s黑帶培訓(xùn)教材英文 3

ProcessCapabilityAnalysis(MeasurePhase)ScopeofModuleProcessVariationProcessCapabilitySpecification,ProcessandControlLimitsProcessPotentialvsProcessPerformanceShort-TermvsLong-TermProcessCapabilityProcessCapabilityforNon-NormalDataCycle-Time (ExponentialDistribution)RejectRate (BinomialDistribution)DefectRate (PoissonDistribution)ProcessVariationProcessVariationistheinevitabledifferencesamongindividualmeasurementsorunitsproducedbyaprocess.SourcesofVariationwithinunit (positionalvariation)betweenunits (unit-unitvariation)betweenlots (lot-lotvariation)betweenlines (line-linevariation)acrosstime (time-timevariation)measurementerror (repeatability&reproducibility)TypesofVariationInherentorNaturalVariationDuetothecumulativeeffectofmanysmallunavoidablecausesAprocessoperatingwithonlychancecausesofvariationpresentissaidtobe“instatisticalcontrol”TypesofVariationSpecialorAssignableVariationMaybedueto a)improperlyadjustedmachine b)operatorerror c)defectiverawmaterialAprocessoperatinginthepresenceofassignablecausesofvariationissaidtobe“out-of-control”ProcessCapabilityProcessCapabilityistheinherentreproducibilityofaprocess’soutput.Itmeasureshowwelltheprocessiscurrentlybehavingwithrespecttotheoutputspecifications.Itreferstotheuniformityoftheprocess.Capabilityisoftenthoughtofintermsoftheproportionofoutputthatwillbewithinproductspecificationtolerances.Thefrequencyofdefectivesproducedmaybemeasuredina) percentage(%)b) partspermillion(ppm)c) partsperbillion(ppb)ProcessCapabilityProcessCapabilitystudiescan

indicatetheconsistencyoftheprocessoutputindicatethedegreetowhichtheoutputmeetsspecificationsbeusedforcomparisonwithanotherprocessorcompetitorProcessCapabilityvsSpecificationLimitsa)b)c)a)Processishighlycapableb)Processismarginallycapablec)ProcessisnotcapableThreeTypesofLimitsSpecificationLimits(LSLandUSL)createdbydesignengineeringinresponsetocustomerrequirementstospecifythetoleranceforaproduct’scharacteristicProcessLimits(LPLandUPL)measuresthevariationofaprocessthenatural6limitsofthemeasuredcharacteristicControlLimits(LCLandUCL)measuresthevariationofasamplestatistic(mean,variance,proportion,etc)ThreeTypesofLimitsDistributionofIndividualValuesDistributionofSampleAveragesProcessCapabilityIndicesTwomeasuresofprocesscapabilityProcessPotentialCpProcessPerformanceCpuCplCpkProcessPotentialTheCpindexassesseswhetherthenaturaltolerance(6)ofaprocessiswithinthespecificationlimits.ProcessPotentialACpof1.0indicatesthataprocessisjudgedtobe““capable””,i.e.iftheprocessiscenteredwithinitsengineeringtolerance,0.27%ofpartsproducedwillbebeyondspecificationlimits.CpRejectRate1.000.270%1.330.007%1.506.8ppm2.002.0ppbProcessPotentiala)b)c)a)Processishighlycapable(Cp>2)b)Processiscapable(Cp=1to2)c)Processisnotcapable(Cp<1)ProcessPotentialTheCpindexcomparestheallowablespread(USL-LSL)againsttheprocessspread(6).Itfailstotakeintoaccountiftheprocessisnotcenteredbetweenthespecificationlimits.ProcessiscenteredProcessisnotcenteredProcessPerformanceTheCpkindexrelatesthescaleddistancebetweentheprocessmeanandthenearestspecificationlimit.ProcessPerformanceCpkRejectRate1.00.13–0.27%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––2ppbProcessPerformancea)Processishighlycapable(Cpk>1.5)b)Processiscapable(Cpk=1to1.5)c)Processisnotcapable(Cpk<1)a)Cp=2Cpk=2b)Cp=2Cpk=1c)Cp=2Cpk<1Example1SpecificationLimits: 4to16gMachineMeanStdDev(a)104(b)102(c)72(d)131DeterminethecorrespondingCpandCpkforeachmachine.Example1AExample1BExample1CExample1DProcessCapabilityForanormallydistributedcharacteristic,thedefectiverateF(x)maybeestimatedviathefollowing:Forcharacteristicswithonlyonespecificationlimit:a) LSLonlyb) USLonlyLSLUSLExample2SpecificationLimits: 4to16gMachineMeanStdDev(a)104(b)102(c)72(d)131Determinethedefectiverateforeachmachine.Example2MeanStdDevZLSLZUSLF(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=16gProcessPotentialvsProcessPerformance(a)PoorProcessPotential (b)PoorProcessPerformanceLSLUSLLSLUSLExperimentalDesigntoreducevariationExperimentalDesigntocentermeantoreducevariationProcessPotentialvsProcessPerformanceProcessPotentialIndex(Cp)Cpk1.01.82.01.02,699.91,363.31,350.01,350.01,350.01,350.01.2318.3159.9159.1159.1159.11.426.713.413.40.10.02.00.0DefectiveRate(measuredindppm)isdependentontheactualcombinationofCpandCpk..ProcessPotentialvsProcessPerformancea)Cp=2Cpk=2b)Cp=2Cpk=1c)Cp=2Cpk<1Cp–CpkMissedOpportunityAlternativeProcessPerformanceIndexProcesscapabilitystatisticsmeasureprocessvariationrelativetospecificationlimits.TheCpstatisticcomparestheengineeringtoleranceagainsttheprocess’snaturalvariation.TheCpkstatistictakesintoaccountthelocationoftheprocessrelativetothemidpointbetweenspecifications.Iftheprocesstargetisnotcenteredbetweenspecifications,theCpmstatisticispreferred.ProcessStabilityAprocessisstableifthedistributionofmeasurementsmadeonthegivenfeatureisconsistentovertime.TimeStableProcessTimeUnstableProcessucllclucllclWithinvsOverallCapabilityWithinCapability(previouslycalledshort-termcapability)showstheinherentvariabilityofamachine/processoperatingwithinabriefperiodoftime.OverallCapability(previouslycalledlong-termcapability)showsthevariabilityofamachine/processoperatingoveraperiodoftime.Itincludessourcesofvariationinadditiontotheshort-termvariability.WithinvsOverallCapabilityWithinOverallSampleSize30––50units100unitsNumberofLotssinglelotseverallotsPeriodofTimehoursordaysweeksormonthsNumberofOperators singleoperatordifferentoperatorsProcessPotentialCpPpProcessPerformanceCpkPpkWithinvsOverallCapabilityWithinCapabilityOverallCapabilityThekeydifferencebetweenthetwosetsofindicesliesintheestimatesforWithinandOverall.EstimatingWithinandOverallConsiderthefollowingobservationsfromaControlChart:S/NX1X2…XkMean Range StdDev1 x1,1x2,1…xk,1X1R1S12 x1,2x2,2…xk,2X2R2S2:::::::m x1,mx2,m…xk,mXmRmSmTheoverallvariationOverallisestimatedby–––EstimatingWithinandOverallThewithinvariationWithinmaybeestimatedbyoneofthefollowing:(a)R-barMethodwhere d2isaShewhartconstant=(k)(b)S-barMethodwhere c4isaShewhartconstant=(k)(c)PooledStandardDeviationMethodInMiniTab,thePooledStandardDeviationisthedefaultmethod.EstimatingWithinandOverallIncaseswherethereisonly1observationpersub-group(i.e.k=1),theMovingRangeMethodisused,where.ThewithinvariationWithinisthenestimatedusingeithera) theAverageMovingRange:b) theMedianMovingRange:Example3Thelengthofacamshaftforanautomobileengineisspecifiedat600±2mm.Controlofthelengthofthetoavoidscrap/rework.Thecamshaftisprovidedbyanexternalsupplier.Assesstheprocesscapabilityforthissupplier.ThedataisavailableinProcessCapabilityAnalysis.MTW.Example3StatQualityToolsCapabilityAnalysis(Normal)Example3Example3AHistogramofcamshaftlengthsuggestsmixedpopulations.Furtherinvestigationrevealedthattherearetwosuppliersforthecamshaft.Datawascollectedovercamshaftsfrombothsources.Arethetwosupplierssimilarinperformance?Ifnot,whatareyourrecommendations?Example3AStatQualityToolsCapabilitySixpack(Normal)Example3AExample3AWhat’’sSixSigmaQuality——ThenOriginalDefinitionbyMotorola:ifthespecificationlimitsareatleast±±6awayfromtheprocessmean,i.e.Cp2,andtheprocessshiftsbylessthan1.5,i.e.Cpk1.5,thentheprocesswillyieldlessthan3.4dppmrejects.66Shift1.54.5What’’sSixSigmaQuality——NowMikelJHarryclaimsthattheprocessmeanbetweenlotswillvary,withanaverageprocessshiftof1.5.k=z+1.5k=z+1.5Shift1.5zNote:SigmaCapability=??(dpmo)?(dppm)ProcessCapabilityforNon-NormalDataNoteverymeasuredcharacteristicisnormallydistributed.CharacteristicDistributionCycleTimeExponentialRejectRate BinomialDefectRate PoissonProcessCapabilityforCycleTimeTheWeibullDistributionisageneralfamilyofdistributionwithwherescaleparameteristhevalueatwhichCDF=68.17%,andshapeparameterdeterminestheshapeofthePDF.ProcessCapabilityforCycleTimeAt=1,theWeibullDistributionisreducedtoForanExponentialDistribution,TheExponentialDistributionisthusaWeibullDistributionwith=1.Weibull(x;=1,)Exponential(x;)Example4Acustomerservicemanagerwantstodeterminetheprocesscapabilityforhisdepartment.Aprimaryperformanceindexisthetimetakentocloseacustomercomplaint.Thegoalforthisindexistocloseacomplaintwithinonecalendarweek.Performanceoverthelast400complaintswasreviewed.Example4StatQualityToolsCapabilityAnalysis(Weibull)Example4Example4AStatQualityToolsCapabilitySixpack(Weibull)Example4AProcessCapabilityforRejectRateForaNormalDistribution,theproportionofpartsproducedbeyondaspecificationlimitisRejectRateProcessCapabilityforRejectRateThus,foreveryrejectratethereisanaccompanyingZ-Score,whereRecallthatHenceProcessCapabilityforRejectRateEstimationofPpkforRejectRateDeterminethelong-termrejectrate(p)Determinetheinversecumulativeprobabilityforp,usingCalcProbabilityDistributionNormalZ-ScoreisthemagnitudeofthereturnedvaluePpkisone-thirdoftheZ-ScoreExample5Asalesmanagerplanstoassesstheprocesscapabilityofhistelephonesalesdepartment’shandlingofincomingcalls.Thefollowingdatawascollectedoveraperiodof20days:numberofincomingcallsperdaynumberofunansweredcallsperdaysExample5StatQualityToolsCapabilityAnalysis(Binomial)Example5Ppk=0.25ProcessCapabilityforDefectRateOtherapplications,approximatingaPoissonDistribution:errorratesparticlecountchemicalconcentrationProcessCapabilityforDefectRateEstimationofYtpforDefectRateDefinesizeofaninspectionunitDeterminethelong-termdefectsperunit(DPU)DPU=TotalDefectsTDeterminethethroughputyield(Ytp) Ytp =exp{–DPU}ProcessCapabilityforDefectRateEstimationofSigma-CapabilityforDefectRateDeterminetheopportunitiesperunitDeterminethelong-termdefectsperopportunity(d)d=defectsperunitopportunitiesperunitDeterminetheinversecumulativeprobabilityford,usingCalcProbabilityDistributionNormalZ-ScoreisthemagnitudeofthereturnedvalueSigma-Capability=Z-Score+1.5Example6Theprocessmanagerforawiremanufacturerisconcernedabouttheeffectivenessofthewireinsulationprocess.Randomlengthsofelectricalwiringaretakenandtestedforweakspotsintheirinsulationbymeansofatestvoltage.Thenumberofweakspotsandthelengthofeachpieceofwirearerecorded.Example6StatQualityToolsCapabilityAnalysis(Poisson)Example6DefectsperUnit=0.0265194ThroughputYield=exp{––DPU}=exp{––0.0265194}=0.9738c.f.First-TimeYield=2/100=0.02Example6Define1InspectionUnit=125unitlengthofwirei.e.Units=Length125Example6AStatQualityToolsCapabilityAnalysis(Poisson)Example6ADefectsperUnit=3.31493ThroughputYield=exp{––DPU}=exp{––3.31493}=0.0363c.f.First-TimeYield=2/100=0.02Example6BDefectsperUnit=3.31493OpportunitiesperUnit=1DefectsperOpportunity=3.31493Z-Score=???Example6B1inspectionunit=1unitlengthofwireOpportunitiesperUnit=1DefectsperOpportunity=32912,406=0.0265Z-Score=Abs{–1(0.0265)}=1.935Sigma-Capability=Z-Score+1.5=3.435DPUZ-ScoresChoiceofSixSigmaMetric9、靜夜四無鄰鄰，荒居舊業(yè)業(yè)貧。。12月-2212月-22Thursday,December8,202210、雨雨中中黃黃葉葉樹樹，，燈燈下下白白頭頭人人。。。。00:32:1400:32:1400:3212/8/202212:32:14AM11、以以我我獨(dú)獨(dú)沈沈久久，，愧愧君君相相見見頻頻。。。。12月月-2200:32:1400:32Dec-2208-Dec-2212、故故人人江江海海別別，，幾幾度度隔隔山山川川。。。。00:32:1400:32:1400:32Thursday,December8,202213、乍乍見見翻翻疑疑夢夢，，相相悲悲各各問問年年。。。。12月月-2212月月-2200:32:1400:32:14December8,202214、他鄉(xiāng)生白白發(fā)，舊國國見青山。。。08十二二月202212:32:14上上午00:32:1412月-2215、比不了得得就不比，，得不到的的就不要。。。。十二月2212:32上午12月-2200:32December8,202216、行動動出成成果，，工作作出財財富。。。2022/12/80:32:1400:32:1408December202217、做前，能能夠環(huán)視四四周；做時時，你只能能或者最好好沿著以腳腳為起點(diǎn)的的射線向前前。。12:32:14上上午12:32上午00:32:1412月-229、沒有失敗，，只有暫時停停止成功！。。12月-2212月-22Thursday,December8,202210、很很多多事事情情努努力力了了未未必必有有結(jié)結(jié)果果，，但但是是不不努努力力卻卻什什么么改改變變也也沒沒有有。。。。00:32:1400:32:1400:3212/8/202212:32:14AM11、成功就就是日復(fù)復(fù)一日那那一點(diǎn)點(diǎn)點(diǎn)小小努努力的積積累。。。12月-2200:32:1400:32Dec-2208-Dec-2212、世間成