MSA測量系統(tǒng)報告

TrainingMaterialfor

MEASUREMENT

SYSTEM

ANALYSIS

Contents:INTRODUCTIONFORMEASUREMENTSYSTEMANALYSISGENERALMETHODSILLUSTRATIONFORMEASUREMENTSYSTEMANALYSISVARIABLEGAGEANALYSISMETHOD1)THEAVERAGE-RANGEMETHOD2)THEANOVAMETHODATTRIBUTEGAGEANALYSISMETHOD1)SHORTMETHOD2)HYPOTHESISTESTANALYSIS3)SIGNALDETECTIONTHEORY4)LONGMETHODACCEPTABILITYCRITERIACONCLUSIONFOURMETHODSCOMPARISONIntroduction:BasicrequirementsbyQS-9000&TS16949BaseonQS9000&TS16949requirements,allmeasurementsystemwhichwerementionedinQualityPlanshouldbeconductedMeasurementSystemAnalysis.MSARequirementIntroduction:ThecategoryofMeasurementSystemMostindustrialmeasurementsystemcanbedividedtwocategories,oneisvariablemeasurementsystem,anotherisattributemeasurementsystem.Anattributegagecannotindicatehowgoodorhowbadapartis,butonlyindicatesthatthepartisacceptedorrejected.ThemostcommonoftheseisaGo/No-gogage.VariableGageAttributeGage(Go/No-goGage)Introduction:WhatisameasurementprocessOperationOutputInputGeneralProcessMeasurementAnalysisValueDecisionProcesstobeManagedMeasurementProcessMeasurement:Theassignmentofanumericalvaluetomaterialthingstorepresenttherelationsamongthemwithrespecttoaparticularprocess.MeasurementProcess:Theprocessofassigningthenumericalvaluetomaterialthings.Introduction:WhatarethevariationsofmeasurementprocessIntroduction:WhatarethevariationsofmeasurementprocessMeasurement(Observed)Value=ActualValue+VarianceofTheMeasurementSystem2σobs=

2σactual+

σvarianceofthemeasurementsystem2Introduction:Wheredoesthevariationofmeasurementsystemcomefrom?TheFiveCharacterizationsofMeasurementSystem:

1.LocationVariation:Bias;Stability;Linearity

Bias

isthedifferencebetweentheobservedaverageofmeasurementsandareferencevalue.Biasisoftenreferredtoasaccuracy.ItisasystematicerrorcomponentofthemeasurementsystemIntroduction:Wheredoesthevariationofmeasurementsystemcomefrom?TheFiveCharacterizationsofMeasurementSystem:

1.LocationVariation:Bias;Stability;Linearity

Stability(Alias:Drift):Stabilityisthetotalvariationinthemeasurementsobtainedwithameasurementsystemonthesamemasterorpartswhenmeasuringasinglecharacteristicoveranextendedtimeperiod.Astablemeasurementprocessisinstatisticalcontrolwithrespecttolocation.StabilityIntroduction:Wheredoesthevariationofmeasurementsystemcomefrom?TheFiveCharacterizationsofMeasurementSystem:

1.LocationVariation:Bias;Stability;Linearity

Linearityisthedifferenceinthebiasvaluesthroughtheexpectedoperatingrangeofthemeasurementinstrument.Itisasystematicerrorcomponentofthemeasurementsystem.LinearityIntroduction:Wheredoesthevariationofmeasurementsystemcomefrom?TheFiveCharacterizationsofMeasurementSystem:2.WidthVariation:Repeatability;Reproducibility;GageR&RRepeatabilityisthevariationinmeasurementsobtainedwithonemeasurementinstrumentwhenusedseveraltimeswhilemeasuringtheidenticalcharacteristiconthesamepartbyanappraiser.ItisaWithin-systemvariation,commonlyreferredtoasE.V.---EquipmentVariation.RepeatabilityIntroduction:Wheredoesthevariationofmeasurementsystemcomefrom?TheFiveCharacterizationsofMeasurementSystem:2.WidthVariation:Repeatability;Reproducibility;GageR&RReproducibilityisthevariationintheaverageofthemeasurementsmadebydifferentappraisersusingthesamegagewhenmeasuringtheidenticalcharacteristicsofthesamepart.Itisbetween-systemvariation,commonlyreferredtoasA.V.---AppraiserVariation.ReproducibilityIntroduction:Wheredoesthevariationofmeasurementsystemcomefrom?TheFiveCharacterizationsofMeasurementSystem:2.WidthVariation:Repeatability;Reproducibility;GageR&RGageR&RmeansGagerepeatabilityandreproducibility,whichcombinedestimateofmeasurementsystemrepeatabilityandreproducibility.ThiscombinedmeasurementerrortheniscomparedwiththeprocessoutputvariabilitytocomputethegagepercentageR&R(%R&R).The%R&Risthebasisformakingajudgmentofwhetherthemeasurementsystemisgoodenoughtomeasuretheprocess.AnalysisTechniques:CurrentlytherearethreetechniquesforvariablemeasurementsystemandfourtechniquesforattributemeasurementsystemanalysiswererecommendedbyAIAGMSAReferenceManual.RangeMethodAverage-RangeMethodANOVAShortMethodLongMethodHypothesisTestAnalysesSignalDetectionTheoryFollowingsaresomepracticalexamplestoillustratehowtoperformfourmethodsrespectively.VariableGageAttributeGageAnalysisTechniques:PreparationbeforeMSATheapproachtobeusedshouldbeplanned.Thenumberofappraisers,numberofsampleparts,andnumberofrepeatreadingsshouldbedeterminedinadvance.Theappraisersshouldbeselectedformthosewhonormallyoperatetheinstrument.Thesamplepartsmustbeselectedfromtheprocessandrepresentitsentireoperatingrange.Theinstrumentmusthaveadiscriminationthatallowsatleastone-tenthoftheexpectedprocessvariationofthecharacteristictobereaddirectly.Themeasurementprocedureshouldbedefinedinadvancetoensuretheconsistentmeasuringmethod.AnalysisTechniques:VariableGageAnalysisGeneralGageR&RStudy:TheAverageandRangeMethodTheANOVAMethodThecommonstepforconductingGageR&Rstudy:1.Verifycalibrationofmeasurementequipmenttobestudied.2.Obtainasampleofpartsthatrepresenttheactualorexpectedrangeofprocessvariation.3.Addaconcealedmarktoeachidentifyingtheunitsasnumbers1through10.Itiscriticalthatyoucanidentifywhichunitiswhich.Atthesametimeitisdetrimentaliftheparticipantsinthestudycantelloneunitfromtheother(maybiastheirmeasurementshouldtheyrecallhowitmeasuredpreviously).4.Request3appraisers.RefertotheseappraisersasaA,B,andCappraisers.Ifthemeasurementwillbedonerepetitivelysuchasinaproductionenvironment,itispreferabletousetheactualappraiserthatwillbeperformingthemeasurement.Forextremecases,aminimumoftwoappraiserscanbeused,butthisisstronglydiscouragedasalessaccurateestimateofmeasurementvariationwillresult.5.LetappraiserAmeasure10partsinarandomorderwhileyourecordthedatanotingtheconcealedmarking.LetappraisersBandCmeasurethesame10partsNote:Donotallowtheappraiserstowitnesseachotherperformingthemeasurement.Thereasonisthesameaswhytheunitmarkingsareconcealed,TOPREVENTBIAS.6.Repeatthemeasurementsforallthreeappraisers,butthistimepresentthesamplestoeachinarandomorderdifferentfromtheoriginalmeasurements.Thisistoagainhelpreducebiasinthemeasurements.AnalysisTechniques:VariableGageAnalysis……10Parts3Appraisers3TrialsTheAverageandRangeMethod:Arangecontrolchartiscreatedtodetermineifthemeasurementprocessisstableandconsistent.Foreachappraisercalculatetherangeoftherepeatedmeasurementsforthesamepart.AnalysisTechniques:VariableGageAnalysisAnalysisTechniques:VariableGageAnalysisTheaveragerangeforeachoperatoristhencomputed.Theaverageofthemeasurementstakenbyanoperatoriscalculated.Acontrolchartofrangesiscreated.Thecenterlinerepresentstheaveragerangeforalloperatorsinthestudy,whiletheupperandlowercontrollimitconstantsarebasedonthenumberoftimeseachoperatormeasuredeachpart(trials).AnalysisTechniques:VariableGageAnalysisThecenterlineandcontrollimitsaregraphedontoacontrolchartandthecalculatedrangesarethenplottedonthecontrolchart.Therangecontrolchartisexaminedtodeterminemeasurementprocessstability.Ifanyoftheplottedrangesfalloutsidethecontrollimitsthemeasurementprocessisnotstable,andfurtheranalysisshouldnottakeplace.However,itiscommontohavetheparticularoperatorre-measuretheparticularprocessoutputagainandusethatdataifitisin-control.AnalysisTechniques:VariableGageAnalysisRepeatability-EquipmentVariation(E.V.)Theconstantd2*isbasedonthenumberofmeasurementsusedtocomputetheindividualranges(n)ortrials,thenumberofpartsinthestudy,andthenumberofdifferentconditionsunderstudy.TheconstantK1isbasedonthenumberoftimesapartwasrepeatedlymeasured(trials).Theequipmentvariationisoftencomparedtotheprocessoutputtoleranceorprocessoutputvariationtodetermineapercentequipmentvariation(%EV).AnalysisTechniques:VariableGageAnalysisReproducibility-AppraiserVariation(A.V.)Xdiffisthedifferencebetweenthelargestaveragereadingbyanoperatorandthesmallestaveragereadingbyanoperator.TheconstantK2isbasedonthenumberofdifferentconditionsanalyzed.Theappraiservariationisoftencomparedtotheprocessoutputtoleranceorprocessoutputvariationtodetermineapercentappraiservariation(%AV).AnalysisTechniques:VariableGageAnalysisRepeatabilityandReproducibility(GageR&R)Thegageerror(R&R)iscomparedtotheprocessoutputtolerancetoestimatetheprecisiontotoleranceratio(P/Tratio).Thisisimportanttodetermineifthemeasurementsystemcandiscriminatebetweengoodandbadoutput.Thebasicinterestofstudyingthemeasurementprocessistodetermineifthemeasurementsystemiscapableofmeasuringaprocessoutputcharacteristicwithitsownuniquevariability.ThisisknowasthePercentR&R(P/Pratio,%R&R),andcalculatedasfollows:AnalysisTechniques:VariableGageAnalysisProcessorTotalVariation:Iftheprocessoutputvariation(m)isnotknown,thetotalvariationcanbeestimatedusingthedatainthestudy.Firstthepartvariationisdetermined:Rpistherangeofthepartaverages,whileK3isaconstantbasedonthenumberofpartsinthestudy.Thetotalvariation(TV)isjustthesquarerootofthesumofthesquaresofR&RandthepartvariationAnalysisTechniques:VariableGageAnalysisTheANOVAMethod:AweaknesswiththeAverage-RangemethodofusingtherangetodeterminegageR&Risthatitdoesnotconsiderthevariationintroducedintoameasurementthroughtheinteractionbetweendifferentconditions(appraiser)andthegage.Consequently,toaccountforthisvariationananalysisofvariancemethod(ANOVA)isutilized.Inaddition,whenthesamplesizeincreases,useoftherangetoestimatethevariationinnotveryprecise.Furthermore,withsoftwarepackagesreadilyavailable,theANOVAmethodisaviablechoice.Thetotalvariationinanindividualmeasurementequals:Theparttopartvariationisestimatedbyp2;theoperatorvariationisestimatedbyo2;theinteractioneffectisestimatedbyop2;whilerepeatabilityisestimatedbyr2AnalysisTechniques:VariableGageAnalysisPart:Operator:Interaction:Repeatability:AnalysisTechniques:VariableGageAnalysisTotal:ThegageR&Rstatisticsarethencalculatedasfollows:MeasurementError:Part:Operator:Interaction:Reproducibility:Repeatability:MeasurementError:Total:AnalysisTechniques:VariableGageAnalysisAcceptabilityCriteria:Thegagerepeatabilityandreproducibility:%R&R(P/Pratio:%totaloftotalvariance;P/Tration:%totaloftolerance):Lessthan10%Outstanding10%to20%Capable20%to30%MarginallyCapableGreaterthan30%NOTCAPABLEFortheP/PratioandtheP/Tratio,eitherorbothapproachescanbetakendependingontheintendeduseofthemeasurementsystemandthedesiresofthecustomer.Generally,Ifthemeasurementsystemisonlygoingtobeusetoinspectiftheproductmeetsthespecs,thenweshouldusethe%R&Rbaseonthetolerance(P/Tratio).Ifthemeasurementsystemisgoingtobeuseforprocessoptimization/characterizationanalysis,thenweshouldusethe%R&Rbaseontotalvariation(P/Pratio).AnalysisTechniques:VariableGageAnalysisAcceptabilityCriteria:ForaGagedeemedtobeINCAPABLEforit’’sapplication.Theteammustreviewthedesignofthegagetoimproveit’’sintendedapplicationandit’sabilitytomeasurecriticalmeasurementscorrectly.Also,ifare-calibrationisrequired,pleasefollowcaliberationsteps.Ifrepeatabilityislargecomparedtoreproducibility,thereasonsmightbe:1)theinstrumentneedsmaintenance,thegageshouldberedesigned2)thelocationforgagingneedstobeimproved3)thereisexcessivewithin-partvariation.Ifreproducibilityislargecomparedtorepeatability,thenthepossiblecausescouldbe:1)inadequatetrainingonthegage,2)calibrationsarenoteffective,3)afixturemaybeneededtohelpusethegagemoreconsistently.AnalysisTechniques:VariableGageAnalysisTheMeasurementBias:Usingacertifiedsample,andacontrolchartofrepeatedmeasurements,thebiasofameasurementprocesscanbedetermined.Biasisthedifferencebetweentheknownvalueandtheaverageofrepeatedmeasurementoftheknownsample.Biasissometimescalledaccuracy.ProcessVariation=6SigmaRangePercentBias=BIASProcessVariationAnalysisTechniques:VariableGageAnalysisLinearity:Linearityofameasurementprocessisthedifferenceinthebiasorprecisionvaluesthroughtheexpectedoperatingrangeofthegauge.Toevaluatelinearity,agraphcomparingthebiasorprecisiontotheexpectedoperatingrangeiscreated.Aproblemwithlinearityexistsifthegraphexhibitsdifferentbiasorprecisionfordifferentexpectedoperatingranges.Byusingthefollowingprocedure,linearitycanbedetermined.1)Selectfivepartswhosemeasurementscovertheoperatingrangeofthegage.2)Verifythetruemeasurementsofeachpart.3)Haveeachpartberandomlymeasured12timesonthegagebyoneoperator.4)Calculatethepartaverageandthebiasforeachpart.5)Plotthebiasandthereferencevalues.6)Calculatethelinearregressionlinethatbestfitsthesepoints.AnalysisTechniques:VariableGageAnalysis7)Calculatethegoodnessoffitstatistic:AnalysisTechniques:VariableGageAnalysis8)Determinelinearityandpercentlinearity:Linearity=SlopexProcessvariation(m)%Linearity=100[linearity/ProcessVariation]TheacceptabilitycriteriaofBias,LinearitydependonQualityControlPlan,characteristicbeingmeasuredandgagespeciality,suggestedcriteriaofESGisasfollowing:Under5%-acceptable5%to15%-maybeacceptablebaseduponimportanceofapplication,costofmeasurementdevice,costofrepairs,etc.,Over15%-Considerednotacceptable-everyeffortshouldbemadetoimprovethesystemThestabilityisdeterminedthroughtheuseofacontrolchart.Itisimportanttonotethat,whenusingcontrolcharts,onemustnotonlywatchforpointsthatfalloutsideofthecontrollimits,butalsocareotherspecialcausesignalssuchastrendsandcenterlinehugging.GuidelineforthedetectionofsuchsignalscanbefoundinmanypublicationsonSPC.AnalysisTechniques:AttributeGageStudyShortMethod:AShortMethodexampleforbatterylengthgo/no-gogagestudy:TheShortmethodneedtobeconductbyselecting20partswhichhavebeenmeasuredbyavariablegageinadvance,someofthepartsareslightlybelowandabovebothspecificationlimits.Twoappraisersthenmeasureallpartstwicerandomly.MeasurementResulttable1AnalysisTechniques:AttributeGageStudyAcceptabilitycriteria:Ifallmeasurementresults(fourperpart)agree,thegageisacceptable.Ifthemeasurementresultsdonotagree,thegagecannotbeaccepted,itmustbeimprovedandre-evaluated.Conclusion:Becausetable1listedmeasurementresultsarenotwholeagreement,atpart15#and17#,appraiser’’sdecisionsarenotagree.sothebatterylengthgagecannotbeusedandmustbeimprovedandre-evaluated.AnalysisTechniques:AttributeGageStudyHypothesisTestAnalysis:Shortmethodshouldknowthevariablereferencevalueofsamplesinadvance.However,insomesituationsitishardtorealizetogetallsamplesvariablereferencevalue.Sointhiscase,Hypothesistestanalysisshallbeappliedforgagestudy.IIII

TargetIIIIIUSLLSLAnalysisTechniques:AttributeGageStudyHypothesistestanalysisdependsoncrosstabulationmethodwhichneedstotakearandomsampleof50partsfromthepresentprocessanduse3appraiserswhomake3measurementsoneachpartanddecideifthepartisacceptableornot.Appraisersmeasurethepartsandifthepartiswithinlimitstheygive“1”andifnottheygive““0”andwritethoseresultsinatable.Inordertoeliminateanybiasproduced,thelabeledsamplesaremixedbeforegivingtoappraisersforidentificationineachtrails.Followingtable2listedfillergagemeasuringresultsforthebattery\weldinggap:……50Samples3Appraisers3TrialsTable2FillergagemeasuringresultTable2FillergagemeasuringresultTable2FillergagemeasuringresultAnalysisTechniques:AttributeGageStudyInordertodeterminethelevelofagreementamongtheappraisers,weappliedCohen’’sKappawhichisusedtoassessinter-raterreliabilitywhenobservingorotherwisecodingqualitative/categoricalvariables.Itcanmeasuretheagreementbetweentheevaluationsoftworaterswhenbothareratingthesameobject.Step1.Organizethescoreintoacontingencytable.Sincethevariablebeingratedhastwocategories,thecontingencytablewillbea2*2table:Table3AnalysisTechniques:AttributeGageStudyA*BCross-TabulationTable3AnalysisTechniques:AttributeGageStudyStep2.Computetherowtotals(sumacrossthevaluesonthesamerow)andcolumntotalsoftheobservedfrequencies.Step3Computetheoveralltotal(showinthetable3).Asacomputationalcheck,besurethattherowtotalsandthecolumntotalssumtothesamevaluefortheoveralltotal,andtheoveralltotalmatchesthenumberofcasesintheoriginaldataset.Step4Computethetotalnumberofagreementsbysummingthevaluesinthediagonalcellsofthetable.Σa=53+89=142Step5Computetheexpectedfrequencyforthenumberofagreementsthatwouldhavebeenexpectedbychanceforeachcodingcategory.ef===21.6Repeattheformulaforothercell,wegototherexpectedcount(showinthetable3).rowtotal*coltotaloveralltotal59*55150Step6Computethesumoftheexpectedfrequenciesofagreementbychance.Σef=21.6+57.6=79.2Step7ComputeKappaK===0.89Step8EvaluateKappa-Ageneralruleofthumbisthatvaluesofkappagreaterthan0.75indicategoodtoexcellentagreement;valueslessthan0.4indicatepooragreement.Repeatabovestep,wecangotfollowingkappameasuresfortheappraisers:Table4AnalysisTechniques:AttributeGageStudyΣa-ΣefN-Σef142-79.2150-79.2Table4Usingthesamestepstocalculatedthekappameasuretodeterminetheagreementofeachappraisertothereferencedecision:Table5TotalsummaryonTable6:AnalysisTechniques:AttributeGageStudyTable5AnalysisTechniques:AttributeGageStudyAnalysisTechniques:AttributeGageStudyTheAIAGMSAreferencemanualedition3providesacceptabilitycriteriaforeachappraisersresults:Definition:FalseAlarm––Thenumberoftimesofwhichtheoperator(s)identifyagoodsampleasabadone.Miss––Thenumberoftimesofwhichtheoperatorsidentifyabadsampleasagoodone.NumberofcorrectdecisionsTotalopportunitiesforadecisionEffectiveness=AnalysisTechniques:AttributeGageStudyNumberofFalseAlarmTotalopportunitiesforadecisionFalseAlarmRate=NumberofFalseAlarmTotalopportunitiesforadecisionMissRate=Sosummarizingalltheinformationoftheexamplewiththistable:Table7AnalysisTechniques:AttributeGageStudyConclusion:ThemeasurementsystemwasacceptablewithappraiserB,marginalwithappraiserA,andunacceptableforC.SoweshalldetermineifthereisamisunderstandingwithappraiserCthatrequiresfurthertrainingandthenneedtore-doMSA.Thefinaldecisioncriteriashouldbebasedontheimpacttotheremainingprocessandfinalcustomer.Generally,themeasurementsystemisacceptableifall3factorsareacceptableormarginal.Minitabalsocanperformattributegageanalysis,butitdidn’tdeclaretheacceptabilitycriteria,soitisnotrecognizedbyQS9000standard.AnalysisTechniques:AttributeGageStudySignalDetectionTheoryistodetermineanapproximationofthewidthoftheregionIIareasoastocalculatethemeasurementsystemGR&R.AlsousedfillergageasexampletoperformSignalDetectionapproach.Thetoleranceis0.45~0.55mm.Theprocessneedstotakearandomsampleof50partsfromthepracticalprocessanduse3appraiserswhomake3measurementsoneachpart,andthengotfollowingtable:Table8IIIITargetIIIIIUSLLSLTable8SignalDetectionTableforFillerGageTable8SignalDetectionTableforFillerGageAnalysisTechniques:AttributeGageStudyAbovetable8showsthe50partsmeasurementresult,“0”standardrejected,““1””standardacceptable,code“-”standardregionI,code““x”standardregionII,code“+”standardregionIII.AndthenbaseonthepartreferencevaluetoarrangeinorderfromMax.toMin.,meanwhiletoshowthecode:Table9RegionIIIRegionIRegionIRegionIIRegionIIAnalysisTechniques:AttributeGageStudyNextstepweshouldfindXavaluewhichlocatedregionI,butisthenearesttoregionII.XbvaluewhichlocatedregionIII,butisthenearesttoregionII.AndthencalculatethedistanceofregionII.dLSL=Xa,LSL-Xb,LSL=0.446697––0.470832=0.024135dUSL=Xa,USL-Xb,USL=0.566152––0.542704=0.0234480.0237910.55––0.45GR&R===0.023791

dUSL+dLSL20.023448+0.0241352%GR&R===0.277=27.7%GR&RUSL-LSLConclusion:The%GR&Rislargerthan10%,butlessthan30%,itmaybeacceptablebaseduponimportanceofapplication,costofmeasurementdevice,costofrepairs,etc.AnalysisTechniques:AttributeGageStudyLongMethodisusedtheconceptoftheGagePerformanceCurve(GPC)todevelopameasurementsystemstudy.Itfocusesonassessingtherepeatabilityandbiasofthemeasurementsystem.ThepurposeofdevelopingaGPCistodeterminetheprobabilityofeitheracceptingorrejectingapartofsomereferencevalue.ThefirststepofLongMethodisthepartselection.Itisnecessarytoknowthepartreferencevaluewhichwasmeasuredwithvariablemeasurementsystem.Theapproachshouldselect8partsasnearlyequidistantintervalsaspractical.TheMaximumandminimumvaluesshouldrepresenttheprocessrange.The8partsmustbemeasured20timeswiththeattributegage.Weuse““m””torepresentthemeasuringtimes,use““a”torepresentthenumberofaccepts.Forthesmallest(orlargest)part,thevaluemustbea=0;Forthelargest(orsmallest)part,thevaluemustbea=20;Forthe6otherparts,thevalue1≤≤a≤≤19.AnalysisTechniques:AttributeGageStudy……8Samples1Appraiser20TrialsAnalysisTechniques:AttributeGageStudyExample:Weuseafillergagetomeasurethefittinggapbetweenbatteryandhandphonewhichs