s黑带培训教材英文4

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––50units100unitsNumberofLotssinglelotseverallotsPeriodofTimehoursordaysweeksormonthsNumberofOperatorssingleoperatordifferentoperatorsProcessPotentialCpPpProcessPerformanceCpkPpkWithinvsOverallCapabilityWithinCapabilityOverallCapabilityThekeydifferencebetweenthetwosetsofindicesliesintheestimatesforWithinandOverall.EstimatingWithinandOverallConsiderthefollowingobservationsfromaControlChart:S/NX1X2…XkMeanRangeStdDev1x1,1x2,1…xk,1X1R1S12x1,2x2,2…xk,2X2R2S2:::::::mx1,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=ƒƒ(dpmo)ƒ(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、静夜四无邻邻，荒居旧业业贫。。12月-2212月-22Thursday,December8,202210、雨中黄黄叶树，，灯下白白头人。。。00:32:2000:32:2000:3212/8/202212:32:20AM11、以我独沈沈久，愧君君相见频。。。12月-2200:32:2000:32Dec-2208-Dec-2212、故故人人江江海海别别，，几几度度隔隔山山川川。。。。00:32:2000:32:2000:32Thursday,December8,202213、乍见翻疑疑梦，相悲悲各问年。。。12月-2212月-2200:32:2000:32:20December8,202214、他乡生白发发，旧国见青青山。。08十二月月202212:32:20上午午00:32:2012月-2215、比比不不了了得得就就不不比比，，得得不不到到的的就就不不要要。。。。。十二月2212:32上上午12月-2200:32December8,202216、行动动出成成果，，工作作出财财富。。。2022/12/80:32:2000:32:2008December202217、做前，能能够环视四四周；做时时，你只能能或者最好好沿着以脚脚为起点的的射线向前前。。12:32:20上上午12:32上午00:32:2012月-229、没没有有失失败败，，只只有有暂暂时时停停止止成成功功！！。。12月月-2212月月-22Thursday,December8,202210、很多多事情情努力力了未未必有有结果果，但但是不不努力力却什什么改改变也也没有有。。。00:32:2000:32:2000:3212/8/202212:32:20AM11、成功功就是是日复复一日日那一一点点点小小小努力力的积积累。。。12月月-2200:32:2000:32Dec-2208-Dec-2212、世间成成事，不不求其绝绝对圆满满，留一一份不足足，