6ProcessCapability

ProcessCapabilityTQM-UniversityofMichigan1PatHammett1ProcessCapabilityAnalysis2ProcessCapabilityAnalysisnobjectiveistodeterminehowwelltheoutputofaprocessmeetsspecificationlimitssetbyengineeringrequirementsorthecustomer.ncompareprocessvariationandtolerancewidth.+3σ-3σLSLUSLTargetProcessCapabilityTQM-UniversityofMichigan2PatHammett3Target,Tolerance&SpecificationnTarget(nominal)-desiredvalueofacharacteristic.nTolerance-specifiesanallowabledeviationrelativetoatargetvaluewhereacharacteristicisstillacceptable.nSpecification25.4+/-0.05mmnNominal___tolerance___USL___LSL___TargetUpperSpecificationLimit(USL)LowerSpecificationLimit(LSL)+t-t4ShiftinQualityPhilosophynOldThinking–(GoalPostMentality)anywhereinsidespecificationlimitsisequallyasgood.nNewThinking(TaguchiPhilosophy)–anydeviationfromtargethasincreasingloss(nominalisbetter).TargetValueLost($$)ValueforaQualityCharacteristicDeviationfromTargetLSLUSLxUSLLSLAnywhereinbetweenisequallyasgoodGoalPostMentalityTaguchiLossFunctionProcessCapabilityTQM-UniversityofMichigan3PatHammett5AssessingProcessCapabilitynProcesscapabilityindicesareusedtoassesstheabilityofaprocesstomeetspecification.Better(LowDispersion,OffTarget)Bad(HighDispersion)Best(LowDispersion,OnTarget)6ProcessCapabilityIndicesnCommonProcessCapabilityIndicesnCp,Pp,CR,PRnCpk,Ppk,CpmnKeyIssues:nExcludeorincludeprocesscentering.nExclude:Cp,Pp,CR,PRnInclude:Cpk,Ppk,CpmnUseshort-termorlong-termvariationnShortTerm(CapabilityIndices):Cp,CR,Cpk,CpmnLongTerm(PerformanceIndices):Pp,PR,PpkProcessCapabilityTQM-UniversityofMichigan4PatHammett7Short-termVs.Long-termVariationnShort-term(inherentprocessvariation)nportionofvariationduetocommoncausesonly,oftenestimatedfromcontrolchartsusing:nTotalprocessvariation-nvariationduetobothcommonandspecialcauses,usuallyestimatedbysamplestandarddeviation.Note:ifnospecialcausesormeanshiftsexist,thisvariationestimatewillbesimilartotheinherentvariation.nInExcel:=stdev(array)()∑=--niinxSx121==ˆ:RangeMovingor,=ˆ:ChartRange22dMRdRss8CpIndexnCpmeasurestherelationshipbetweenthetolerancewidthandthetotalrangeofprocessvariation.nCpdoesnotconsiderthelocationofthemeanandthereforerepresentsthepotentialoftheprocesstoproducecharacteristicswithinspecification.26LSL-USL=sigma)(6ionWidthSpecificatdRCp==ssProcessCapabilityTQM-UniversityofMichigan5PatHammett9CpExamplesCp=0.6745,500defects/MillionCp=1.02700defects/millionCp=2.0lessthan1defect/millionnHigherCpindexvalue,thefewerdefectsweexpecttoproduceifprocessiscentered.nexamplesbelowassumenormaldistribution.10PpVs.CpnPpusesthesameformulaasCp,however,thelong-termvariationisused.s6LSL-USL=sigma)(6ionWidthSpecificat=PpWhereσisestimatedbyS(samplestandarddeviation)ProcessCapabilityTQM-UniversityofMichigan6PatHammett11CR–CapabilityRationCR=1/CpPR=1/PpnTheCapabilityRatio(CR)isoftenpreferredtoCpbecauseithasagreaterintuitiveappeal.nCRrepresentsthepercentofthetolerancewidthusedbyvariation.nCR=0.5à50%oftoleranceisusednRefertopreviousslideshowingCp=2.012CpExamplenAseatpostmanufacturerisrequiredtomakepoststoaspecificationof25.4+/-0.05mm.nSupposetheirshort-termvariationis0.015andtheirlongtermvariationis0.022.nComputeCp,Pp,CR,andPR?nOverthelong-term,whatpercentageoftheirtoleranceisusedbyvariation?Howmanypostsaredefective?ProcessCapabilityTQM-UniversityofMichigan7PatHammett13CpkIndexnCpktakesintoaccountanydifferencebetweenthedesigntargetandtheactualprocessmean.LSLUSLTargetXCpkUCpkLs3=UXUSLCpk-s3=LLSLXCpk-Cpk=min(CpkL,CpkU)14PpknPpk=sameasCpkexceptitusesthelongtermvariation(i.e.,samplestandarddeviation).s3=UXUSLPpk-s3=LLSLXPpk-Ppk=min(PpkL,PpkU)ProcessCapabilityTQM-UniversityofMichigan8PatHammett15Cpm(TaguchiIndex)nMorealignedwithtaguchilossfunctionbecauseitgivesmoreimportancetotarget(T).22)(6sm+--=TLSLUSLCpmDecision-MakingwithCpandCpkSomeitemstoconsiderpriortomakingdecisionstoreworkaprocesstoimproveitscapabilityratio.ntheprocesswhichproducesthedataisstableor(in-statisticalcontrol).EstablishesPredictability.nindividualmeasurementsfromtheprocessdataarefromanormaldistribution(orapproximatelynormal).(note:ifnotmoreadvancedtechniquesmaybeappropriate).ncomputedindexreasonablyestimates“true”value.ncapabilityindicesarestatisticsandthereforemaychangewithsamplesize(i.e,confidenceincreaseswithmoredata--typically~100(min.30).nexample,acomputedCpkof1.05maybefromaprocesswhose“Cpk”is1.40or0.90ifmoredataweretaken.(refertoconfidencelimits).ProcessCapabilityTQM-UniversityofMichigan9PatHammett17TranslatingProcessCapabilityintoDefectsPerMillion(DPM)nIfdataarenormallydistributedandin-control,wemayusethenormaldistributionfunctiontoestimatethenumberofdefects.nNote:Zequationstandardizesavariablesothatitmaybeusedwithnormaldistributionfunctions.nToday’sbenchmarkistoexpressdefectsintermsofdefectspermillion(DPM)withthegoalbeinglessthan1defectpermillion.Z=X-μσ18CapabilityandNormalDistributionnToestimatethenumberofdefects,thevalueXwillbeeithertheUSLorLSL.nToestimateμ,wemayusetheprocessmeanorthegrandmean(Xdouble-bar)fromX-barcharts.nToestimateσ:nifrangecontrolchartdataavailable--useR-bar/d2nifnocontrolch