工程方法-sigma-工序能力

CapabilityAnalysis

过程能力分析1测量阶段流程图流程图(Processmapping)C&E矩阵初步分析可能因子FMEA进一步分析可能因子测量系统定义,MSAY的稳定性判定,过程能力分析二次FMEA可能因子总结分析阶段定义阶段鱼骨图(Fishbone)2LearningObjectives学习目的ProcessControlvsProcessCapability

过程控制和过程能力ProcessCapability过程能力:Specification,ProcessandControlLimits.规格,过程和控制界限ProcessPotentialvsProcessPerformance过程潜在的和实际的表现Short-TermvsLong-TermProcessCapability短期和长期过程能力“SixSigma”Quality;“6Sigma”水平;IntroductiontoZ-scoreZ-值介绍ProcessCapabilityforNon-NormalData非正态分布的过程能力Cycle-Time(ExponentialDistribution)循环时间(指数分布)RejectRate(BinomialDistribution)不合格(剔除)率(二项式分布)DefectRate(PoissonDistribution)缺陷率(泊松分布)3ProcessControlvsProcessCapability过程控制和过程能力1. ProcessControl过程控制Meanstheprocessisoperatinginstatisticalcontrol,moncausesaretheonlysourceofvariation.意味是过程在稳定状态下生产,也就是说,一般原因(偶然原因)是变异的唯一原因Refersto“voiceoftheprocess”,i.e.oneonlyneedsdatafromtheprocesstodetermineifaprocessisincontrol.起源于”过程的声音”,也就是说,唯一来源于过程的数据来判定过程是否受控.Trackperformanceoftheprocesstoverifyifitformsastabledistributionovertime,typicallywithacontrolchartwithcontrollimitscomputedfromtheprocessdataonly.随着时间过去,反馈过程的表现来验证它是否来自于一个稳定的分布,一般地,利用从过程数据计算控制界限的控制图来完成.Justbecauseaprocessisincontroldoesnotnecessarilymeanitisagoodprocess.仅仅因为过程受控并不一定说它是个好过程.42. ProcessCapability过程能力The“goodness”ofaprocessismeasuredbyprocesscapability过程的“好坏”是过程能力测量的Compares“voiceoftheprocess”with“voice

ofthecustomer”,whichisgivenintermsofspecs.orrequirements比较“过程声音”和“客户声音”,哪一个是根据规格或需要给出的?Measureshowwellastabledistribution(processincontrol)matchesupwithcustomer’sspecs.测量一个稳定的分布(过程受控)符合客户规格的程度.ProcessControlvsProcessCapability过程控制和过程能力首先判定过程稳定,确定数据分布是正态的,再计算过程能力和西格码质量水平.5WhatisCapability过程能力是....Whenprocessisundercontrol,capabilityisdecidedbycustomerdemandandprocessperformance(Productorservicequalityshiftingdegree).Themoretheprocessmeetsthecustomerneed,thebetterthecapabilitywillbe.过程在受控状态下时,客户要求与过程表现(产品品质或服务的品质变动程度)的比值,如果过程表现越能满足客户要求,则过程能力越充分,反之则不足.6ProcessCapability过程能力ProcessCapabilitystudiescan过程能力研究可以:

indicatetheconsistencyoftheprocessoutput显示过程输出的稳定性indicatethedegreetowhichtheoutputmeetsspecifications表明输出满足规格的程度beusedforcomparisonwithanotherprocessorcompetitor可以与另一过程或竟争对手相比较7ProcessVariation过程变异ProcessVariationistheinevitabledifferencesamongindividualmeasurementsorunitsproducedbyaprocess.过程变异是不可避免的差别在单个测量或过程生产单位之间.SourcesofVariation变异的来源:withinunit

产品内

(positionalvariation)

位置的变异betweenunits

单位之间

(unit-unitvariation)

产品-产品的变异betweenlots

产品批之间

(lot-lotvariation)

批—批的变异betweenlines

生产线之间

(line-linevariation)

线---线之间的变异acrosstime

不同时间

(time-timevariation)

时间--时间的变异measurementerror

测量误差

(repeatability&reproducibility)

重复性和再现性8TypesofVariation变异的类型1. PositionalVariation位置变异

Sameprocess,variationatdifferinglocationssimultaneously:

相同的过程,随不同位置而产生的变异Temperaturevariationsinsideathermalchamber温度变异在一个烘箱中Cavity-to-cavityvariationsinaninjectionmold洞坑差别在一个注塑模中2. CyclicalVariation重复误差

Sequentialrepetitionsofaprocessoverfairlyshorttime,say,lessthan15mins:

在一定短的时间内某过程的连续重复,比方说,少于15分钟:Variationsbetweenconsecutivebatchesofaprocess同一过程的连续批次之间的变异Differencesfromlottolotofrawmaterials不同批次原材料之间的差别3.TemporalVariation时间的变异 Variationsoverlongerperiodsoftime,suchaseveralhours,daysorweeks.

长期的变异,例如几个小时,几天或几个星期.9InherentorNaturalVariation固有有或或自自然然的的变变异异Duetothecumulativeeffectofmanysmallunavoidablecauses归因因于于许许多多小小的的,不不可可避避免免的的因因素素共共同同的的结结果果Aprocessoperatingwithonlychancecausesofvariationpresentissaidtobe““instatisticalcontrol””如果果一一个个过过程程运运行行时时只只存存在在固固有有原原因因变变异异的的作作用用,就就说说它它处处在在““统统计计控控制制状状态态””.TypesofVariation变异异的的类类型型一般般原原因因10SpecialorAssignableVariation特殊殊的的可可查查明明的的变变异异Maybedueto可能能归归因因与与:a)improperlyadjustedmachine不正正确确的的调调机机b)operatorerror员工工错错误误c)defectiverawmaterial有缺缺陷陷的的原原材材料料Aprocessoperatinginthepresenceofassignablecausesofvariationissaidtobe““out-of-control””.如果果一一个个过过程程运运行行时时存存在在可可指指出出原原因因变变异异,则则称称该该过过程程““失失控控TypesofVariation变异异的的类类型型异常常原原因因11ProcessCapabilityvsSpecificationLimits过程程能能力力和和规规格格界界限限a)b)c)a)Processishighlycapableb)Processismarginallycapablec)Processisnotcapablea)过程能力高b)过程能力一般般c)过程能力差12ThreeTypesofLimits三种类型的界界限SpecificationLimits(LSLandUSL)createdbydesignengineeringinresponsetocustomerrequirementstospecifythetoleranceforaproduct’’scharacteristicProcessLimits(LPLandUPL)measuresthevariationofaprocessthenatural6limitsofthemeasuredcharacteristicControlLimits(LCLandUCL)measuresthevariationofasamplestatistic(mean,variance,proportion,etc)规格界限(LSLandUSL)·由设计工程部部门根据客户户要求确定的的产品性能公公差。过程界限(LPLandUPL)．．用来测量过程程的变异．·为所测量特性性的自然公差差(六倍标准准差(6δ))界限控制界限(LCLandUCL)·用来测量样本本统计量的变变异(均值，方差．．比例等)13DistributionofIndividualValues(x)DistributionofSampleAverages(x)ThreeTypesofLimits三种类型的界界限单值分布样本均值分布布14ProcessCapabilityIndices过程能力指数数Twomeasuresofprocesscapability:过程能力的两两种测量ProcessPotential过程潜力CpProcessPerformance过程表现CpuCplCpk15ProcessPotential过程潜力TheCpindexassesseswhetherthenaturaltolerance(6)ofaprocessiswithinthespecificationlimits.工序能力指数数Cp用以评价是否否一个过程的的自然公差(6δ)处于规格界限限以内.16Traditionally,aCpof1.0indicatesthataprocessisjudgedtobe“capable”.iftheprocessiscenteredwithinitsengineeringtolerance,0.27%ofpartsproducedwillbebeyondspecificationlimits.CpRejectRate1.000.270%1.330.007%1.506.8ppm2.002.0ppbProcessPotential过程潜力一般地:Cp等于1.0代代表该过程被被判断为有能能力的.----比如,如果过过程中心与规规格中心重合合,此时该过过程有0.27%的产品品出现在规格格以外.供参考17a)b)c)a)Processishighlycapable(Cp>2)b)Processiscapable(Cp=1to2)c)Processisnotcapable(Cp<1)ProcessPotential过程潜潜力a)过程能能力很很高(Cp>2)b)过程能能力尚尚可(Cp=1to2)c)过程能能力差差(Cp<1)18TheCpindexcomparestheallowablespread(USL-LSL)againsttheprocessspread(6).Itfailstotakeintoaccountiftheprocessiscenteredbetweenthespecificationlimits.Processiscentered过程中心和规格中心重合Processisnotcentered过程中心和规格中心不重合ProcessPotential过程潜潜力工序能能力Cp指数比比较允允许分分布宽宽度(USL-LSL)与过程程分布布宽度度(6δ).并未考考虑过过程中中心与与规格格中心心不重重合的的情形形.19ProcessPerformance过程表表现TheCpkindexrelatesthescaleddistancebetweentheprocessmeanandthenearestspecificationlimit.工序能力Cpk指数与过程程均值与最最近的规格格界限之间间的距离有有关.20CpkRejectRate1.00.13–0.27%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––2ppbProcessPerformance过程表现21a)Processishighlycapable(Cpk>1.5)b)Processiscapable(Cpk=1to1.5)c)Processisnotcapable(Cpk<1)a)Cp=2Cpk=2b)Cp=2Cpk=1c)Cp=2Cpk<1ProcessPerformance过程表现a)过程绩效好好(Cpk>1.5)b)过程绩效一般般(Cpk=1to1.5)c)过程绩效差(Cpk<1)22Example1例1SpecificationLimits规格界限: 4to16gMachine机器Mean平均值StdDev标准偏差(a)104(b)102(c)72(d)131DeterminethecorrespondingCpandCpkforeachmachine.计算每一台台机器相应应的CpandCpk23Example1A24Example1B25Example1C26Example1D27ProcessCapability过程能力Foranormallydistributedcharacteristic,thedefectiverateF(x)maybeestimatedviathefollowing:对于服从正正态分布的的特性,缺缺陷率F(x)可以通过下下式求得Forcharacteristicswithonlyonespecificationlimit:对于只存在在单边规格格的特性,缺陷率计计算如下:a) LSLonlyb) USLonlyLSLUSL28Example2例2SpecificationLimits规格界限: 4to16gMachine机器Mean平均值StdDev标准偏差(a)104(b)102(c)72(d)131Determinethedefectiverateforeachmachine.试计算每一一机器的不不合格品率率29Example2MeanStdDevZLSLZUSLF(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=16g30Example3Of1000componentsproducedbyamachine,248piecesaregreaterthan10.27cminlength(customer’sspecification).Ifthelengthsofthecomponentsarenormallydistributedwithameanof10.10cm,whatisthestandarddeviation?在1000个同一机器器生产的产产品中,248个长度大于于10.27cm(客户规格),如产品的长长度是平均均值为10.10cm,问其标准偏偏差是多少少?31ProcessPotentialvsProcessPerformance过程潜力和和过程能力力(a)PoorProcessPotential(b)PoorProcessPerformanceLSLUSLLSLUSLExperimentalDesigntoreducevariationExperimentalDesigntocentermeantoreducevariation(a)差的过程潜潜力(b)差的过程能能力试验设计降降低变异试验设计均值对中降低变异32AlternativeProcessPerformanceIndex选择性的工工序表现指指数Processcapabilitystatisticsmeasureprocessvariationrelativetospecificationlimits.过程能力统统计量用以以测量过程程输出相对对于规格界界限的变异异TheCpstatisticcomparestheengineeringtoleranceagainsttheprocess’snaturalvariation.Cp统计量比较较设计公差差和过程自自然变异.TheCpkstatistictakesintoaccountthelocationoftheprocessrelativetothemidpointbetweenspecifications.Iftheprocesstargetisnotcenteredbetweenspecifications,theCpmstatisticispreferred.Cpk统计量考虑虑了过程位位置相对于于规格中心心的变化.如果过程程目标不是是规格中心心,选用Cpm统计量更适适用33ProcessStability过程稳定性性Aprocessisstableifthedistributionofmeasurementsmadeonthegivenfeatureisconsistentovertime.当一个过程程的某个给给定的特性性在一段时时间内测量量结果的分分布呈现一一致的特性性,则说该该过程是稳稳定的.TimeStableProcess稳定过程TimeUnstableProcess不稳定过程程ucllclucllcl34WithinvsOverallCapability短期和长期期过程能力力WithinCapability(previouslycalledshort-termcapability)showstheinherentvariabilityofamachine/processoperatingwithinabriefperiodoftime.内部能力力(又叫叫短期能能力)代代表了一一个过程程或设备备在短期期内的固固有变异异.OverallCapability(previouslycalledlong-termcapability)showsthevariabilityofamachine/processoperatingoveraperiodoftime.Itincludessourcesofvariationinadditiontotheshort-termvariability.总体能力力(又叫叫长期能能力)代代表了一一个过程程或设备备在经过过长时间间运行后后的变异异.它包包含了除除短期变变异之外外的变异异来源.35WithinvsOverallCapability短期和长长期过程程能力Within OverallSampleSize30–50units100unitsNumberofLotssinglelotseverallotsPeriodofTimehoursordaysweeksormonthsNumberofOperatorssingleoperatordifferentoperatorsProcessPotentialCpPpProcessPerformanceCpkPpk供参考36WithinCapability OverallCapabilityThekeydifferencebetweenthetwosetsofindicesliesintheestimatesforWithinandOverall.评估内部能力力和总体能力力的主要区别别在于评估所所用的标准差差有区别δwithinandδoverallWithinvsOverallCapability短期和长期过过程能力37Estimating计算WithinandOverallConsiderthefollowingobservationsfromacontrolchart:从一个控制图图中考虑以下下观测值:S/N X1X2…XkMeanRangeStdDev1 x1,1x2,1…xk,1X1R1S12 x1,2x2,2…xk,2X2R2S2: ::::::m x1,mx2,m…xk,mXmRmSmTheoverallvariationOverallisestimatedby:总体标准差δOverall的估计可用以以下公式38Estimating计算WithinandOverallThewithinvariationWithinmaybeestimatedbyoneofthefollowingmethods:内部标准差δOverall可按下列方法法中的一种进进行评价(a)R-barMethodR-bar方法方法whered2isaShewhartconstant=(k)其中d2为常数(b)S-barMethodS-bar方法wherec4isaShewhartconstant=(k)其中c4为常数(c)PooledStandardDeviationMethod普尔标准偏差差方法InMiniTab,thePooledStandardDeviationisthedefaultmethod.在MiniTab中,pooledStandardDeviation方法为默认方方法.39Estimating计算WithinandOverallIncaseswherethereisonly1observationpersub-group(i.e.k=1),theMovingRangeMethodisused,where在子组容量为为1时,使用用移动极差方方法(MovingRangeMethod),ThewithinvariationWithinisthenestimatedusingeither短期标准差Within可用下式中的的一个计算theAverageMovingRange:方法移动极差差平均值theMedianMovingRange:移动极差中位位数:40Example4例4Thelengthofacamshaftforanautomobileengineisspecifiedat600±2mm.Controlofthelengthofthecamshaftiscriticaltoavoidscrap/rework.Thecamshaftisprovidedbyexternalsuppliers.Assesstheprocesscapabilityforthissupplier.“Thedataisavailablein“01-03”.Dataarecollectedinsubgroupsof5each.某汽车发动动机的凸轮轮轴长度规规格为600±2mm.控制该长度度可以避免免报废和返返工,每个个子组收集集5个长度度数据,该该轴由外部部供应商供供应,请评评估该供应应商的过程程能力.数据存储在在“01-03”中.实际操作MiniTab41Example例5Histogramofthecamshaftlengthsuggestsmixedpopulations.Furtherinvestigationrevealedthattherearetwosuppliersforthecamshaft.Datawerenowcollectedoncamshaftsfromeachsourcewithoutcombiningboth.Subgroupsizeis5foreachsupplier.Arethetwosupplierssimilarinperformance?Ifnot,whatareyourrecommendations?从直方图上上可看出轴轴的长度为为几个总体体的混合数数据.进一一步调查显显示有两个个供应商向向公司供应应该凸轮轴轴.数据来来源于两家家供应商的的产品.该两家供应应商的过程程能力相同同吗?如果不同,你推荐使使用哪一家家的产品?实际操作MiniTab42Example5MiniTab:StatQualityToolsCapabilitySixpack(Normal)43Example544Example545Motorola的原始定义义:如果规格界界限至少离离过程均值值μ为±6σ的距离,即即Cp≥2并且过程偏偏移小于1.5σ,即Cp≥1.5那么过程缺缺陷率将小小于3.4ppm.6σ6σ4.5σ什么是六西西格玛品质质?---------过去去46MikelJHarry认为过程不不同产品批批之间的均均值将发生生变化平均均变化量量为1.5σ注意:Sigma能力=f(dpmo)≠f(dppm)2σ什么是六西西格玛品质质?---------现在在Kσ=2σσ+1.5σKσ=2σσ+1.5σ47CapabilityAnalysiswithBox-CoxTransformationBox-Cox转化分析过过程能力Whentheprocessdataarenotnormal,theCpkorPpkindicesarenotaccurateorreliable,becausetheseindicesarecomputedonthebasisthatthedataarenormallydistributed.当过程数据据是非正态态的,过程能力指指数CpkorPpk是不正确的的或可信的的,因为这些数数据是假定定数据是正正态分布的的基础上.Dppmvaluesassociatedwiththeindiceswillnotbeneartotheactualperformancewhenthenormalcurvedoesnotmodeltheactualdatawell.当正态曲线线不能很好好的符合实实际数据时时,和指数相关关的DPPM值不和实际际表现相符符.48Iftheprocessdataaresomewhatbell-shapedbutskewed,Box-Coxtransformationcanbeusedtomakethedatanormalbeforeweassesstheprocesscapability.如果过程数数据有些钟钟型但歪斜斜的,在我们评估估过程能力力之前,Box-Cox转化可帮助助将数据转转化成正态态RemembertotransformthespecificationlimitstoobeforewecomputeCpkorPpk!记住在计算算过程能力力指数前也也要将规格格界限进行行转化!CapabilityAnalysiswithBox-CoxTransformationBox-Cox转化分析过过程能力49Minitab:StatQualityToolsCapabilityAnalysis(Normal)CapabilityAnalysiswithBox-CoxTransformationBox-Cox转化化分分析析过过程程能能力力50Example例6Openthefilenamed01-04.MTW,Computetheprocesscapabilitywiththespecificationlimits:打开开01-04文件件,用规规格格界界限限计计算算过过程程能能力力(samplesize=1)LSL:0.1USL:10Arethedatanormallydistributed?数据据是是正正态态分分布布吗吗?ComputetheprocesscapabilityagainwithBox-Coxtransformation.利用用Box-Cox转化化计计算算过过程程能能力力CapabilityAnalysiswithBox-CoxTransformationBox-Cox转化化分分析析过过程程能能力力51Cpkof0.41isreportedintheSSATpackage.Thisvalueisnotreliableoraccurateifthedataarenotnormal.Dataisnotnormal数据据不不是是正正态态的的Example6CapabilityAnalysiswithBox-CoxTransformationBox-Cox转化化分分析析过过程程能能力力在SSAT的Cpk0.41.如数数据据不不是是正正态态的的,此数数据据不不是是可可信信的的或或不不正正确确的的.52Example6Cpkhasincreasedfrom0.41to0.81CapabilityAnalysiswithBox-CoxTransformationBox-Cox转化分析析过程能能力计算值和和此值会会有差别别5354AssumingNormality...假设正态态USLZisNormallydistributedwithMean=0andSD=1Z-值平均值值为“0”标准偏差差为“1”的正态分分布值.LSLZscoreZScoresZ-值55ZLSL,ZUSLUSLLSLZLSLZUSL多少s过程USLZ-Scoreinterpretation:Howmanystandarddeviations,sors-hats,isthemean,x-bar,fromsomespecifiedvalue,x.Z-值解释:是一个到到平均值值有几个个标准偏偏差的的的特定值值Let’’sassumethereisonlyanUSL让我们假假设只有有只有规规格下限限?s0.001ppmUSLTmASixSigmaProcess25,000ppmUSLTmATwoSigmaProcessBasicInstructionsforMinitabComputingStandardNormalProbabilities计算标准准正态概概率的MiniTab基本操作作57Select““Calc”,““ProbabilityDistributions”and““Normal”.Select““CumulativeProbability”,enterthe““Mean”and““StandardDeviation”,clickon““Inputconstant”,enterthevalueandclickon“OK”.ComputingPercentFalloutCumulativeDistributionFunctionNormalwithmean=11.0000andstandarddeviation=1.00000xP(X<=x)12.00000.841358MinitabOutputUSL=12Tm=11AOneSigmaProcessDPPM=(1-0.8413)x1,000,000=158700CumulativeDistributionFunctionNormalwithmean=11.0000andstandarddeviation=1.00000xP(X<=x)12.00000.841359ComputingZ-ScoreFromPercentFalloutSelect““InverseCumulativeprobability”,setthe“Mean”=0and““StandardDeviation”=1,clickon““Inputconstant”,enterthetotalareaassociatedwithfalloutandclickon““OK”.p=0.8413InverseCumulativeDistributionFunctionNormalwithmean=0andstandarddeviation=1.00000P(X<=x)x0.84130.999860s=1LSL=9USL=12Tm=11DeterminetheDPPMZLSL,ZUSLandtheZscoreExercise61Select““Calc”,““ProbabilityDistributions”and““Normal”.Select““Cumulativeprobability”,enterthe““Mean”and““StandardDeviation”,clickon““Inputconstant”,enterthevalueandclickon“OK”.CumulativeDistributionFunctionNormalwithmean=11.0000andstandarddeviation=1.00000xP(X<=x)12.00000.8413Solution:Minitab62Select““Cumulativeprobability”,enterthe““Mean”and““StandardDeviation”,clickon““Inputconstant”,enterthevalueandclickon““OK”.CumulativeDistributionFunctionNormalwithmean=11.0000andstandarddeviation=1.00000xP(X<=x)9.00000.0228DPPM=((0.0228)+(1-0.8413))x1,000,000=181500Solution:MinitabZLSL=(9-11)/163Select““InverseCumulativeprobability”,setthe““Mean”=0and““StandardDeviation”=1,clickon““Inputconstant”,enterthetotalareaassociatedwithfalloutandclickon““OK”.p=1-((0.0228)+(1-0.8413))=1-0.1815=0.8185InverseCumulativeDistributionFunctionNormalwithmean=0andstandarddeviation=1.00000P(X<=x)x0.81850.9097Solution:Minitab64ProcessCapabilityforNon-NormalData非正态的过过程能力65ProcessCapabilityforNon-NormalData非正态数据据的过程能能力Noteverymeasuredcharacteristicisnormallydistributed.Somedatafollowsdistributionsthatareknown,andthesemaybeabletohavetheircapabilitymeasuredaccuratelyusingthatknowledge不是所有的的测量参数数都是正态态分布的,一些数据分分布已知,就可以准确确地应用自自己的过程程能力分析析方法去测测量过程能能力Characteristic参数Distribution分布CycleTime循环时间Weibull(Exponential)威布尔(指数)分布RejectRate不合格率Binomial二项式分布布DefectRate缺陷率Poisson泊松分布66TheWeibullDistributionisageneralfamilyofdistributionwith威布尔分布布为一个常常见的分布布,用下式式表示:wherescaleparameteristhevalueatwhichCDF=68.17%,andshapeparameterdeterminestheshapeofthePDF.上式中,尺尺度参数数θ为CDF=68.17%时的值形状参数β确定了PDF的形状ProcessCapabilityforCycleTime周期时间的的过程能力力67At=1,theWeibullDistributionisreducedto当β=1,威布尔分布布可简化为为::ForanExponentialDistribution,对指数分布布,有TheExponentialDistributionisthusaWeibullDistributionwith=1.指数分布为为β=1时的威布尔尔分布.Weibull(x;=1,)Exponential(x;)ProcessCapabilityforCycleTime周期时间的的过程能力力68Example4Acustomerservicemanagerwantstodeterminetheprocesscapabilityforhisdepartment.Aprimaryperformanceindexisthetimetakentocloseacustomercomplaint.Thegoalforthisindexistocloseacomplaintwithinonecalendarweek.Performanceoverthelast400complaintswasreviewed.一位客户服服务经理想想确定他的的部门过程程能力,主主要评价指指标为处理理客户投诉诉的时间周周期,目标标为在一周周内处理完完一单客户户投诉,过过去的400%次投投诉作为测测量数据.数据在此期期01-03Days69Example4StatQualityToolsCapabilityAnalysis(Weibull)70Example471Example4AStatQualityToolsCapabilitySixpack(Weibull)72Example4A73AlternativesforNon-NormalData非正态数据解解释Whenallothermethodsfail,itmaybenecessarytofallbackonasimpleassessmentofthetotalamountoutofspecifications.Simplycountthenumberofdefectiveunitsanddividebythetotaltocomputethefractiondefective.AnotherstandardmetricforthisistheDPPM.当所有方法失失败,它需要返回到到一个评估超超出控制界限限数量的简单单方法,简单地查一下下不合格品和和全部产品的的数量,然后计算不合合格率,另一个标准刻刻度也是DPPMIfaCapabilityIndexmustbereported,theDPPMcanbeconvertedbackintoaZvalue,andtheneitherPpk=Z/3orCpk=Z/3dependinguponwhetherthedataislongtermorshortterm.如果要得到过过程能力指数数,DPPM可以转化为Z-值,然后根据此数数据是长期或或短期得PPK=Z/3或Cpk=Z/374ProcessCapabilityforRejectRate不合格率的过过程能力ForaNormalDistribution,theproportionofpartsproducedbeyondaspecificationlimitis对于一个正态态分布,在控制界限下下的比例部分分.RejectRate75Thus,foreveryrejectratethereisanaccompanyingZ-Score,这样一来,对于每一个不不合格率都有有一个对应的的Z-值Where这里Recallthat原先Hence因此ProcessCapabilityforRejectRate不合格率的过过程能力76EstimationofPpkforRejectRate不合格率Ppk的计算:Determinethelong-termrejectrate(p)计算长期不合合格率(p)Determinetheinversecumulativeprobabilityforp,usingCalcProbabilityDistributionNormal计算相反的累累计概率p,,点击CalcProbabilityDistributionNormalZ-ScoreisthemagnitudeofthereturnedvalueZ-值是反推值的的多少.Ppkisone-thirdoftheZ-ScorePpk是Z-值的三分之一一.ProcessCapabilityforRejectRate不合格率的过过程能力77ExampleofProcessCapabilityStudyforRejectRate不合格率过程程能力的例子子Asalesmanagerplanstoassesstheprocesscapabilityofhistelephonesalesdepartment’shandlingofincomingcalls.一个销售经理理打算评估他他的电话销售售部门处理接接入电话的过过程能力.01-03文件Thefollowingdatawascollectedoveraperiodof20days:以下数据收据据20天numberofincomingcallsperday每天的接入电电话数量numberofunansweredcallsperdays每天的未应答答电话数量.78StatQualityToolsCapabilityAnalysis(Binomial)ExampleofProcessCapabilityStudyforRejectRate不合格率过程程能力的例子子79Ppk=0.25ExampleofProcessCapabilityStudyforRejectRate不合格率过程程能力的例子子80ProcessCapabilityforDefectRate缺陷率的过程程能力Otherapplications,approximatingaPoissonDistribution:errorratesparticlecountchemicalconcentration以下应用,近近似于泊淞分分布:缺陷率缺点数溶液浓度81EstimationofYtpforDefectRateDefinesizeofaninspectionunitDeterminethelong-termdefectsperunit(DPU)DPU =TotalDefectsTotalUnitsDeterminethethroughputyield(Ytp)Ytp=exp{–DPU}ProcessCapabilityforDefectRate缺陷率的过程程能力评价缺陷率的的Ytp确定检查单元元的大小确定长期单位位缺陷数(DPU)DPU=TotalDefects÷TotalUnits确定(Ytp)82EstimationofSigma-CapabilityforDefectRate评估缺陷率的的Sigma能力Determinetheopportunitiesperunit确定每个产品品单元的机会会数Determinethelong-termdefectsperopportunity(d)确定每个机会会的长期缺陷陷数(dd =defectsperunitopportunitiesperunitDeterminetheinversecumulativeprobabilityford,计算相反的累累计概率值dusingCalcProbabilityDistributionNormalZ-ScoreisthemagnitudeofthereturnedvalueZ-值是反推值的的多少.Sigma-Capability=Z-Score+1.5ProcessCapabilityforDefectRate缺陷率的过程程能力83Example6Theprocessmanagerforawiremanufacturerisconcernedabouttheeffectivenessofthewireinsulationprocess.Randomlengthsofelectricalwiringaretakenandtestedforweakspotsintheirinsulationbymeansofatestvoltage.Thenumberofweakspotsandthelengthofeachpieceofwirearerecorded.1inspectionunitisdefinedas125unitlengthofwire.某线材制造商商的工程经理理关注线材绝绝缘过程的有有效性.随机机长度的导线线被通过加压压测试绝缘不不良点.不良良点数和每段段线的长度都都做以记录.一个检查单单元定为125单位长长度的导线.01-03文件weakspot84Example6StatQualityToolsCapabilityAnalysis(Poisson)85Example6DefectsperUnit=0.0265194ThroughputYield=exp{–DPU}=exp{–0.0265194}=0.9738c.f.First-TimeYield=2/100=0.0286Example6Define1InspectionUnit =125unitlengthofwirei.e.Units=Length12587Example6AStatQualityToolsCapabilityAnalysis(Poisson)88Example6ADefectsperUnit=3.31493ThroughputYield=exp{–DPU}=exp{–3.31493}=0.0363c.f.First-TimeYield=2/100=0.0289Example6BDefectsperUnit=3.31493OpportunitiesperUnit=1DefectsperOpportunity=3.31493Z-Score=???90Example6B1inspectionunit=1unitlengthofwireOpportunitiesperUnit=1DefectsperOpportunity=