ProcessCapabilityAnalysis(MeasurePhase)ScopeofModuleProcessVariationProcessCapabilitySpecification,ProcessandControlLimitsProcessPotentialvsProcessPerformanceShort-TermvsLong-TermProcessCapabilityProcessCapabilityforNon-NormalDataCycle-Time (ExponentialDistribution)RejectRate (BinomialDistribution)DefectRate (PoissonDistribution)ProcessVariationProcessVariationistheinevitabledifferencesamongindividualmeasurementsorunitsproducedbyaprocess.SourcesofVariationwithinunit (positionalvariation)betweenunits (unit-unitvariation)betweenlots (lot-lotvariation)betweenlines (line-linevariation)acrosstime (time-timevariation)measurementerror (repeatability&reproducibility)TypesofVariationInherentorNaturalVariationDuetothecumulativeeffectofmanysmallunavoidablecausesAprocessoperatingwithonlychancecausesofvariationpresentissaidtobe“instatisticalcontrol”TypesofVariationSpecialorAssignableVariationMaybedueto a)improperlyadjustedmachine b)operatorerror c)defectiverawmaterialAprocessoperatinginthepresenceofassignablecausesofvariationissaidtobe“out-of-control”ProcessCapabilityProcessCapabilityistheinherentreproducibilityofaprocess’soutput.Itmeasureshowwelltheprocessiscurrentlybehavingwithrespecttotheoutputspecifications.Itreferstotheuniformityoftheprocess.Capabilityisoftenthoughtofintermsoftheproportionofoutputthatwillbewithinproductspecificationtolerances.Thefrequencyofdefectivesproducedmaybemeasuredina) percentage(%)b) partspermillion(ppm)c) partsperbillion(ppb)ProcessCapabilityProcessCapabilitystudiescan

indicatetheconsistencyoftheprocessoutputindicatethedegreetowhichtheoutputmeetsspecificationsbeusedforcomparisonwithanotherprocessorcompetitorProcessCapabilityvsSpecificationLimitsa)b)c)a)Processishighlycapableb)Processismarginallycapablec)ProcessisnotcapableThreeTypesofLimitsSpecificationLimits(LSLandUSL)createdbydesignengineeringinresponsetocustomerrequirementstospecifythetoleranceforaproduct’scharacteristicProcessLimits(LPLandUPL)measuresthevariationofaprocessthenatural6limitsofthemeasuredcharacteristicControlLimits(LCLandUCL)measuresthevariationofasamplestatistic(mean,variance,proportion,etc)ThreeTypesofLimitsDistributionofIndividualValuesDistributionofSampleAveragesProcessCapabilityIndicesTwomeasuresofprocesscapabilityProcessPotentialCpProcessPerformanceCpuCplCpkProcessPotentialTheCpindexassesseswhetherthenaturaltolerance(6)ofaprocessiswithinthespecificationlimits.ProcessPotentialACpof1.0indicatesthataprocessisjudgedtobe“capable”,i.e.iftheprocessiscenteredwithinitsengineeringtolerance,0.27%ofpartsproducedwillbebeyondspecificationlimits.CpRejectRate1.000.270%1.330.007%1.506.8ppm2.002.0ppbProcessPotentiala)b)c)a)Processishighlycapable(Cp>2)b)Processiscapable(Cp=1to2)c)Processisnotcapable(Cp<1)ProcessPotentialTheCpindexcomparestheallowablespread(USL-LSL)againsttheprocessspread(6).Itfailstotakeintoaccountiftheprocessisnotcenteredbetweenthespecificationlimits.ProcessiscenteredProcessisnotcenteredProcessPerformanceTheCpkindexrelatesthescaleddistancebetweentheprocessmeanandthenearestspecificationlimit.ProcessPerformanceCpkRejectRate1.00.13––0.27%1.10.05––0.10%1.20.02––0.03%1.348.1––96.2ppm1.413.4––26.7ppm1.53.4––6.8ppm1.6794–1589ppb1.7170–340ppb1.833–67ppb1.96––12ppb2.01––2ppbProcessPerformancea)Processishighlycapable(Cpk>1.5)b)Processiscapable(Cpk=1to1.5)c)Processisnotcapable(Cpk<1)a)Cp=2Cpk=2b)Cp=2Cpk=1c)Cp=2Cpk<1Example1SpecificationLimits: 4to16gMachineMeanStdDev(a)104(b)102(c)72(d)131DeterminethecorrespondingCpandCpkforeachmachine.Example1AExample1BExample1CExample1DProcessCapabilityForanormallydistributedcharacteristic,thedefectiverateF(x)maybeestimatedviathefollowing:Forcharacteristicswithonlyonespecificationlimit:a) LSLonlyb) USLonlyLSLUSLExample2SpecificationLimits:4to16gMachineMeanStdDev(a)104(b)102(c)72(d)131Determinethedefectiverateforeachmachine.Example2MeanStdDevZLSLZUSLF(x<LSL)F(x>USL)F(x)104-1.51.566,80766,807133,614102-3.03.01,3501,3502,70072-1.54.566,807366,811131-9.03.001,3501,350LowerSpecLimit=4gUpperSpecLimit=16gProcessPotentialvsProcessPerformance(a)PoorProcessPotential(b)PoorProcessPerformanceLSLUSLLSLUSLExperimentalDesigntoreducevariationExperimentalDesigntocentermeantoreducevariationProcessPotentialvsProcessPerformanceProcessPotentialIndex(Cp)Cpk1.01.82.01.02,699.91,363.31,350.01,350.01,350.01,350.01.2318.3159.9159.1159.1159.11.426.713.413.40.10.02.00.0DefectiveRate(measuredindppm)isdependentontheactualcombinationofCpandCpk..ProcessPotentialvsProcessPerformancea)Cp=2Cpk=2b)Cp=2Cpk=1c)Cp=2Cpk<1Cp–CpkMissedOpportunityAlternativeProcessPerformanceIndexProcesscapabilitystatisticsmeasureprocessvariationrelativetospecificationlimits.TheCpstatisticcomparestheengineeringtoleranceagainsttheprocess’’snaturalvariation.TheCpkstatistictakesintoaccountthelocationoftheprocessrelativetothemidpointbetweenspecifications.Iftheprocesstargetisnotcenteredbetweenspecifications,theCpmstatisticispreferred.ProcessStabilityAprocessisstableifthedistributionofmeasurementsmadeonthegivenfeatureisconsistentovertime.TimeStableProcessTimeUnstableProcessucllclucllclWithinvsOverallCapabilityWithinCapability(previouslycalledshort-termcapability)showstheinherentvariabilityofamachine/processoperatingwithinabriefperiodoftime.OverallCapability(previouslycalledlong-termcapability)showsthevariabilityofamachine/processoperatingoveraperiodoftime.Itincludessourcesofvariationinadditiontotheshort-termvariability.WithinvsOverallCapabilityWithinOverallSampleSize30––50units100unitsNumberofLotssinglelotseverallotsPeriodofTimehoursordaysweeksormonthsNumberofOperators singleoperatordifferentoperatorsProcessPotentialCpPpProcessPerformanceCpkPpkWithinvsOverallCapabilityWithinCapabilityOverallCapabilityThekeydifferencebetweenthetwosetsofindicesliesintheestimatesforWithinandOverall.EstimatingWithinandOverallConsiderthefollowingobservationsfromaControlChart:S/NX1X2…XkMean Range StdDev1 x1,1x2,1…xk,1X1R1S12 x1,2x2,2…xk,2X2R2S2:::::::m x1,mx2,m…xk,mXmRmSmTheoverallvariationOverallisestimatedby–––EstimatingWithinandOverallThewithinvariationWithinmaybeestimatedbyoneofthefollowing:(a)R-barMethodwhered2isaShewhartconstant=(k)(b)S-barMethodwherec4isaShewhartconstant=(k)(c)PooledStandardDeviationMethodInMiniTab,thePooledStandardDeviationisthedefaultmethod.EstimatingWithinandOverallIncaseswherethereisonly1observationpersub-group(i.e.k=1),theMovingRangeMethodisused,where.ThewithinvariationWithinisthenestimatedusingeithera)theAverageMovingRange:b)theMedianMovingRange:Example3Thelengthofacamshaftforanautomobileengineisspecifiedat600±±2mm.Controlofthelengthofthecamshaftiscriticaltoavoidscrap/rework.Thecamshaftisprovidedbyanexternalsupplier.Assesstheprocesscapabilityforthissupplier.ThedataisavailableinProcessCapabilityAnalysis.MTW.Example3StatQualityToolsCapabilityAnalysis(Normal)Example3Example3AHistogramofcamshaftlengthsuggestsmixedpopulations.Furtherinvestigationrevealedthattherearetwosuppliersforthecamshaft.Datawascollectedovercamshaftsfrombothsources.Arethetwosupplierssimilarinperformance?Ifnot,whatareyourrecommendations?Example3AStatQualityToolsCapabilitySixpack(Normal)Example3AExample3AWhat’sSixSigmaQuality——ThenOriginalDefinitionbyMotorola:ifthespecificationlimitsareatleast±±6awayfromtheprocessmean,i.e.Cp2,andtheprocessshiftsbylessthan1.5,i.e.Cpk1.5,thentheprocesswillyieldlessthan3.4dppmrejects.66Shift1.54.5What’sSixSigmaQuality——NowMikelJHarryclaimsthattheprocessmeanbetweenlotswillvary,withanaverageprocessshiftof1.5.k=z+1.5k=z+1.5Shift1.5zNote:SigmaCapability=??(dpmo)?(dppm)ProcessCapabilityforNon-NormalDataNoteverymeasuredcharacteristicisnormallydistributed.CharacteristicDistributionCycleTimeExponentialRejectRate BinomialDefectRate PoissonProcessCapabilityforCycleTimeTheWeibullDistributionisageneralfamilyofdistributionwithwherescaleparameteristhevalueatwhichCDF=68.17%,andshapeparameterdeterminestheshapeofthePDF.ProcessCapabilityforCycleTimeAt=1,theWeibullDistributionisreducedtoForanExponentialDistribution,TheExponentialDistributionisthusaWeibullDistributionwith=1.Weibull(x;=1,)Exponential(x;)Example4Acustomerservicemanagerwantstodeterminetheprocesscapabilityforhisdepartment.Aprimaryperformanceindexisthetimetakentocloseacustomercomplaint.Thegoalforthisindexistocloseacomplaintwithinonecalendarweek.Performanceoverthelast400complaintswasreviewed.Example4StatQualityToolsCapabilityAnalysis(Weibull)Example4Example4AStatQualityToolsCapabilitySixpack(Weibull)Example4AProcessCapabilityforRejectRateForaNormalDistribution,theproportionofpartsproducedbeyondaspecificationlimitisRejectRateProcessCapabilityforRejectRateThus,foreveryrejectratethereisanaccompanyingZ-Score,whereRecallthatHenceProcessCapabilityforRejectRateEstimationofPpkforRejectRateDeterminethelong-termrejectrate(p)Determinetheinversecumulativeprobabilityforp,usingCalcProbabilityDistributionNormalZ-ScoreisthemagnitudeofthereturnedvaluePpkisone-thirdoftheZ-ScoreExample5Asalesmanagerplanstoassesstheprocesscapabilityofhistelephonesalesdepartment’shandlingofincomingcalls.Thefollowingdatawascollectedoveraperiodof20days:numberofincomingcallsperdaynumberofunansweredcallsperdaysExample5StatQualityToolsCapabilityAnalysis(Binomial)Example5Ppk=0.25ProcessCapabilityforDefectRateOtherapplications,approximatingaPoissonDistribution:errorratesparticlecountchemicalconcentrationProcessCapabilityforDefectRateEstimationofYtpforDefectRateDefinesizeofaninspectionunitDeterminethelong-termdefectsperunit(DPU)DPU =TotalDefectsTotalUnitsDeterminethethroughputyield(Ytp)Ytp=exp{–DPU}ProcessCapabilityforDefectRateEstimationofSigma-CapabilityforDefectRateDeterminetheopportunitiesperunitDeterminethelong-termdefectsperopportunity(d)d =defectsperunitopportunitiesperunitDeterminetheinversecumulativeprobabilityford,usingCalcProbabilityDistributionNormalZ-ScoreisthemagnitudeofthereturnedvalueSigma-Capability=Z-Score+1.5Example6Theprocessmanagerforawiremanufacturerisconcernedabouttheeffectivenessofthewireinsulationprocess.Randomlengthsofelectricalwiringaretakenandtestedforweakspotsintheirinsulationbymeansofatestvoltage.Thenumberofweakspotsandthelengthofeachpieceofwirearerecorded.Example6StatQualityToolsCapabilityAnalysis(Poisson)Example6DefectsperUnit=0.0265194ThroughputYield=exp{––DPU}=exp{––0.0265194}=0.9738c.f.First-TimeYield=2/100=0.02Example6Define1InspectionUnit=125unitlengthofwirei.e.Units=Length125Example6AStatQualityToolsCapabilityAnalysis(Poisson)Example6ADefectsperUnit=3.31493ThroughputYield=exp{––DPU}=exp{––3.31493}=0.0363c.f.First-TimeYield=2/100=0.02Example6BDefectsperUnit=3.31493OpportunitiesperUnit=1DefectsperOpportunity=3.31493Z-Score=???Example6B1inspectionunit=1unitlengthofwireOpportunitiesperUnit=1DefectsperOpportunity=32912,406=0.0265Z-Score=Abs{–1(0.0265)}=1.935Sigma-Capability=Z-Score+1.5=3.435DPUZ-ScoresChoiceofSixSigmaMetric9、靜夜夜四無無鄰，，荒居居舊業(yè)業(yè)貧。。。12月月-2212月月-22Wednesday,December7,202210、雨中黃葉葉樹，燈下下白頭人。。。22:58:4122:58:4122:5812/7/202210:58:41PM11、以我獨(dú)沈沈久，愧君君相見頻。。。12月-2222:58:4122:58Dec-2207-Dec-2212、故人江海海別，幾度度隔山川。。。22:58:4122:58:4122:58Wednesday,December7,202213、乍乍見見翻翻疑疑夢夢，，相相悲悲各各問問年年。。。。12月月-2212月月-2222:58:4122:58:41December7,202214、他鄉(xiāng)生白白發(fā)，舊國國見青山。。。07十二二月202210:58:41下下午22:58:4112月-2215、比不不了得得就不不比，，得不不到的的就不不要。。。。十二月月2210:58下下午12月月-2222:58December7,202216、行動(dòng)出成成果，工作作出財(cái)富。。。2022/12/722:58:4122:58:4107December202217、做前，能能夠環(huán)視四四周；做時(shí)時(shí)，你只能能或者最好好沿著以腳腳為起點(diǎn)的的射線向前前。。10:58:41下下午10:58下午22:58:4112月-229、沒有失敗敗，只有暫暫時(shí)停止成成功！。12月-2212月月-22Wednesday,December7,202210、很很多多事事情情努努力力了了未未必必有有結(jié)結(jié)果果，，但但是是不不努努力力卻卻什什么么改改變變也也沒沒有有。。。。22:58:4122:58:4122:5812/7/202210:58:41PM11、成功就是日日復(fù)一日那一一點(diǎn)點(diǎn)小小努努力的積累。。。12月-2222:58:4222:58Dec-2207-Dec-2212、