExampleComputetheaccuracyandlinearityforthedatainpreviousexample,usingMiniTab’s

GageLinearityStudy.StatQualityToolsGageLinearityStudy19Example20GageVariation-StabilityStabilityistheabilityofthemeasurementsystemtoproducethesameaveragemeasurementsonthesameunitatdifferenttimes.x1–x2–x1–21GageVariation-StabilityMeasurementsysteminstabilityistheresultofvariousfactors:Time(longidleperiods),numberofmeasurementstaken,airpressurechange,warm-up,drift,etc.Ifthecausativefactor(s)is/areknown,thefrequencyofcalibrationcanbeadjustedaccordinglytominimizetheerrorduetoinstability.22GageVariation-PrecisionPrecisionreferstotheabilityofameasurementsystemtoproducethesamevalueonrepeatedmeasurementsofthesameunit.Itismeasuredbythestandarddeviation(orvariance).s1s2System1System223AccuracyvsPrecision1)accuratebutnotprecise 2)precisebutnotaccurate3)neitheraccuratenorprecise 4)bothaccurateandprecise24AccuracyvsPrecision1)accuratebutnotprecise 2)precisebutnotaccurate3)neitheraccuratenorprecise 4)bothaccurateandprecise25ComponentsofPrecisionPrecisionmaybebrokendownintotwoseparateparts:RepeatabilitytheabilityofameasurementsystemtorepeatameasurementonthesameunitunderthesameoperatingconditionsReproducibilitytheabilityofameasurementsystemtoreproduceameasurementonthesameunitunderdifferentmeasurementconditions26SourceofVariabilityProcessVariabilitytruevariabilitywithinandbetweenunitsduetovariationinproductionprocess,rawmaterial,equipmentconditionandenvironmentMeasurementVariabilityvariabilityoverandabovetheactualunit-to-unitvariability,arisingfromthemeasurementitself27BasicModelProductVariability(Actualvariability)MeasurementVariabilityTotalVariability(Observedvariability)+=28Whichoneisgood?Line1Line2TotalVariability(observed)MeasurementVariabilityTrueProcessVariabilitys2(trueprocess)+s2

(meas)=s2

(observed)29BasicModelObservedvalue=mastervalue+measurementoffsetObservedvariability=productvariability+measurementvariabilityMeasurementSystemBias:assessedthroughcalibration.(accuracy)MeasurementSystemVariability:assessedthroughthevariableR&Rstudy(precision)TruevaluesMeasuredvaluesmeasurementoffsetTruevaluesMeasuredvalues30SourcesofMeasurementVariation'Measurement

Variation'HumidityCleanlinessVibrationLine

Voltage

VariationTemperature

FluctuationOperator

TechniqueStandard

ProceduresSufficient

Work

TimeMaintenance

StandardCalibration

FrequencyOperator

TrainingEase

of

Data

EntryAlgorithm

InstabiltyElectrical

InstabilityWearMechanicalinstabilityToolEnvironmentWorkMethods31DiscriminationThenumberofdecimalplacesthatcanbemeasuredbythesystem.Incrementsofmeasureshouldbeatleastone-tenthofthewidthoftheproductspecificationorprocessvariation.12Whichrulershouldbeusedtomeasurepartsfortheprocessrepresentedbythedistributionabove?32AssessingMeasurementVariabilityThreecommonlyusedcriteria:? or? or ? orPrecisiontoToleranceRatioor%Toelrance%R&Ror%contribution?(DistinctCategories)233EffectofMeasurementVariability(1)ExcessiveMeasurementVariability AcceptableMeasurementVariabilityProcessVarianceMeasurementVarianceTotalVarianceProcessVarianceMeasurementVarianceTotalVarianceObservedProcessCapabilityActualProcessCapability34EffectofMeasurementVariability(1A)From Cp ObservedCp

ActualCp35Effectof2Measurement/2Total36EffectofMeasurementVariability(1B)Alternatively,37Effectof5.15

(Measurement/Tolerance)38EffectofMeasurementVariability(2)UnitisGoodUnitisBadPr(UnitisAccepted)Pr(UnitisRejected)39GageRepeatability&ReproducibilityStudy40GageRepeatability&ReproducibilityStudyMethod1:XandRBreaksdowntheoverallvariationintothreecategoriespart-to-partrepeatabilityReproducibility(Willnotbediscussed)Method2:ANOVAFurtherbreakdowninthereproducibilitycomponentpart-to-partrepeatabilityreproducibility —operatormaineffect —operator×partinteraction41ExampleABlackBeltseekstoassessthecapabilityofoxygenanalyzersusedinthemeasurementofoxygencontentinnitrogen-purgedreflowovens.Fourflowratesofnitrogenwereselectedforhisstudy.Twoanalyzerswererandomlyselected.Verifyifthecurrentoxygenanalyzersareadequate.Thetoleranceoftheprocess300.ThedatacanbefoundinMeasurementSystemAnalysis.MTW.42ExampleStatQualityToolsGageR&RStudy(Crossed)43ExampleSessionWindowGageR&RStudy-ANOVAMethodGageR&R %ContributionStdDevStudyVar%StudyVar%ToleranceSource

VarComp

(ofVarComp)

(SD)

(5.15*SD)

(%SV)

(SV/Toler)TotalGageR&R5.4507.382.334512.022727.164.01Repeatability0.4000.540.63223.25567.361.09Reproducibility5.0506.842.247311.573626.153.86Analyzer3.7245.041.92989.938222.453.31Analyzer*FlowRate1.3261.801.15175.931213.401.98Part-To-Part68.41092.628.271042.595896.2414.20TotalVariation73.860100.008.594244.2600100.0014.75NumberofDistinctCategories=544NumberofDistinctCategoriesThenumberofdistinctcategoriesrepresentsthenumberofgroupswithintheprocessdatathatthemeasurementsystemcandiscern.

If10differentpartswereusedinthegagemeasurementstudy,and4distinctcategoriesweredistinguished.Thismeansthatsomeofthose10partsarenotdifferentenoughtobediscernedasbeingdifferentbythemeasurementsystem.Highernumberofdistinctcategoriesimpliesamoreprecisegage.45NumberofDistinctCategoriesAutomobileIndustryActionGroup(AIAG)recommendations:Categories Remarks <2 Systemcannotdiscernonepartfromanother =2 Systemcanonlydividedataintwogroups e.g.highandlow =3 Systemcanonlydividedatainthreegroups e.g.low,middleandhigh

4 Systemisacceptable46UsesofP/TandP/PV(%R&R)TheP/Tratioisthemostcommonestimateofmeasurementsystemprecision.Thisestimatemaybeappropriateforevaluatinghowwellthemeasurementsystemcanperformwithrespecttothespec.Specifications,however,mustbeappropriatelyselected.Generally,theP/Tratioisagoodestimatewhenthemeasurementsystemisonlyusedtoclassifyproductionsamples.Eventhen,ifprocesscapability(Cpk)isnotadequate,theP/Tratiomaygiveyouafalsesenseofsecurity.TheP/TV(%R&R)isthebestmeasurefortheBlackBelt.Thisestimateshowwellthemeasurementsystemperformswithrespecttotheoverallprocessvariation.%R&Risthebestestimatewhenperformingprocessimprovementstudies.Caremus