过程能力分析 课件

CapabilityAnalysis

过程能力分析1MPTConfidentialCapabilityAnalysis

过程能力分析1MPT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)2MPTConfidential测量阶段流程图流程图(Processmapping)C&ELearningObjectives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)3MPTConfidentialLearningObjectives学习目的ProcessProcessControlvsProcessCapability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.4MPTConfidentialProcessControlvsProcessCap2. 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.5MPTConfidential2. ProcessCapability过程能力ProcWhatisCapability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.6MPTConfidentialWhatisCapability过程能力是....WhProcessCapability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7MPTConfidentialProcessCapability过程能力ProcessProcessVariation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8MPTConfidentialProcessVariation过程变异ProcessVTypesofVariation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.9MPTConfidentialTypesofVariation变异的类型1. PosInherentorNaturalVariation固有或自然的变异Duetothecumulativeeffectofmanysmallunavoidablecauses归因于许多小的,不可避免的因素共同的结果Aprocessoperatingwithonlychancecausesofvariationpresentissaidtobe“instatisticalcontrol”如果一个过程运行时只存在固有原因变异的作用,就说它处在“统计控制状态”.TypesofVariation变异的类型一般原因10MPTConfidentialInherentorNaturalVariation固SpecialorAssignableVariation特殊的可查明的变异Maybedueto可能归因与:

a)improperlyadjustedmachine

不正确的调机 b)operatorerror

员工错误 c)defectiverawmaterial

有缺陷的原材料Aprocessoperatinginthepresenceofassignablecausesofvariationissaidtobe“out-of-control”.如果一个过程运行时存在可指出原因变异,则称该过程“失控TypesofVariation变异的类型异常原因11MPTConfidentialSpecialorAssignableVariatiProcessCapabilityvsSpecificationLimits

过程能力和规格界限a)b)c)a)Processishighlycapableb)Processismarginallycapablec)Processisnotcapablea)过程能力高b)过程能力一般c)过程能力差12MPTConfidentialProcessCapabilityvsSpecificThreeTypesofLimits三种类型的界限SpecificationLimits(LSLandUSL)

createdbydesignengineeringinresponsetocustomerrequirementstospecifythetoleranceforaproduct’scharacteristicProcessLimits(LPLandUPL)measuresthevariationofaprocessthenatural6limitsofthemeasuredcharacteristicControlLimits(LCLandUCL)measuresthevariationofasamplestatistic(mean,variance,proportion,etc)规格界限(LSLandUSL)·由设计工程部门根据客户要求确定的产品性能公差。过程界限(LPLandUPL)．用来测量过程的变异．·为所测量特性的自然公差(六倍标准差(6δ))界限控制界限(LCLandUCL)·用来测量样本统计量的变异(均值，方差．比例等)13MPTConfidentialThreeTypesofLimits三种类型的界限SpDistributionofIndividualValues(x)DistributionofSampleAverages(x)ThreeTypesofLimits三种类型的界限单值分布样本均值分布14MPTConfidentialThreeTypesofLimits三种类型的界限单值ProcessCapabilityIndices过程能力指数Twomeasuresofprocesscapability:过程能力的两种测量ProcessPotential过程潜力Cp

ProcessPerformance过程表现Cpu

Cpl

Cpk

15MPTConfidentialProcessCapabilityIndices过程能力ProcessPotential过程潜力TheCpindexassesseswhetherthenaturaltolerance(6)ofaprocessiswithinthespecificationlimits.

工序能力指数Cp用以评价是否一个过程的自然公差(6δ)处于规格界限以内.16MPTConfidentialProcessPotential过程潜力TheCpinTraditionally,aCpof1.0indicatesthataprocessisjudgedtobe“capable”.iftheprocessiscenteredwithinitsengineeringtolerance,0.27%ofpartsproducedwillbebeyondspecificationlimits. Cp RejectRate 1.00 0.270% 1.33 0.007% 1.50 6.8ppm 2.00 2.0ppbProcessPotential过程潜力一般地:Cp等于1.0代表该过程被判断为有能力的.----比如,如果过程中心与规格中心重合,此时该过程有0.27%的产品出现在规格以外.供参考17MPTConfidentialTraditionally,aCpof1.0inda)b)c)a)Processishighlycapable(Cp>2)b)Processiscapable(Cp=1to2)c)Processisnotcapable(Cp<1)ProcessPotential过程潜力a)过程能力很高(Cp>2)b)过程能力尚可(Cp=1to2)c)过程能力差(Cp<1)18MPTConfidentiala)b)c)ProcessPotential过程潜力a)过TheCpindexcomparestheallowablespread(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过程潜力工序能力Cp指数比较允许分布宽度(USL-LSL)与过程分布宽度(6δ).并未考虑过程中心与规格中心不重合的情形.19MPTConfidentialTheCpindexcomparesthealloProcessPerformance过程表现TheCpkindexrelatesthescaleddistancebetweentheprocessmeanandthenearestspecificationlimit.工序能力Cpk指数与过程均值与最近的规格界限之间的距离有关.20MPTConfidentialProcessPerformance过程表现TheCpk

Cpk RejectRate 1.0 0.13–0.27% 1.1 0.05–0.10% 1.2 0.02–0.03% 1.3 48.1–96.2ppm 1.4 13.4–26.7ppm 1.5 3.4–6.8ppm 1.6 794–1589ppb 1.7 170–340ppb 1.8 33–67ppb 1.9 6–12ppb 2.0 1–2ppbProcessPerformance过程表现21MPTConfidential Cpk RejectRateProcessPerfa)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(Cpk>1.5)b)过程绩效一般(Cpk=1to1.5)c)过程绩效差(Cpk<1)22MPTConfidentiala)Cp=2b)Cp=2c)Cp=2ProcesExample1例1SpecificationLimits规格界限

: 4to16gMachine机器

Mean平均值

StdDev标准偏差 (a) 10 4 (b) 10 2 (c) 7 2 (d) 13 1DeterminethecorrespondingCpandCpkforeachmachine.计算每一台机器相应的CpandCpk

23MPTConfidentialExample1例1SpecificationLimitExample1A24MPTConfidentialExample1A24MPTConfidentialExample1B25MPTConfidentialExample1B25MPTConfidentialExample1C26MPTConfidentialExample1C26MPTConfidentialExample1D27MPTConfidentialExample1D27MPTConfidentialProcessCapability过程能力Foranormallydistributedcharacteristic,thedefectiverateF(x)maybeestimatedviathefollowing:对于服从正态分布的特性,缺陷率F(x)可以通过下式求得Forcharacteristicswithonlyonespecificationlimit:对于只存在单边规格的特性,缺陷率计算如下:a) LSLonlyb) USLonlyLSLUSL28MPTConfidentialProcessCapability过程能力ForanoExample2例2SpecificationLimits规格界限

: 4to16gMachine机器

Mean平均值

StdDev标准偏差 (a) 10 4 (b) 10 2 (c) 7 2 (d) 13 1Determinethedefectiverateforeachmachine.试计算每一机器的不合格品率29MPTConfidentialExample2例2SpecificationLimitExample2MeanStdDevZLSLZUSLF(x<LSL)F(x>USL)F(x) 10 4 -1.5 1.5 66,807 66,807 133,614 10 2 -3.0 3.0 1,350 1,350 2,700 7 2 -1.5 4.5 66,8073 66,811 13 1 -9.0 3.0 0 1,350 1,350 LowerSpecLimit =4gUpperSpecLimit =16g30MPTConfidentialExample2MeanStdDevZLExample3Of1000componentsproducedbyamachine,248piecesaregreaterthan10.27cminlength(customer’sspecification).Ifthelengthsofthecomponentsarenormallydistributedwithameanof10.10cm,whatisthestandarddeviation?在1000个同一机器生产的产品中,248个长度大于10.27cm(客户规格),如产品的长度是平均值为10.10cm,问其标准偏差是多少?31MPTConfidentialExample3Of1000componentsprProcessPotentialvsProcessPerformance

过程潜力和过程能力(a)PoorProcessPotential (b)PoorProcessPerformanceLSLUSLLSLUSLExperimentalDesigntoreducevariationExperimentalDesigntocentermeantoreducevariation(a)差的过程潜力(b)差的过程能力试验设计降低变异试验设计均值对中降低变异32MPTConfidentialProcessPotentialvsProcessPAlternativeProcessPerformance

Index

选择性的工序表现指数Processcapabilitystatisticsmeasureprocessvariationrelativetospecificationlimits.过程能力统计量用以测量过程输出相对于规格界限的变异TheCpstatisticcomparestheengineeringtoleranceagainsttheprocess’snaturalvariation.Cp统计量比较设计公差和过程自然变异.TheCpkstatistictakesintoaccountthelocationoftheprocessrelativetothemidpointbetweenspecifications.Iftheprocesstargetisnotcenteredbetweenspecifications,theCpmstatisticispreferred.Cpk统计量考虑了过程位置相对于规格中心的变化.如果过程目标不是规格中心,选用Cpm统计量更适用33MPTConfidentialAlternativeProcessPerformancProcessStability过程稳定性Aprocessisstableifthedistributionofmeasurementsmadeonthegivenfeatureisconsistentovertime.当一个过程的某个给定的特性在一段时间内测量结果的分布呈现一致的特性,则说该过程是稳定的.TimeStableProcess稳定过程TimeUnstableProcess不稳定过程ucllclucllcl34MPTConfidentialProcessStability过程稳定性AprocesWithinvsOverallCapability短期和长期过程能力WithinCapability(previouslycalledshort-termcapability)showstheinherentvariabilityofamachine/processoperatingwithinabriefperiodoftime.内部能力(又叫短期能力)代表了一个过程或设备在短期内的固有变异.OverallCapability(previouslycalledlong-termcapability)showsthevariabilityofamachine/processoperatingoveraperiodoftime.Itincludessourcesofvariationinadditiontotheshort-termvariability.总体能力(又叫长期能力)代表了一个过程或设备在经过长时间运行后的变异.它包含了除短期变异之外的变异来源.35MPTConfidentialWithinvsOverallCapability短期WithinvsOverallCapability短期和长期过程能力

Within OverallSampleSize

30–50units 100unitsNumberofLots

singlelot

severallotsPeriodofTime

hoursordays weeksormonthsNumberofOperators

singleoperator differentoperatorsProcessPotential

Cp Pp

ProcessPerformance

Cpk Ppk

供参考36MPTConfidentialWithinvsOverallCapability短期

WithinCapability OverallCapability ThekeydifferencebetweenthetwosetsofindicesliesintheestimatesforWithinandOverall.评估内部能力和总体能力的主要区别在于评估所用的标准差有区别δwithinandδoverallWithinvsOverallCapability短期和长期过程能力37MPTConfidential WithinCapability OverallCaEstimating计算

Within

andOverall

Considerthefollowingobservationsfromacontrolchart:从一个控制图中考虑以下观测值:

S/N X1 X2 …Xk Mean Range StdDev 1 x1,1 x2,1 …xk,1 X1 R1 S1 2 x1,2 x2,2 …xk,2 X2 R2 S2 : : : : : : : m x1,m x2,m …xk,m

Xm Rm SmTheoverallvariationOverall

isestimatedby:总体标准差δOverall的估计可用以下公式38MPTConfidentialEstimating计算WithinandOverEstimating计算

Within

andOverall

ThewithinvariationWithin

maybeestimatedbyoneofthefollowingmethods:内部标准差δOverall可按下列方法中的一种进行评价(a)R-barMethodR-bar方法方法 where d2isaShewhartconstant=(k)其中d2为常数(b)S-barMethodS-bar方法 where c4isaShewhartconstant=(k)

其中c4为常数(c)PooledStandardDeviationMethod普尔标准偏差方法InMiniTab,thePooledStandardDeviationisthedefault

method.在MiniTab中,pooledStandardDeviation方法为默认方法.39MPTConfidentialEstimating计算WithinandOverEstimating计算

Within

andOverallIncaseswherethereisonly1observationpersub-group(i.e.k=1),theMovingRangeMethodisused,where在子组容量为1时,使用移动极差方法(MovingRangeMethod),

Thewithinvariation

Within

isthenestimatedusingeither短期标准差Within

可用下式中的一个计算theAverageMovingRange:方法移动极差平均值theMedianMovingRange:移动极差中位数:40MPTConfidentialEstimating计算WithinandOverExample4例4Thelengthofacamshaftforanautomobileengineisspecifiedat600±2mm.Controlofthelengthofthecamshaftiscriticaltoavoidscrap/rework.Thecamshaftisprovidedbyexternalsuppliers.Assesstheprocesscapabilityforthissupplier.“Thedataisavailablein“01-03”.Dataarecollectedinsubgroupsof5each.某汽车发动机的凸轮轴长度规格为600±2mm.控制该长度可以避免报废和返工,每个子组收集5个长度数据,该轴由外部供应商供应,请评估该供应商的过程能力.数据存储在“01-03”中.实际操作MiniTab41MPTConfidentialExample4例4ThelengthofacamExample例5Histogramofthecamshaftlengthsuggestsmixedpopulations.Furtherinvestigationrevealedthattherearetwosuppliersforthecamshaft.Datawerenowcollectedoncamshaftsfromeachsourcewithoutcombiningboth.Subgroupsizeis5foreachsupplier.Arethetwosupplierssimilarinperformance?Ifnot,whatareyourrecommendations?从直方图上可看出轴的长度为几个总体的混合数据.进一步调查显示有两个供应商向公司供应该凸轮轴.数据来源于两家供应商的产品.该两家供应商的过程能力相同吗?如果不同,你推荐使用哪一家的产品?实际操作MiniTab42MPTConfidentialExample例5HistogramofthecamExample5MiniTab:StatQualityToolsCapabilitySixpack(Normal)43MPTConfidentialExample5MiniTab:43MPTConfideExample544MPTConfidentialExample544MPTConfidentialExample545MPTConfidentialExample545MPTConfidentialMotorola的原始定义:如果规格界限至少离过程均值μ为±6σ的距离,即Cp≥2并且过程偏移小于1.5σ,即Cp≥1.5那么过程缺陷率将小于3.4ppm.

6σ6σ4.5σ什么是六西格玛品质?---------过去46MPTConfidentialMotorola的原始定义:6σ6σ4.5σ什么是六西格玛MikelJHarry认为过程不同产品批之间的均值将发生变化平均变化量为1.5σ

注意:Sigma能力=f(dpmo)≠f(dppm)2σ什么是六西格玛品质?---------现在Kσ=2σ+1.5σKσ=2σ+1.5σ47MPTConfidentialMikelJHarry认为过程不同产品批之间的均值将CapabilityAnalysiswithBox-CoxTransformation

Box-Cox转化分析过程能力Whentheprocessdataarenotnormal,theCpkorPpkindicesarenotaccurateorreliable,becausetheseindicesarecomputedonthebasisthatthedataarenormallydistributed.当过程数据是非正态的,过程能力指数CpkorPpk是不正确的或可信的,因为这些数据是假定数据是正态分布的基础上.Dppmvaluesassociatedwiththeindiceswillnotbeneartotheactualperformancewhenthenormalcurvedoesnotmodeltheactualdatawell.当正态曲线不能很好的符合实际数据时,和指数相关的DPPM值不和实际表现相符.48MPTConfidentialCapabilityAnalysiswithBox-CIftheprocessdataaresomewhatbell-shapedbutskewed,Box-Coxtransformationcanbeusedtomakethedatanormalbeforeweassesstheprocesscapability.如果过程数据有些钟型但歪斜的,在我们评估过程能力之前,Box-Cox转化可帮助将数据转化成正态RemembertotransformthespecificationlimitstoobeforewecomputeCpkorPpk!记住在计算过程能力指数前也要将规格界限进行转化!

CapabilityAnalysiswithBox-CoxTransformation

Box-Cox转化分析过程能力49MPTConfidentialIftheprocessdataaresomewhMinitab:StatQualityToolsCapabilityAnalysis(Normal)CapabilityAnalysiswithBox-CoxTransformation

Box-Cox转化分析过程能力50MPTConfidentialMinitab:CapabilityAnalysiswiExample例6Openthefilenamed01-04.MTW

,Computetheprocesscapabilitywiththespecificationlimits:打开01-04文件,用规格界限计算过程能力(samplesize=1)LSL:0.1 USL:10Arethedatanormallydistributed?数据是正态分布吗?ComputetheprocesscapabilityagainwithBox-Coxtransformation.利用Box-Cox转化计算过程能力CapabilityAnalysiswithBox-CoxTransformation

Box-Cox转化分析过程能力51MPTConfidentialExample例6OpenthefilenamedCpkof0.41isreportedintheSSATpackage.Thisvalueisnotreliableoraccurateifthedataarenotnormal.Dataisnotnormal数据不是正态的Example6CapabilityAnalysiswithBox-CoxTransformation

Box-Cox转化分析过程能力在SSAT的Cpk0.41.如数据不是正态的,此数据不是可信的或不正确的.52MPTConfidentialCpkof0.41isreportedintheExample6Cpkhasincreasedfrom0.41to0.81CapabilityAnalysiswithBox-CoxTransformation

Box-Cox转化分析过程能力计算值和此值会有差别53MPTConfidentialExample6Cpkhasincreasedfro54AssumingNormality...假设正态USLZisNormallydistributedwithMean=0andSD=1Z-值平均值为“0”标准偏差为“1”的正态分布值.LSLZscoreZScoresZ-值54AssumingNormality...USLZis55ZLSL,ZUSLUSLLSLZLSLZUSL55ZLSL,ZUSLUSLLSLZLSLZUSL多少s

过程USLZ-Scoreinterpretation:Howmanystandarddeviations,sors-hats,isthemean,x-bar,fromsomespecifiedvalue,x.Z-值解释:是一个到平均值有几个标准偏差的的特定值Let’sassumethereisonlyanUSL让我们假设只有只有规格下限?s0.001ppmUSLTmASixSigmaProcess25,000ppmUSLTmATwoSigmaProcess多少s过程USLZ-ScoreinterpretatiBasicInstructionsforMinitab

ComputingStandardNormalProbabilities

计算标准正态概率的MiniTab基本操作57MPTConfidentialBasicInstructionsforMinitabSelect“Calc”,“ProbabilityDistributions”and“Normal”.Select“CumulativeProbability”,enterthe“Mean”and“StandardDeviation”,clickon“Inputconstant”,enterthevalueandclickon“OK”.ComputingPercentFalloutCumulativeDistributionFunctionNormalwithmean=11.0000andstandarddeviation=1.00000x P(X<=x)12.0000 0.841358MPTConfidentialSelect“Calc”,“ProbabilityDiMinitabOutputUSL=12Tm=11AOneSigmaProcessDPPM=(1-0.8413)x1,000,000 =158700CumulativeDistributionFunctionNormalwithmean=11.0000andstandarddeviation=1.00000x P(X<=x)12.0000 0.841359MPTConfidentialMinitabOutputUSL=12Tm=11AComputingZ-ScoreFromPercentFalloutSelect“InverseCumulativeprobability”,setthe“Mean”=0and“StandardDeviation”=1,clickon“Inputconstant”,enterthetotalareaassociatedwithfalloutandclickon“OK”.

p=0.8413InverseCumulativeDistributionFunctionNormalwithmean=0andstandarddeviation=1.00000P(X<=x)x0.84130.999860MPTConfidentialComputingZ-ScoreFromPercents=1LSL=9USL=12Tm=11DeterminetheDPPMZLSL,ZUSLandtheZscoreExercise61MPTConfidentials=1LSL=9USL=12Tm=11DeteSelect“Calc”,“ProbabilityDistributions”and“Normal”.Select“Cumulativeprobability”,enterthe“Mean”and“StandardDeviation”,clickon“Inputconstant”,enterthevalueandclickon“OK”.CumulativeDistributionFunctionNormalwithmean=11.0000andstandarddeviation=1.00000x P(X<=x)12.0000 0.8413Solution:Minitab62MPTConfidentialSelect“Calc”,“ProbabilityDiSelect“Cumulativeprobability”,enterthe“Mean”and“StandardDeviation”,clickon“Inputconstant”,enterthevalueandclickon“OK”.CumulativeDistributionFunctionNormalwithmean=11.0000andstandarddeviation=1.00000x P(X<=x)9.0000 0.0228DPPM=((0.0228)+(1-0.8413))x1,000,000 =181500Solution:MinitabZLSL=(9-11)/163MPTConfidentialSelect“CumulativeprobabilitySelect“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:Minitab64MPTConfidentialSelect“InverseCumulativeproProcessCapabilityfor

Non-NormalData

非正态的过程能力65MPTConfidentialProcessCapabilityfor

Non-NoProcessCapabilityforNon-NormalData

非正态数据的过程能力Noteverymeasuredcharacteristicisnormallydistributed.Somedatafollowsdistributionsthatareknown,andthesemaybeabletohavetheircapabilitymeasuredaccuratelyusingthatknowledge不是所有的测量参数都是正态分布的,一些数据分布已知,就可以准确地应用自己的过程能力分析方法去测量过程能力

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 DefectRate缺陷率 Poisson泊松分布66MPTConfidentialProcessCapabilityforNon-NorTheWeibullDistributionisageneralfamilyofdistributionwith威布尔分布为一个常见的分布,用下式表示:where scaleparameter

isthevalueatwhichCDF=68.17%,and shapeparameterdeterminestheshapeofthePDF.上式中,尺度参数θ为CDF=68.17%时的值形状参数β确定了PDF的形状ProcessCapabilityforCycleTime

周期时间的过程能力67MPTConfidentialTheWeibullDistributionisaAt=1, theWeibullDistributionisreducedto当β=1,威布尔分布可简化为::

ForanExponentialDistribution,对指数分布,有TheExponentialDistributionisthusaWeibullDistributionwith=1.指数分布为β=1时的威布尔分布.Weibull(x;=1,)Exponential(x;)ProcessCapabilityforCycleTime

周期时间的过程能力68MPTConfidentialAt=1, theWeibullDistributiExample4Acustomerservicemanagerwantstodeterminetheprocesscapabilityforhisdepartment.Aprimaryperformanceindexisthetimetakentocloseacustomercomplaint.Thegoalforthisindexistocloseacomplaintwithinonecalendarweek.Performanceoverthelast400complaintswasreviewed.一位客户服务经理想确定他的部门过程能力,主要评价指标为处理客户投诉的时间周期,目标为在一周内处理完一单客户投诉,过去的400%次投诉作为测量数据.数据在此期01-03Days69MPTConfidentialExample4AcustomerservicemaExample4StatQualityToolsCapabilityAnalysis(Weibull)70MPTConfidentialExample4StatQualityToolsExample471MPTConfidentialExample471MPTConfidentialExample4AStatQualityToolsCapabilitySixpack(Weibull)72MPTConfidentialExample4AStatQualityToolsExample4A73MPTConfidentialExample4A73MPTConfidentialAlternativesforNon-NormalData

非正态数据解释Whenallothermethodsfail,itmaybenecessarytofallbackonasimpleassessmentofthetotalamountoutofspecifications.Simplycountthenumberofdefectiveunitsanddividebythetotaltocomputethefractiondefective.AnotherstandardmetricforthisistheDPPM.当所有方法失败,它需要返回到一个评估超出控制界限数量的简单方法,简单地查一下不合格品和全部产品的数量,然后计算不合格率,另一个标准刻度也是DPPMIfaCapabilityIndexmustbereported,theDPPMcanbeconvertedbackintoaZvalue,andtheneitherPpk=Z/3or Cpk=Z/3dependinguponwhetherthedataislongtermorshortterm.如果要得到过程能力指数,DPPM可以转化为Z-值,然后根据此数据是长期或短期得PPK=Z/3或Cpk=Z/374MPTConfidentialAlternativesforNon-NormalDaProcessCapabilityforRejectRate

不合格率的过程能力ForaNormalDistribution,theproportionofpartsproducedbeyondaspecificationlimitis对于一个正态分布,在控制界限下的比例部分.RejectRate75MPTConfidentialProcessCapabilityforRejectThus,foreveryrejectratethereisanaccompanyingZ-Score,这样一来,对于每一个不合格率都有一个对应的Z-值Where这里Recallthat原先Hence因此ProcessCapabilityforRejectRate

不合格率的过程能力76MPTConfidentialThus,foreveryrejectratethEstimationofPpkforRejectRate不合格率Ppk的计算:Determinethelong-termrejectrate(p)计算长期不合格率(p)Determinetheinversecumulativeprobabilityforp,usingCalcProbabilityDistributionNormal计算相反的累计概率p,,点击CalcProbabilityDistributionNormalZ-ScoreisthemagnitudeofthereturnedvalueZ-值是反推值的多少.Ppkisone-thirdoftheZ-ScorePpk

是Z-值的三分之一.ProcessCapabilityforRejectRate

不合格率的过程能力77MPTConfidentialEstimationofPpkforRejectRExampleofProcessCapabilityStudyforRejectRate不合格率过程能力的例子Asalesmanagerplanstoassesstheprocesscapabilityofhistelephonesalesdepartment’shandlingofincomingcalls.一个销售经理打算评估他的电话销售部门处理接入电话的过程能力.01-03文件Thefollowingdatawascollectedoveraperiodof20days:以下数据收据20天numberofincomingcallsperday每天的接入电话数量numberofunansweredcallsperdays每天的未应答电话数量.78MPTConfidentialExampleofProcessCapabilityStatQualityToolsCapabilityAnalysis(Binomial)ExampleofProcessCapabilityStudyforRejectRate不合格率过程能力的例子79MPTConfidentialStatQualityToolsCapabilPpk=0.25ExampleofProcessCapabilityStudyforRejectRate不合格率过程能力的例子80MPTConfidentialPpk=0.25ExampleofProcessCProcessCapabilityforDefectRate

缺陷率的过程能力Otherapplications,approximatingaPoissonDistribution:errorratesparticlecountchemicalconcentration以下应用,近似于泊淞分布:缺陷率缺点数溶液浓度81MPTConfidentialProcessCapabilityforDefectEstimationofYtpforDefectRateDefinesizeofaninspectionunitDeterminethelong-termdefectsperunit(DPU) DPU =TotalDefectsTotalUnitsDeterminethethroughputyield(Ytp) Ytp =exp{–DPU}ProcessCapability