六西格瑪工序控制與工序能力教材

Six-SigmaTrainingBook

Six-SigmaDec18,20011

數(shù)據(jù)分布2

NormalExponentialWeibullLognormaltc2fContinuousDistributionsSamplingDistributions數(shù)據(jù)分布3Themostwidelyusedmodelforthedistributionofcontinuousrandomvariable.Arisesinthestudyofnumerousphysicalphenomena,suchasthevelocityofmolecules.正態(tài)分布PlotisknownasProbabilityDensityFunctionofX4Manynaturalphenomenaandman-madeprocessesareobservedtohavenormaldistributions,orcanbecloselyrepresentedasnormallydistributed.Forexample,thelengthofamachinedpartisobservedtovaryaboutitsmeandueto:temperaturedrift,humiditychange,vibrations,cuttinganglevariations,cuttingtoolwear,bearingwear,rotationalspeedvariations,fixturingvariations,rawmaterialchangesandcontaminationlevelchangesIfthesesourcesofvariationaresmall,independentandequallylikelytobepositiveornegative,thelengthwillcloselyapproximateanormaldistribution.正態(tài)分布5FirstintroducedbyFrenchmathematicianAbrahamDeMoivrein1733.Madefamousin1809byGermanmathematicianK.F.Gausswhenhealsodevelopedanormaldistributionindependentlyanduseditinhisstudyofastronomy.Asaresult,itisalsoknownastheGaussiandistribution.Duringmidtolatenineteenthcentury,manystatisticiansbelievedthatitwas“normal”formostwell-behaveddatatofollowthiscurve.正態(tài)分布-歷程表KarlFriedrichGauss6正態(tài)分布易于理解,具有特性,統(tǒng)計(jì)學(xué)提供了許多基于正態(tài)分布的強(qiáng)有力的分析方法來(lái)幫助人們做決定.因此,我們通常會(huì)試圖用正態(tài)分布去近似模擬其它分布(如可能)或轉(zhuǎn)化數(shù)據(jù)以“使”它遵從正態(tài)分布.它是分析過(guò)程能力的首選分布形式.正態(tài)分布7Anormaldistributioncanbecompletelydescribedbyknowingonlythe:Mean(m)Variance(s2)正態(tài)分布的一些特性DistributionOneDistributionTwoDistributionThreeWhatisthedifferencebetweenthe3normaldistributions?X~N(m,s2)18A~Normal(A,A2)B~Normal(B,B2)A~Normal(A,A2)B~Normal(B,B2)A~Normal(A,A2)B~Normal(B,B2)WhatisthedifferencebetweenprocessA&Bforeachcase?正態(tài)分布的一些特性9Themean,medianandmodeallcoincideatthesamevalue-m.Thereisperfectsymmetry.μ+￥-￥MeanMedianMode2Themeanrepresentsthearithmeticaverageofallobservationsinadataset. Ifasetofobservationsisarrangedinanincreasingorderofmagnitude(rankeddata),themiddlevalueiscalledthemedian.Ifthenumberofobservationsisodd,themedianisthevalueofthemiddlenumber.Ifthenumberofobservationsiseven,thereare2middlenumbers,andthemedianistheaverageofthe2values.Themodeistheobservationthatoccursmostfrequentlyinthesample.正態(tài)分布的一些特性10Theareaundersectionsofthecurvecanbeusedtoestimatethecumulativeprobabilityofacertain““event””occurring:μPointofInflection1s+￥-￥68.27%95.45%99.73%m+/-3sisoftenreferredtoasthewidthofanormaldistribution3正態(tài)態(tài)分分布布的的一一些些特特性性11Let’’scomputethecumulativeprobabilitiesofthefollowingdistributions:+￥-￥m=3.5s=0.61.8+￥-￥20.0m=16.6s=2.8+￥-￥m=-1.5s=0.9-2.80.5正態(tài)態(tài)分分布布的的一一些些特特性性12MiniTab:CalceProbabilityDistributionseNormal...EntermvalueEntersvalueEnterxvalue正態(tài)態(tài)分分布布的的一一些些特特性性13什么么是是6σ???146σ簡(jiǎn)介介15TheFocusofSixSigmaIdentifyingcriticalaspectsofthebusinesswithproblemsoropportunitiesforimprovement.TargetingthosecriticalareasanddesignatingimprovementeffortsasSixSigmaBlackBeltprojects.Selectingtoppeopletoworkontheprojects--fulltime.Ensuringthesepeoplehavethetime,tools,andresourcestheyneedtosucceed.16CustomerFocus:AModelForSuccessTechnologyTechnologyCapabilityCapabilityOrganizationOrganizationPeoplePeopleProcessesProcesses商務(wù)上的生生存競(jìng)爭(zhēng)有有賴(lài)于我們們多大程度度上讓我們們的客戶滿滿意.客戶滿意才才能體現(xiàn)品品質(zhì),價(jià)價(jià)格,和和貨期的意意義.品質(zhì),成本本,準(zhǔn)時(shí)時(shí)走貨無(wú)不不依耐于工工序能力.WhatpurposeisSix-sigma?17SixSigmaVisionTheVisionofSixSigmaistodelightcustomersbydeliveringworld-classqualityproductsthroughtheachievementofSixSigmalevelsofperformanceineverythingwedo.WhatpurposeisSix-sigma?SixSigmaPhilosophyThephilosophyofSixSigmaistoapplyastructured,systematicapproachtoachievebreakthroughimprovementacrossallareasofourbusiness.18PPMProcessCapabilityDefectsperMillionOpp.SixSigma-AggressiveGoalWhatpurposeisSix-sigma?19StatisticalDefinitionofn-SigmaLSLLSLUSLUSLProcessWidthmoDesignWidthTTscaleLSLLSLUSLUSLscaleTT+nsscale-nsThisistheso-calledn-sigmaSigmaisastatisticalunitofmeasurethatreflectsprocesscapability.Thesigmascaleofmeasureisperfectlycorrelatedtosuchcharacteristicsasdefects-per-unit,parts-permilliondefective,andtheprobabilityofafailure/error.20StatisticalDefinitionof6σThisisthesix-sigmawesaidLSLLSLUSLUSLProcessWidthmoDesignWidth-3sst+3sstTT.001ppm>USL.001ppm<LSLscaleLSLLSLUSLUSLscaleTT+6sstscale-6sst213Sigma6Sigma5Sigma4Sigma93.32%99.379%99.9767%99.99966%HistoricalCurrentIntermediateLong-RunSigmaLong-TermYieldStandard6σ-PerformanceTarget22CharacterizeOptimizeBreakthroughUSLTLSLUSLTLSLTUSLLSLUSL’LSL’TheStrategy23BreakthroughStrategyCharacterizationPhase1:MeasurementPhase2:AnalysisOptimizationPhase3:ImprovementPhase4:ControlTheBreakthroughPhases24Phase2:AnalysisCapabilitystudy(Cpk)GR&RstudyCause&effectanalysisFishboneandC&EmatrixDotplot,Boxplot,Histogramchart,ParetochartTheBreakthroughPhasesAnalysistoolandmethod25ImprovementAnalysisrolledthroughputyieldSetupprocessMapSetupFMEAandcontrol…………….TheBreakthroughPhasesImprovementtoolandmethod26工序能能力力分分析析Dec18,200127學(xué)習(xí)習(xí)目目標(biāo)標(biāo)工序控控制與與工序序能力力工序能能力:規(guī)格,工工藝和和控制制的界界限工序潛潛力與與工序序表現(xiàn)現(xiàn)短期與與長(zhǎng)期期工序序能力力“6σ”品品質(zhì)28工序控控制與與工序序能力力1.工序控控制意即工工序運(yùn)運(yùn)作處處于統(tǒng)計(jì)控控制狀狀態(tài),換換言言之,普普遍的的原因因是變變化的的僅有有來(lái)源源.鑒于““用事實(shí)實(shí)說(shuō)話話”,即即一個(gè)人人僅需需要用用源于于工序序的數(shù)數(shù)據(jù)來(lái)來(lái)判判定工工序是是處于于受控控狀態(tài)態(tài).過(guò)程的的跟蹤蹤表現(xiàn)現(xiàn)來(lái)証証實(shí)它它是否否建立立了長(zhǎng)長(zhǎng)時(shí)間間穩(wěn)定定的數(shù)數(shù)據(jù)分分布表表現(xiàn),典型型地,用用帶有有“僅從工工序中中的數(shù)數(shù)據(jù)計(jì)計(jì)算出出的”控制制圖表表.“而且一一個(gè)工工序在在受控控”并并不一一定意意味著著它是是一個(gè)個(gè)好工工序.29工序控控制與與工序序能力力2.工工序能能力“好處處”是是工工序序能能力力可可被被度度量量比較較““工序序的的現(xiàn)現(xiàn)狀狀”與與““客戶戶的的要要求求”,均均須須以以規(guī)規(guī)格格為為依依據(jù)據(jù)度量量一一個(gè)個(gè)穩(wěn)穩(wěn)定定的的工工序序狀狀態(tài)態(tài)(受受控控制制)在在多多大大程程度度上上能能滿滿足足客客戶戶的的規(guī)規(guī)格格.30變化化的的類(lèi)類(lèi)型型固有有的的或或定定值值的的變變化化許多多微微小小又又不不可可避避免免的的原原因因?qū)?dǎo)致致的的累累積積效效果果只有有微微小小的的機(jī)機(jī)會(huì)會(huì)導(dǎo)導(dǎo)致致變變化化的的運(yùn)運(yùn)作作工工序序稱(chēng)稱(chēng)為為““統(tǒng)統(tǒng)計(jì)計(jì)控控制制””31變化化的的類(lèi)類(lèi)型型特定定或或確確定定的的變變化化可能能由由于于a)不正正確確的的調(diào)調(diào)機(jī)機(jī)b)操操作作者者錯(cuò)錯(cuò)誤誤c)有有缺缺陷陷的的原原材材料料一個(gè)個(gè)工工序序如如果果出出現(xiàn)現(xiàn)上上面面的的變變化化則則稱(chēng)稱(chēng)為為““失失控控””.32工序序能能力力工序序能能力力研究究能能:顯示示工工序序輸輸出出的的恒恒定定性性顯示示輸輸出出符符合合規(guī)規(guī)格格的的程程度度用于于和和另另一一工工序序或或競(jìng)競(jìng)爭(zhēng)爭(zhēng)對(duì)對(duì)手手比比較較33工序序能能力力與與規(guī)規(guī)格格極極限限a)b)c)a)工工序序能能力力高高b)工工序序能能力力能能夠夠滿滿足足c)工工序序能能力力不不足足夠夠34三種種極極限限類(lèi)類(lèi)型型規(guī)格格極極限限(LSLandUSL)createdbydesignengineeringinresponsetocustomerrequirementstospecifythetoleranceforaproduct’’scharacteristic工序極限限(LPLandUPL)measuresthevariationofaprocessthenatural6limitsofthemeasuredcharacteristic控制極限限(LCLandUCL)measuresthevariationofasamplestatistic(mean,variance,proportion,etc)35工序能力力指數(shù)工序能力力的兩種種度量:工序潛力力Cp工序表現(xiàn)現(xiàn)CpuCplCpk36工序潛力力Cp指標(biāo)顯示示實(shí)際工工差(6)是否超超出規(guī)格格.公式37工序潛力力傳統(tǒng)上,Cp有1.0時(shí)時(shí)顯示工工序能力力被判為為“有能能力考核核成績(jī)””.若數(shù)據(jù)集集中于工工程工差差內(nèi),將將僅有有0.27%的的工件件會(huì)超差差.Cp拒貨率1.000.270%1.330.007%1.506.8ppm2.002.0ppb38工序潛力力a)b)c)a)工工序能力力高(Cp>2)b)工工序能力力可(Cp=1to2)c)工工序能力力差(Cp<1)39工序潛力力TheCpindexcomparestheallowablespread(USL-LSL)againsttheprocessspread(6).Itfailstotakeintoaccountiftheprocessiscenteredbetweenthespecificationlimits.ProcessiscenteredProcessisnotcentered40工序表現(xiàn)現(xiàn)TheCpkindexrelatesthescaleddistancebetweentheprocessmeanandthenearestspecificationlimit.41工序表現(xiàn)現(xiàn)Cpk不良率1.00.13––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––2ppb42工序表現(xiàn)現(xiàn)a)工序序能力高高(Cpk>1.5)b)工序序能力可可(Cpk=1to1.5)c)工序序能力差差(Cpk<1)a)Cp=2Cpk=2b)Cp=2Cpk=1c)Cp=2Cpk<143工序潛力力與工序序表現(xiàn)(a)PoorProcessPotential(b)PoorProcessPerformanceLSLUSLLSLUSLExperimentalDesigntoreducevariationExperimentalDesigntocentermeantoreducevariation44工序潛力力與工序序表現(xiàn)a)Cp=2Cpk=2b)Cp=2Cpk=1c)Cp=2Cpk<145工序穩(wěn)定定性Aprocessisstableifthedistributionofmeasurementsmadeonthegivenfeatureisconsistentovertime.TimeStableProcessTimeUnstableProcessucllclucllcl46短期工序序能力與與長(zhǎng)期工工序能力力短期工序序能力(previouslycalledshort-termcapability)showstheinherentvariabilityofamachine/processoperatingwithinabriefperiodoftime.長(zhǎng)期工序序能力(previouslycalledlong-termcapability)showsthevariabilityofamachine/processoperatingoveraperiodoftime.Itincludessourcesofvariationinadditiontotheshort-termvariability.47WithinOverallSampleSize30––50units100unitsNumberofLotssinglelotseverallotsPeriodofTimehoursordays weeksormonthsNumberofOperatorssingleoperatordifferentoperatorsProcessPotentialCpPpProcessPerformanceCpkPpk短期工序能能力與長(zhǎng)期期工序能力力48實(shí)戰(zhàn)演練Thelengthofacamshaftforanautomobileengineisspecifiedat600±2mm.Controlofthelengthofthecamshaftiscriticaltoavoidscrap/rework.Thecamshaftisprovidedbyexternalsuppliers.Assesstheprocesscapabilityforthissupplier.ThedataisavailableinCamshaft.MTW.Dataarecollectedinsubgroupsof5each.49Example4Minitab:StatQualityToolsCapabilityAnalysis(Normal)50Example451Example5Histogramofthecamshaftlengthsuggestsmixedpopulations.Furtherinvestigationrevealedthattherearetwosuppliersforthecamshaft.Datawerenowcollectedoncamshaftsfromeachsourcewithoutcombiningboth.Subgroupsizeis5foreachsupplier.Arethetwosupplierssimilarinperformance?Ifnot,whatareyourrecommendations?52Example5MiniTab:StatQualityToolsCapabilitySixpack(Normal)53Example554Example555用Box-Cox轉(zhuǎn)轉(zhuǎn)化后的的工序能力力分析Whentheprocessdataarenotnormal,theCpkorPpkindicesarenotaccurateorreliable,becausetheseindicesarecomputedonthebasisthatthedataarenormallydistributed.Dppmvaluesassociatedwiththeindiceswillnotbeneartotheactualperformancewhenthenormalcurvedoesnotmodeltheactualdatawell.56Iftheprocessdataaresomewhatbell-shapedbutskewed,Box-Coxtransformationcanbeusedtomakethedatanormalbeforeweassesstheprocesscapability.RemembertotransformthespecificationlimitstoobeforewecomputeCpkorPpk!用Box-Cox轉(zhuǎn)轉(zhuǎn)化后的的工序能能力分析析57Minitab:StatQualityToolsCapabilityAnalysis(Normal)用Box-Cox轉(zhuǎn)轉(zhuǎn)化后的的工序能能力分析析58Example6OpenthefilenamedDimension.MTWintheDay-2folderagain.Computetheprocesscapabilitywiththespecificationlimits:LSL:0.1USL:10Arethedatanormallydistributed?ComputetheprocesscapabilityagainwithBox-Coxtransformation.用Box-Cox轉(zhuǎn)轉(zhuǎn)化后的的工序能能力分析析59Cpkof0.41isreportedintheSSATpackage.Thisvalueisnotreliableoraccurateifthedataarenotnormal.DataisnotnormalExample6用Box-Cox轉(zhuǎn)轉(zhuǎn)化后的的工序能能力分析析60Example6Cpkhasincreasedfrom0.41to0.81用Box-Cox轉(zhuǎn)轉(zhuǎn)化后的的工序能能力分析析61What’s““6”Quality——ThenOriginalDefinitionbyMotorola:Intheshortterm,thespecificationlimitsareatlea