TRAINING SIX-SIGMA.ppt

Dec18 2001 BPTLConfidential 1 Six SigmaTrainingBook Six Sigma BPTLConfidential 2 數据分布 BPTLConfidential 3 NormalExponentialWeibullLognormaltc2f ContinuousDistributions SamplingDistributions 數据分布 BPTLConfidential 4 Themostwidelyusedmodelforthedistributionofcontinuousrandomvariable Arisesinthestudyofnumerousphysicalphenomena suchasthevelocityofmolecules 正態分布 PlotisknownasProbabilityDensityFunctionofX BPTLConfidential 5 Manynaturalphenomenaandman madeprocessesareobservedtohavenormaldistributions orcanbecloselyrepresentedasnormallydistributed Forexample thelengthofamachinedpartisobservedtovaryaboutitsmeandueto temperaturedrift humiditychange vibrations cuttinganglevariations cuttingtoolwear bearingwear rotationalspeedvariations fixturingvariations rawmaterialchangesandcontaminationlevelchangesIfthesesourcesofvariationaresmall independentandequallylikelytobepositiveornegative thelengthwillcloselyapproximateanormaldistribution 正態分布 BPTLConfidential 6 FirstintroducedbyFrenchmathematicianAbrahamDeMoivrein1733 Madefamousin1809byGermanmathematicianK F Gausswhenhealsodevelopedanormaldistributionindependentlyanduseditinhisstudyofastronomy Asaresult itisalsoknownastheGaussiandistribution Duringmidtolatenineteenthcentury manystatisticiansbelievedthatitwas normal formostwell behaveddatatofollowthiscurve 正態分布 歷程表 KarlFriedrichGauss BPTLConfidential 7 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 BPTLConfidential 8 Anormaldistributioncanbecompletelydescribedbyknowingonlythe Mean m Variance s2 正態分布的一些特性 Whatisthedifferencebetweenthe3normaldistributions X N m s2 1 BPTLConfidential 9 WhatisthedifferencebetweenprocessA Bforeachcase 正態分布的一些特性 BPTLConfidential 10 Themean medianandmodeallcoincideatthesamevalue m Thereisperfectsymmetry MeanMedianMode 2 Themeanrepresentsthearithmeticaverageofallobservationsinadataset Ifasetofobservationsisarrangedinanincreasingorderofmagnitude rankeddata themiddlevalueiscalledthemedian Ifthenumberofobservationsisodd themedianisthevalueofthemiddlenumber Ifthenumberofobservationsiseven thereare2middlenumbers andthemedianistheaverageofthe2values Themodeistheobservationthatoccursmostfrequentlyinthesample 正態分布的一些特性 BPTLConfidential 11 Theareaundersectionsofthecurvecanbeusedtoestimatethecumulativeprobabilityofacertain event occurring PointofInflection 1s 68 27 95 45 99 73 m 3sisoftenreferredtoasthewidthofanormaldistribution 3 正態分布的一些特性 BPTLConfidential 12 Let scomputethecumulativeprobabilitiesofthefollowingdistributions m 3 5s 0 6 1 8 20 0 m 16 6s 2 8 m 1 5s 0 9 2 8 0 5 正態分布的一些特性 BPTLConfidential 13 MiniTab Calc ProbabilityDistributions Normal Entermvalue Entersvalue Enterxvalue 正態分布的一些特性 BPTLConfidential 14 什么是6 BPTLConfidential 15 6 簡介 BPTLConfidential 16 TheFocusofSixSigma Identifyingcriticalaspectsofthebusinesswithproblemsoropportunitiesforimprovement TargetingthosecriticalareasanddesignatingimprovementeffortsasSixSigmaBlackBeltprojects Selectingtoppeopletoworkontheprojects fulltime Ensuringthesepeoplehavethetime tools andresourcestheyneedtosucceed BPTLConfidential 17 CustomerFocus AModelForSuccess Technology Technology Capability Capability Organization Organization People People Processes Processes 商務上的生存競爭有賴于我們多大程度上讓我們的客戶滿意 客戶滿意才能体現品質 价格 和貨期的意義 品質 成本 准時走貨無不依耐于工序能力 WhatpurposeisSix sigma BPTLConfidential 18 SixSigmaVision TheVisionofSixSigmaistodelightcustomersbydeliveringworld classqualityproductsthroughtheachievementofSixSigmalevelsofperformanceineverythingwedo WhatpurposeisSix sigma SixSigmaPhilosophy ThephilosophyofSixSigmaistoapplyastructured systematicapproachtoachievebreakthroughimprovementacrossallareasofourbusiness BPTLConfidential 19 PPM ProcessCapability DefectsperMillionOpp SixSigma AggressiveGoal WhatpurposeisSix sigma BPTLConfidential 20 StatisticalDefinitionofn Sigma LSL LSL USL USL ProcessWidth m o DesignWidth T T scale LSL LSL USL USL scale T T n s scale n s Thisistheso calledn sigma Sigmaisastatisticalunitofmeasurethatreflectsprocesscapability Thesigmascaleofmeasureisperfectlycorrelatedtosuchcharacteristicsasdefects per unit parts permilliondefective andtheprobabilityofafailure error BPTLConfidential 21 StatisticalDefinitionof6 Thisisthesix sigmawesaid LSL LSL USL USL ProcessWidth m o DesignWidth 3 s st T T 001 ppm USL 001 ppm LSL scale LSL LSL USL USL scale T T 6 s st scale BPTLConfidential 22 3Sigma 6Sigma 5Sigma 4Sigma 93 32 99 379 99 9767 99 99966 Historical Current Intermediate Long Run Sigma Long TermYield Standard 6 PerformanceTarget BPTLConfidential 23 CharacterizeOptimizeBreakthrough USL T LSL USL T LSL T USL LSL USL LSL TheStrategy BPTLConfidential 24 Characterization Phase1 Measurement Phase2 Analysis Optimization Phase3 Improvement TheBreakthroughPhases BPTLConfidential 25 Phase2 Analysis Capabilitystudy Cpk GR Rstudy Cause effectanalysisFishboneandC Ematrix Dotplot Boxplot Histogramchart Paretochart TheBreakthroughPhasesAnalysistoolandmethod BPTLConfidential 26 Improvement Analysisrolledthroughputyield SetupprocessMap SetupFMEA andcontrol TheBreakthroughPhasesImprovementtoolandmethod Dec18 2001 BPTLConfidential 27 工序能力分析 BPTLConfidential 28 學習目標 工序控制与工序能力工序能力 規格 工藝和控制的界限工序潛力与工序表現短期与長期工序能力 6 品質 BPTLConfidential 29 工序控制与工序能力 1 工序控制意即工序運作處于統計控制狀態 換言之 普遍的原因是變化的僅有來源 鑒于 用事實說話 即一個人僅需要用源于工序的數据來判定工序是處于受控狀態 過程的跟蹤表現來証實它是否建立了長時間穩定的數据分布表現 典型地 用帶有 僅從工序中的數据計算出的 控制圖表 而且一個工序在受控 并不一定意味著它是一個好工序 BPTLConfidential 30 工序控制与工序能力 2 工序能力 好處 是工序能力可被度量比較 工序的現狀 与 客戶的要求 均須以規格為依据度量一個穩定的工序狀態 受控制 在多大程度上能滿足客戶的規格 BPTLConfidential 31 變化的類型 固有的或定值的變化許多微小又不可避免的原因導致的累積效果只有微小的机會導致變化的運作工序稱為 統計控制 BPTLConfidential 32 變化的類型 特定或確定的變化可能由于a 不正確的調机b 操作者錯誤c 有缺陷的原材料一個工序如果出現上面的變化則稱為 失控 BPTLConfidential 33 工序能力 工序能力研究能 顯示工序輸出的恒定性顯示輸出符合規格的程度用于和另一工序或競爭對手比較 BPTLConfidential 34 工序能力與規格极限 a b c a 工序能力高b 工序能力能夠滿足c 工序能力不足夠 BPTLConfidential 35 三種极限類型 規格极限 LSLandUSL createdbydesignengineeringinresponsetocustomerrequirementstospecifythetoleranceforaproduct scharacteristic工序极限 LPLandUPL measuresthevariationofaprocessthenatural6 limitsofthemeasuredcharacteristic控制极限 LCLandUCL measuresthevariationofasamplestatistic mean variance proportion etc BPTLConfidential 36 工序能力指數 工序能力的兩种度量 工序潛力Cp工序表現CpuCplCpk BPTLConfidential 37 工序潛力 Cp指標顯示實際工差 6 是否超出規格 公式 BPTLConfidential 38 工序潛力 傳統上 Cp有1 0時顯示工序能力被判為 有能力考核成績 若數据集中于工程工差內 將僅有0 27 的工件會超差 Cp拒貨率1 000 270 1 330 007 1 506 8ppm2 002 0ppb BPTLConfidential 39 工序潛力 a b c a 工序能力高 Cp 2 b 工序能力可 Cp 1to2 c 工序能力差 Cp 1 BPTLConfidential 40 工序潛力 TheCpindexcomparestheallowablespread USL LSL againsttheprocessspread 6 Itfailstotakeintoaccountiftheprocessiscenteredbetweenthespecificationlimits Processiscentered Processisnotcentered BPTLConfidential 41 工序表現 TheCpkindexrelatesthescaleddistancebetweentheprocessmeanandthenearestspecificationlimit BPTLConfidential 42 工序表現 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 2ppb BPTLConfidential 43 工序表現 a 工序能力高 Cpk 1 5 b 工序能力可 Cpk 1to1 5 c 工序能力差 Cpk 1 BPTLConfidential 44 工序潛力与工序表現 a PoorProcessPotential b PoorProcessPerformance ExperimentalDesigntoreducevariation ExperimentalDesigntocentermeantoreducevariation BPTLConfidential 45 工序潛力与工序表現 BPTLConfidential 46 工序穩定性 Aprocessisstableifthedistributionofmeasurementsmadeonthegivenfeatureisconsistentovertime Time StableProcess Time UnstableProcess BPTLConfidential 47 短期工序能力与長期工序能力 短期工序能力 previouslycalledshort termcapability showstheinherentvariabilityofamachine processoperatingwithinabriefperiodoftime 長期工序能力 previouslycalledlong termcapability showsthevariabilityofamachine processoperatingoveraperiodoftime Itincludessourcesofvariationinadditiontotheshort termvariability BPTLConfidential 48 WithinOverallSampleSize30 50units 100unitsNumberofLotssinglelotseverallotsPeriodofTimehoursordaysweeksormonthsNumberofOperatorssingleoperatordifferentoperatorsProcessPotentialCpPpProcessPerformanceCpkPpk 短期工序能力与長期工序能力 BPTLConfidential 49 實戰演練 Thelengthofacamshaftforanautomobileengineisspecifiedat600 2mm Controlofthelengthofthecamshaftiscriticaltoavoidscrap rework Thecamshaftisprovidedbyexternalsuppliers Assesstheprocesscapabilityforthissupplier ThedataisavailableinCamshaft MTW Dataarecollectedinsubgroupsof5each BPTLConfidential 50 Example4 Minitab Stat QualityTools CapabilityAnalysis Normal BPTLConfidential 51 Example4 BPTLConfidential 52 Example5 Histogramofthecamshaftlengthsuggestsmixedpopulations Furtherinvestigationrevealedthattherearetwosuppliersforthecamshaft Datawerenowcollectedoncamshaftsfromeachsourcewithoutcombiningboth Subgroupsizeis5foreachsupplier Arethetwosupplierssimilarinperformance Ifnot whatareyourrecommendations BPTLConfidential 53 Example5 MiniTab Stat QualityTools CapabilitySixpack Normal BPTLConfidential 54 Example5 BPTLConfidential 55 Example5 BPTLConfidential 56 用Box Cox轉化后的工序能力分析 Whentheprocessdataarenotnormal theCpkorPpkindicesarenotaccurateorreliable becausetheseindicesarecomputedonthebasisthatthedataarenormallydistributed Dppmvaluesassociatedwiththeindiceswillnotbeneartotheactualperformancewhenthenormalcurvedoesnotmodeltheactualdatawell BPTLConfidential 57 Iftheprocessdataaresomewhatbell shapedbutskewed Box Coxtransformationcanbeusedtomakethedatanormalbeforeweassesstheprocesscapability RemembertotransformthespecificationlimitstoobeforewecomputeCpkorPpk 用Box Cox轉化后的工序能力分析 BPTLConfidential 58 Minitab Stat QualityTools CapabilityAnalysis Normal 用Box Cox轉化后的工序能力分析 BPTLConfidential 59 Example6 OpenthefilenamedDimension MTWintheDay 2folderagain Computetheprocesscapabilitywiththespecificationlimits LSL 0 1USL 10Arethedatanormallydistributed ComputetheprocesscapabilityagainwithBox Coxtransformation 用Box Cox轉化后的工序能力分析 BPTLConfidential 60 Cpkof0 41isreportedintheSSATpackage Thisvalueisnotreliableoraccurateifthedataarenotnormal Dataisnotnormal Example6 用Box Cox轉化后的工序能力分析 BPTLConfidential 61 Example6 Cpkhasincreasedfrom0 41to0 81 用Box Cox轉化后的工序能力分析 BPTLConfidential 62 What s 6 Quality Then OriginalDefinitionbyMotorola Intheshortterm thespecificationlimitsareatle