2) Process Capability Analysis.ppt

ProcessCapabilityAnalysis制程能力分析,EWOoiRegionalMasterBlackBeltManagerJune9,2020,1,UnderstandProcessVariation理解制程波动UnderstandProcessPotentialversusProcessCapability理解PP潜在制程能力，PC制程能力Differentiatebetweenshort-termandlong-termcapabilityestimates区分短期和长期制程能力评价ComputeZ-scores,Cp,Cpk,Pp,Ppk计算Z，Cp,Cpk,Pp,PpkInterpretdifferentcapabilitymeasures解释不同的能力测量Analyzeprocesscapabilityforvariabledata,bothnormalandnon-normal正态和非正态分析制程能力Analyzeprocesscapabilityforattributedata.离散型数据的制程能力分析,ModuleObjectives,2,Define/Measure,Analyze,Improve,Control,BaselineCapability基线,Capabilityofneworimprovedprocess新的或者改善后的制程能力,MethodologyRoadMapWhereItIsUsed?,3,ProcessVariationistheinevitabledifferencesamongindividualmeasurementsorunitsproducedbyaprocess.过程波动由测量或是生产制程中必然产生的波动SourcesofVariation波动的来源Withinunit产品内(positionalvariation)Betweenunits产品间（unit-unitvariation)Betweenlots批次间(lot-lotvariation)Betweenlines线体间(line-linevariation)Acrosstime不同时间间(time-to-timevariation)Measurementerror测量误差(repeatability&reproducibility重复性和再现性),ProcessVariation过程波动,4,InherentorNaturalVariation固有波动（偶然误差）Duetothecumulativeeffectofmanysmallunavoidablecauses.Aprocessoperatingwithonlychancecausesofvariationpresentissaidtobe“instatisticalcontrol”由很多小的不可避免的累加的影响造成的。整个制程仅有偶然原因（随机）导致的波动我们叫“统计受控”。,TypeofVariations波动的类型,5,SpecialorAssignableVariation特殊波动Maybeduetoi)Operator操作员来源于ii)Improperlyadjustedmachine不恰当的机器调整ii)Wrongmethod错误的方法iii)Defectiverawmaterial原材料不良Aprocessoperatinginthepresenceofassignablecausesofvariationissaidtobe“out-of-control”制程中表现出特殊波动称为超出控制（制程不可控）,TypeofVariations,6,Aprocessiscapablewhenitsnaturalvariabilityisabletomeetthecustomersspecification(theprocessdistributionfitswellinsidethespec.).当随机波动可以满足客户的规格时，我们称这个制程是有制程能力,ProcessCapability制程能力,7,ProcessCapabilityistheinherentreproducibilityofaprocesssoutput.Itmeasureshowwelltheprocessiscurrentlybehavingwithrespecttotheoutputspecifications.Itreferstotheuniformityoftheprocess.制程能力是制程输出的具有的能力。一个制程能力好坏是与产品的规格相关。,ProcessCapability制程能力,8,Capabilityisoftenthoughtofintermsoftheproportionofoutputthatwillbewithinproductspecificationtolerances.Thefrequencyofdefectivesproducedmaybemeasuredin:能力经常认为是生产的产品满足规格的比例。不良发生的频率可以用下面的来衡量。Percentage(%)比率Partspermillion(ppm)PPM百万不良品Z-scoreZ得分ProcessCapabilityMetrics(Cp,Cpk,Cpm,Pp,Ppk),ProcessCapability制程能力,9,ProcessCapabilitystudiescan制程能力研究可以得到ProvidecurrentlevelofprocessperformanceatMeasurephase在测量阶段，提供当前的制程的水平Indicatethedegreetowhichtheoutputmeetscustomersspecifications指出它们满足客户规格的程度Beusedforcomparisonwithanotherprocessorcompetitor用来对比其他的制程或者竞争对手的能力Provideinformationonprocessentitlement提供制程资格授权的信息Providethemeasureofgainsaftertheimprovementsareinplaceatcontrolphase在控制阶段，提供改善后的成果展示。,ProcessCapability制程能力,10,SpecificationLimits(LSLandUSL)规格界限createdbydesignengineeringinresponsetocustomerrequirementstospecifythetoleranceforaproductscharacteristic基于客户的要求，设计工程师针对产品特性定义的规格ProcessLimits(LPLandUPL)-ProcessMean+3制程界限measuresthevariationofaprocess.thenatural6limitsofthemeasuredcharacteristic过程的变异。用量测参数的6作为界限（整体的individual）ControlLimits(LCLandUCL)SPCControlLimits控制界限measuresthevariationofasamplestatistics(mean,variance,proportion,etc)基于统计样品的变异。（均值XBar）,TypeofLimits界限类型,11,DistributionofIndividualValues单值的分布,DistributionofSampleAverages样品平均值的分布,TypeofLimits界限类型,12,Processishighlycapable高的制程能力b)Processismarginallycapable边缘制程能力c)Processisnotcapable差的制程能力,(a),(b),(c),ProcessCapabilityversusSpecLimits制程能力VS规格,13,Twomeasuresofprocesscapability制程能力的两种衡量：(1)ProcessPotential过程潜在能力指数Cp(2)ProcessPerformance过程绩效CpuCplCpk,ProcessCapabilityIndices过程能力指标,14,TheProcessPotentialorCpindexassesseswhetherthenaturaltolerance6ofaprocessiswithinthespecificationlimits.PP和Cp评估制程的能力是否在规格限内，与均值无关。,ProcessPotential潜在过程能力,15,Cprepresentsthebestaprocesscouldbeifallshiftsanddriftswereperfectlycontrolled.Cpcalculationassumedprocessisrunningontarget.Cp表示制程最好能够做到的。不考虑偏移，假定过程输出的均值与规范中心重合。Itprovidesaninitialtargetforimprovement.Thedifferencebetweentheentitlementandtheactualprocessperformanceisrepresentativeoftheopportunityforimprovement.Cp提供改善最初始的目标。制程授权和实际制程绩效的差异表示改善的机会。,ProcessEntitlement制程授权,16,ACpof1.0indicatesthataprocessisjudgedtobe“capable”,i.e.iftheprocessiscenteredwithinitsengineeringtolerance,0.27%ofpartsproducedwillbebeyondspecificationlimits.Cp=1.0表示过程能力是够的。如果制程中心与设计中心重合，会有0.27%的产品超出规格。CpRejectRate1.000.270%1.330.007%1.506.8ppm2.002.0ppb,ProcessPotential潜在过程能力,17,Processishighlycapable(Cp2)制程能力高（Cp2),b)Processiscapable(Cp=1to2)制程能力够,c)Processisnotcapable(Cp1.5),b)Processiscapable(Cpk=1to1.5),c)Processisnotcapable(CpkQualityToolsCapabilityAnalysisNormal,Example2,43,Includethetargetvalueof10,Example2,44,Example2,45,Thelengthofacamshaftforanautomobileengineisspecifiedat6002Controlofthelengthofthecamshaftiscriticaltoavoidscrap/rework.Eachsubgroupconsistsof5camshafts.Thecamshaftisprovidedbyanexternalsupplier.Assesstheprocesscapabilityforthissupplier.ThedataisavailableinCapability.mtw(C4,C5,C6)一个汽车发动机的凸轮的规格是6002。每个子组中有5个凸轮长度的尺寸。这个凸轮是由外部供应商提供的。根据数据评估一下这个供应商的制程能力。,Example3例3,46,StatQualityToolsCapabilityAnalysisNormal,6002mm,Example3,47,Includethetargetvalueof600mm.,Example3,48,Histogramofcamshaftlengthsuggestsmixedpopulations.FurtherinvestigationRevealedthattherearetwosuppliersforthecamshaft.Datawascollectedovercamshaftsfrombothsources.Arethetwosupplierssimilarinperformance?Ifnot,whatareyourrecommendations?从凸轮长度的直方图上看有多个分布。进一步调查，发现凸轮来自于两个不同的供应商。那么这两个供应商的能力近似吗？如果不是，你的建议是什么？,Example3,49,StatQualityToolsCapabilitySixPackNormal,Example3,50,Example3,51,Adiskischemicallyetchedintoasurface.Thepartscanbereworkedifnotsufficientlyetchedbutwillbescrappedifovertetched.TheSpecificationsare573光盘表面化学蚀刻，蚀刻不充分是可以重工的，过蚀刻的需要报废。规格是573Asamplingofthirtygroupsof5sampleseachweretakenatdifferenttimesintheprocessaftertheetchprocess.按照不同的时间抽检，每次抽检5个样品，共30组。ThedataisavailableinCapability.mtw(C8,C9)数据见Capability.mtw(C8,C9)CalculatethecapabilityoftheEtchingprocessandcommentontheIssuesaBBfacesinreducingrework.计算蚀刻制程能力并且给出建议以减少重工。,Exercise1练习1,52,IncaseswherethebetweenSubgroupsvariations:两个子组间的变异Cannotbeavoided不能避免Becomemajorpartofthetotalprocessvariationcomparedtowithinsubgroupvariation相对于组内变异过程的变异是主要的部分（组内变异远小于过程的变异）thenwewilluseMinitabWithin/BetweenAnalysis那么我用MinitabWithin/Between来分析过程能力,Within/BetweenSubgroupsVariationAnalysis,53,Inthisexample,amanufacturerEngineerwouldliketostudytheprocesscapabilityofthemachinetopouracertainamountofliquidintoeachbottle.Thefillingspecificationsare1003ml.制造工程师希望研究一下倒水灌液体的机器的制程能力，规格是1003ml.Thesamplesaretakenfromfinishedgoods.Thesebottlesaresomewherebetweenoneshiftandthreemonthsold.Ifwesample20randomgroupsof5,whattypeoftestshouldwerun?从成品中抽取样品，这些样品是过去三个月生产出来的，如果我们任意抽20组，每组5个样品，那么我们用哪种方法做制程能力分析。ThedataisavailableinCapability.mtw(C11,C12)NOTE:ExamineandcompareusingbothNormalandBetween/Withinmethods对比用两种不同的方法分析的结果,Example4例4,54,StatQualityToolsCapabilityAnalysisNormal,Example4,55,Example4,56,ResultsofExample4clearlyshowthatscrapisbeingmadeentirelywithinshort-termsamplegroups,butthisisnotreflectedinthecapabilitystudy.Why?结果清楚的表明报废全部是短期的样品组，但是这个不能反映制程能力。为什么？Whendataiscollectedinsubgroups,randomerrorwithinsubgroupsmaynotbetheonlysourceofvariationtoconsider.Theremayalsoberandomerrorbetweensubgroups.ThisconditionishighlightedinthedifferencebetweenCpandPp.当我们收集数据时，变异不仅仅只来自组内的随机误差，也要考虑组间的随机误差。这种情况充分体现了Cp和Pp的不同。However,ifthisbetween-subgroupvariationistrulyunavoidable,understandingandcombiningbothsourcesofsubgroupvariationmayprovideyouwithamorerealisticestimateofthepotentialcapabilityofaprocess不管怎样.组间变异是不可避免的，了解并考虑两种变异的来源可以更真实的评价潜在的制程能力。,Example4,57,Example4,58,Example4,59,Example4,60,CapabilityAnalysis(Between/Within)computesstandarddeviationswithinsubgroupsandbetweensubgroups,oryoumayspecifyhistoricalstandarddeviations.制程能力分析（组间、组内）计算组内和组间的变异，或者可以指定历史的标准的变异。Thesewillbecombined(pooled)tocomputethetotalstandarddeviation.合并计算总的标准变异Thetotalstandarddeviationwillbeusedtocalculatethecapabilitystatistics,suchasCpandCpk.过去我们习惯用总的变异来计算CpandCpk.,CapabilityAnalysis(Between/Within),61,TheLTresultsremainthesamesinceitiscalculatedfromtheoverallstandarddeviationwhichwillnotchange.ThesameholdstruefortheCpm,asitdoesnotuseanestimateofthestandarddeviation.TheshorttermcapabilityisnowusingtheStDev(B/W)2.129incalculationsratherthanStDev(Within)0.17.Thisismoreindicativeofwhatmightbehappeningintheprocess.Withmostofthevariationbeingbatch-to-batch,thisapproachcouldbebetterindeterminingtheSTprocesscapability.长期的制程能力的数据保持不变，由于所用的总变异不变。Cpm也是一样的。短期的过程能力用的是StDev(B/W)2.129而不是StDev(Within)0.17。这就说明过程中有些什么在发生。由于批和批间为最大的变异，这个方法能更好的得到短期过程能力。,CapabilityAnalysis(Between/Within),62,Insomecases,onlyshortterm(within-subgroup)orlongterm(overall)dataisavailable.WhatdoyoudotocomputeCapability?在一些案例中，仅仅得到短期或者长期的数据。我们怎么计算过程能力呢？TheSixSigmamethodologyevolvedbyMotorolahassuggestedthattheLongTermCapabilityberelatedtotheShortTermCapabilitybyaddinga1.5shifttotheShortTermmetrics.源于摩托罗拉的6西格玛的方法建议长期的制程能力就是在短期的制程能力上增加1.5偏移。Zlong=Zshort-1.5Thus,allLongTermmeansareadjustedbyaddinganadditional1.5shifttothemean-inadirectionawayfromthetargetvalue.因此，所有长期的中心值被调整增加1.5偏移-在远离目标的方向上偏移。,The1.5shift,63,This1.5shiftisusedasanoffsetinthecenteringofthemeantogenerallyaccountfordynamicrandomshiftsintheprocess.Itsupposedlyrepresentstheaverage(estimated)amountofchangeatypicalprocesswillexhibitovermanycyclesofthatprocess.随着时间的推移，平均值会动态的发生1.5偏移。,The1.5shift,64,2.0ppm,LSL,USL,T,ASTSixSigmaProcessCentered,ASixSigmaProcessWithSDInflatedby1.3s,The1.5consistentshiftimpliesthatthecompanyisincometenttocontrolandre-centeritsprocesses.Insomecompanies,theyhavechosentoaccountforlongtermvariationbyinflatingtheshorttermsigmaby30%:固定1.5偏移暗示着公司没有能力改善制程的中心。在一些公司，他们选择用1.3倍的短期Sigma来计算长期的变异。,LT=1.3ST,The1.5shift,65,PNC(Total)=PNC(L)+PNC(U)ZLT=ZST-1.5Intraditional6methodology,theZ-scoreiscomputedonthebasisofthetotalamountoutsidespecifications.ThentheZscoreisderivedbyfindingtheZvaluecorrespondingtoPNC(Total).Motorolathenaddsorsubtractsthe1.5tothisZ.传统的6方法，Z计算基于在总的规格之外的数量。然后找到对应的Z。摩托罗拉+/-1.5得到Z。,The1.5shift,66,Whenthedataisnotnormallydistributed.Cycletimes,rejectratesanddefectratesaresomecommonexamples.Wehavethreeoptionstofindtheprocesscapability:当数据不是正态分布，比如周期时间，批退率和不良率，我们有下面三种方法计算过程能力。Usingfractiondefective废品率UsingWeiBullDistributions韦伯分布TransformthedatausingBox-CoxTransformation用Box-Cox方法转换成正态分布,NonNormalData非正态分布,67,CalcProbabilityDistributionsNormal,Capabilityusingtotaloutofspecs(Normal&nonnormaldata),Simplycountthenumberofdefectiveunitsanddividebythetotaltocomputethefractiondefective.简单用不良数除以总数来计算不合格率。Forexampleifaprocessproduces3%defectivepartsinlongterm.WecanuseminitabtofindouttheZscore.例如：如果在长期有3%的不合格品，我们可以用Mini-tab计算出西格玛Z水平。计算FY时，可用这种方法计算CPK.,68,Z=1.88AssumingLT,Ppk=ZLT/3=0.63,TheWeibullisafamilyofdistributionsranging(typically)fromanexponentialtoanormaldistribution.韦伯是一个典型的分布。随着的增大，从指数分布到正态分布,=0.5,=2.0,=3.5,shapeparameterdeterminestheshapeofthePDF(ProbabilityDensityFunction).形状参数来决定概率密度分布函数的形状,ProcessCapabilityforCycleTime,69,Acustomerservicemanagerwantstodeterminetheprocesscapabilityforhisdepartment.Aprimaryperformanceindexisthetimetakentocloseacustomercomplaint.Thegoalforthisindexistocloseacomplaintwithinonecalendarweek(5days).Performanceoverthelast400complaintswasreviewed.ThedatacanbefoundinfileCapability.mtw(C14)客户服务经理希望确定他们部门的制程能力。该部门一个主要的指标是处理客户抱怨的时间。目标是在5个日历日内完成客户客户抱怨。以最近的400个客户抱怨做为数据进行分析，详细的数据见Capability.mtw(C14),Example5例5,70,StatQualityToolsCapabilityAnalysisNon-normal,Example5,71,Example5,72,Example6Acompanywouldliketostudytheprocesscapabilityofitssalesdepartmentshandlingofincomingcalls.公司评估销售部门处理来电的过程能力。Datawascollectedoveraperiodof25days:numberofincomingcallsperdaynumberofunansweredcallsperdays收集25天的数据。每天来电的数量；每天未接的电话数量；DatacanbeobtainedinCapability.mtw(C16,C17),ProcessCapabilityforRejectRate(BinomialDistribution),73,Example6,74,Example6,75,Thepercentageofabsenteeismforeachdayinthelastmonth.上个月每天旷课的比率；Thedailypercentageofdropdiskinsputtermachines每天Sputtermachine掉片的比例Theproportionoflateinvoicepaymentsinthelastmonth.上个月发票支付的延迟的比率Thedailypercentageofdamagedshipmentsmadeinthelastmonth.上个月每天运输损坏的百分比。Theweeklyvoidpercentage每周失效的比例,ExampleofRejectRates批退率的例子,76,EstimationofYtpforDefectRateDefinesizeofaninspectionunit定义一个检验单元的大小Determinethelong-termdefectsperunit(DPU)确定长期的DPU（单位缺陷率）DPU=TotalDefectsTotalUnits(iii)Determinethethroughputyield(Ytp)确定直通率Ytp=expDPU,ProcessCapabilityforDefectRate,77,EstimationofSigma-CapabilityforDefectRate用不良率评估西格玛水平(i)Determinetheopportunitiesperunit确定单位机会数(ii)Determinethelong-termdefectsperopportunity(d)d=defectsperunitopportunitiesperunit确定长期DPO(iii)Determinetheinversecumulativeprobabilityford,usingCalcProbabilityDistributionNormal确定1-DPO(iv)Z-Scoreisthemagn