六西格玛工序控制与工序能力教材

Six-SigmaTrainingBook

Six-SigmaDec18,20011

數据分布2

NormalExponentialWeibullLognormaltc2fContinuousDistributionsSamplingDistributions數据分布3Themostwidelyusedmodelforthedistributionofcontinuousrandomvariable.Arisesinthestudyofnumerousphysicalphenomena,suchasthevelocityofmolecules.正態分布PlotisknownasProbabilityDensityFunctionofX4Manynaturalphenomenaandman-madeprocessesareobservedtohavenormaldistributions,orcanbecloselyrepresentedasnormallydistributed.Forexample,thelengthofamachinedpartisobservedtovaryaboutitsmeandueto:temperaturedrift,humiditychange,vibrations,cuttinganglevariations,cuttingtoolwear,bearingwear,rotationalspeedvariations,fixturingvariations,rawmaterialchangesandcontaminationlevelchangesIfthesesourcesofvariationaresmall,independentandequallylikelytobepositiveornegative,thelengthwillcloselyapproximateanormaldistribution.正態分布5FirstintroducedbyFrenchmathematicianAbrahamDeMoivrein1733.Madefamousin1809byGermanmathematicianK.F.Gausswhenhealsodevelopedanormaldistributionindependentlyanduseditinhisstudyofastronomy.Asaresult,itisalsoknownastheGaussiandistribution.Duringmidtolatenineteenthcentury,manystatisticiansbelievedthatitwas“normal”formostwell-behaveddatatofollowthiscurve.正態分布-歷程表KarlFriedrichGauss6正態分布易于理解,具有特性,統計學提供了許多基于正態分布的強有力的分析方法來幫助人們做決定.因此,我們通常會試圖用正態分布去近似模擬其它分布(如可能)或轉化數据以“使”它遵從正態分布.它是分析過程能力的首選分布形式.正態分布7Anormaldistributioncanbecompletelydescribedbyknowingonlythe:Mean(m)Variance(s2)正態分布的一些特性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?正態分布的一些特性9Themean,medianandmodeallcoincideatthesamevalue-m.Thereisperfectsymmetry.µ+¥-¥MeanMedianMode2Themeanrepresentsthearithmeticaverageofallobservationsinadataset. Ifasetofobservationsisarrangedinanincreasingorderofmagnitude(rankeddata),themiddlevalueiscalledthemedian.Ifthenumberofobservationsisodd,themedianisthevalueofthemiddlenumber.Ifthenumberofobservationsiseven,thereare2middlenumbers,andthemedianistheaverageofthe2values.Themodeistheobservationthatoccursmostfrequentlyinthesample.正態分布的一些特性10Theareaundersectionsofthecurvecanbeusedtoestimatethecumulativeprobabilityofacertain““event””occurring:µPointofInflection1s+¥-¥68.27%95.45%99.73%m+/-3sisoftenreferredtoasthewidthofanormaldistribution3正態態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正態態分分布布的的一一些些特特性性12MiniTab:CalcðProbabilityDistributionsðNormal...EntermvalueEntersvalueEnterxvalue正態態分分布布的的一一些些特特性性13什么么是是6σ???146σ簡介介15TheFocusofSixSigmaIdentifyingcriticalaspectsofthebusinesswithproblemsoropportunitiesforimprovement.TargetingthosecriticalareasanddesignatingimprovementeffortsasSixSigmaBlackBeltprojects.Selectingtoppeopletoworkontheprojects--fulltime.Ensuringthesepeoplehavethetime,tools,andresourcestheyneedtosucceed.16CustomerFocus:AModelForSuccessTechnologyTechnologyCapabilityCapabilityOrganizationOrganizationPeoplePeopleProcessesProcesses商務上的生生存競爭有有賴于我們們多大程度度上讓我們們的客戶滿滿意.客戶滿意才才能体現品品質,价价格,和和貨期的意意義.品質,成本本,准時時走貨無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學習習目目標標工序控控制与与工序序能力力工序能能力:規格,工工藝和和控制制的界界限工序潛潛力与与工序序表現現短期与与長期期工序序能力力“6σ”品品質28工序控控制与与工序序能力力1.工序控控制意即工工序運運作處處于統計控控制狀狀態,換換言言之,普普遍的的原因因是變變化的的僅有有來源源.鑒于““用事實實說話話”,即即一個人人僅需需要用用源于于工序序的數數据來來判判定工工序是是處于于受控控狀態態.過程的的跟蹤蹤表現現來証証實它它是否否建立立了長長時間間穩定定的數數据分分布表表現,典型型地,用用帶有有“僅從工工序中中的數數据計計算出出的”控制制圖表表.“而且一一個工工序在在受控控”并并不一一定意意味著著它是是一個個好工工序.29工序控控制与与工序序能力力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““工序序的的現現狀狀”与与““客戶戶的的要要求求”,均均須須以以規規格格為為依依据据度量量一一個個穩穩定定的的工工序序狀狀態態(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規格格.30變化化的的類類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導導致致的的累累積積效效果果只有有微微小小的的机机會會導導致致變變化化的的運運作作工工序序稱稱為為““統統計計控控制制””31變化化的的類類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)不正正確確的的調調机机b)操操作作者者錯錯誤誤c)有有缺缺陷陷的的原原材材料料一個個工工序序如如果果出出現現上上面面的的變變化化則則稱稱為為““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規格格的的程程度度用于于和和另另一一工工序序或或競競爭爭對對手手比比較較33工序序能能力力與與規規格格极极限限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34三種種极极限限類類型型規格格极极限限(LSLandUSL)createdbydesignengineeringinresponsetocustomerrequirementstospecifythetoleranceforaproduct’’scharacteristic工序极限限(LPLandUPL)measuresthevariationofaprocessthenatural6limitsofthemeasuredcharacteristic控制极限限(LCLandUCL)measuresthevariationofasamplestatistic(mean,variance,proportion,etc)35工序能力力指數工序能力力的兩种种度量:工序潛力力Cp工序表現現CpuCplCpk36工序潛力力Cp指標顯示示實際工工差(6)是否超超出規格格.公式37工序潛力力傳統上,Cp有1.0時時顯示工工序能力力被判為為“有能能力考核核成績””.若數据集集中于工工程工差差內,將將僅有有0.27%的的工件件會超差差.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工序表現現TheCpkindexrelatesthescaleddistancebetweentheprocessmeanandthenearestspecificationlimit.41工序表現現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工序表現現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工序潛力力与工序序表現(a)PoorProcessPotential(b)PoorProcessPerformanceLSLUSLLSLUSLExperimentalDesigntoreducevariationExperimentalDesigntocentermeantoreducevariation44工序潛力力与工序序表現a)Cp=2Cpk=2b)Cp=2Cpk=1c)Cp=2Cpk<145工序穩定定性Aprocessisstableifthedistributionofmeasurementsmadeonthegivenfeatureisconsistentovertime.TimeStableProcessTimeUnstableProcessucllclucllcl46短期工序序能力与与長期工工序能力力短期工序序能力(previouslycalledshort-termcapability)showstheinherentvariabilityofamachine/processoperatingwithinabriefperiodoftime.長期工序序能力(previouslycalledlong-termcapability)showsthevariabilityofamachine/processoperatingoveraperiodoftime.Itincludessourcesofvariationinadditiontotheshort-termvariability.47WithinOverallSampleSize30––50units100unitsNumberofLotssinglelotseverallotsPeriodofTimehoursordays weeksormonthsNumberofOperatorssingleoperatordifferentoperatorsProcessPotentialCpPpProcessPerformanceCpkPpk短期工序能能力与長期期工序能力力48實戰演練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轉轉化后的的工序能力力分析Whentheprocessdataarenotnormal,theCpkorPpkindicesarenotaccurateorreliable,becausetheseindicesarecomputedonthebasisthatthedataarenormallydistributed.Dppmvaluesassociatedwiththeindiceswillnotbeneartotheactualperformancewhenthenormalcurvedoesnotmodeltheactualdatawell.56Iftheprocessdataaresomewhatbell-shapedbutskewed,Box-Coxtransformationcanbeusedtomakethedatanormalbeforeweassesstheprocesscapability.RemembertotransformthespecificationlimitstoobeforewecomputeCpkorPpk!用Box-Cox轉轉化后的的工序能能力分析析57Minitab:StatQualityToolsCapabilityAnalysis(Normal)用Box-Cox轉轉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轉轉化后的的工序能能力分析析59Cpkof0.41isreportedintheSSATpackage.Thisvalueisnotreliableoraccurateifthedataarenotnormal.DataisnotnormalExample6用Box-Cox轉轉化后的的工序能能力分析析60Example6Cpkhasincreasedfrom0.41to0.81用Box-Cox轉轉化后的的工序能能力分析析61What’s““6”Quality——ThenOriginalDefinitionbyMotorola:Intheshortterm,thespecificationlimitsareatlea