諾機(jī)亞培訓(xùn)教材(PPT)

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ProcessCapability(Cp/Cpk/Pp/Ppk)GlobalTrainingMaterialCreator:GlobalMechanicsProcessManagerFunction:MechanicsApprover:GaryBradley/GlobalProcessTeamDocumentID:DMT00018-ENVersion/Status:V.1.0/ApprovedLocation:Notes:\\…\NMP\DOCMANR4\PCP\PCProcessLibraryDocManChangeHistory:IssueDateHandledByComments1.021stDec’01JimChristy&S?renLundsfrydApprovedforGlobalUseNOTE–Allcommentsandimprovementsshouldbeaddressedtothecreatorofthisdocument.第一頁，共五十六頁。

1ContentsSectionHeading/DescriptionPage1Variation,TolerancesandDimensionalControl42Population,SampleandNormalDistribution153CpandCpkConcept284UseoftheNMPDataCollectionSpreadsheet445ConfidenceofCpk52第二頁，共五十六頁。

2ProcessCapability-EvaluatingManufacturingVariationAcknowledgementsBennyMatthiassen(NMPCMT,Copenhagen,Denmark)FrankAdler(NMPAlliance,Dallas,USA)JoniLaakso(NMPR&D,Salo,Finland)JimChristy(NMPSRC,Southwood,UK)第三頁，共五十六頁。

3Section1Variation,TolerancesandDimensionalControl第四頁，共五十六頁。

4TwoTypesofProductCharacteristicsVariable:Acharacteristicmeasuredinphysicalunits,e.g.millimetres,volts,amps,decibelandseconds.ONOFFAttribute:Acharacteristicthatbycomparisontosomestandardisjudged“good”or“bad”,e.g.freefromscratches(visualquality).Inthistrainingwedealwithvariablesonly第五頁，共五十六頁。

5TheSourcesofProcess/SystemVariationMethodsOperatorsCustomerSatisfactionMaterialEnvironmentEquipmentProcess第六頁，共五十六頁。

6TwoTypesofProcessesAllprocesseshave:Natural(random)variability=>duetocommoncausesStableProcess:AprocessinwhichvariationinoutcomesarisesonlyfromcommoncausesUnstableProcess:AprocessinwhichvariationisaresultofbothcommonandspecialcausesUSLLSLnominalvalueDefectUSLLSLnominalvalueUnnaturalvariability=>duetospecialcauses第七頁，共五十六頁。

7Shewhart(1931)TheTwoCausesofVariationCommonCauses:Causesthatareimplementedintheprocessduetothedesignoftheprocess,andaffectalloutcomesoftheprocessIdentifyingthesetypesofcausesrequiresmethodssuchasDesignofExperiment(DOE),etc.SpecialCauses:Causesthatarenotpresentintheprocessallthetimeanddonotaffectalloutcomes,butarisebecauseofspecificcircumstancesSpecialcausescanbeidentifiedusingStatisticalProcessControl(SPC)USLLSLNominalvalueDefectUSLLSLnominalvalue第八頁，共五十六頁。

8TolerancesLSL(lowerspecificationlimit)10,7USL(upperspecificationlimit)10,9AcceptablepartRejectedPartRejectedProductNominal10,8?0,1RejectedPartAtoleranceisaallowedmaximumvariationofadimension.第九頁，共五十六頁。

9MeasurementReportInmostcaseswemeasureonlyonepartpercavityformeasurementreport第十頁，共五十六頁。

10ExampleofCapabilityAnalysisDataForsomecriticaldimensionsweneedtomeasuremorethan1partForcapabilitydataweusuallymeasure5pcs2times/hour=100pcs(butsamplingplanneedstobemadeonthebasisofproductionquantity,rundurationandcycletime)第十一頁，共五十六頁。

11ProcessCapability-Whatisit?ProcessCapabilityisameasureoftheinherentcapabilityofamanufacturingprocesstobeabletoconsistentlyproducecomponentsthatmeettherequireddesignspecificationsProcessCapabilityisdesignatedbyCpandCpkProcessPerformanceisameasureoftheperformanceofaprocesstobeabletoconsistentlyproducecomponentsthatmeettherequireddesignspecifications.ProcessPerformanceincludesspecialcausesofvariationnotpresentinProcessCapabilityProcessPerformanceisdesignatedPpandPpk第十二頁，共五十六頁。

12WhyMakeProcessCapabilityStudiesLSL(lowerspecificationlimit)10,7USL(upperspecificationlimit)10,9Nominal10,8?0,1Thispartiswithinspec.ThetoolwouldbeapprovedifonlythispartwasmeasuredThesepartsareoutofspecandcouldbeapprovedifonlyonegoodpartwasmeasuredAprocesscapabilitystudywouldrevealthatthetoolshouldnotbeacceptedWhenadimensionneedstobekeptproperlywithinspec,wemuststudytheprocesscapability….butstillthisisnoguaranteefortheactualperformanceoftheprocessasitisonlyaninitialcapabilitystudy第十三頁，共五十六頁。

13E1.5E1E2E3E4E5TheNokiaProcessVerificationProcessBlackdiamondstobefixedbyE3(oftenachangeofawhitediamond)ProposalforblackdiamondstobediscussedwithSupplier.Max:105,85OngoingProcessControl(SPC)TolerancesappliedtodrawingType1FunctionalCharacteristics-1part/cavitymeasuredformeasurementreportWhitediamonds(s)tobeagreedWhitediamonds(s)tobediscussedwithsupplier10parts/cavitymeasuredformeasurementreportCapabilitystudy:Requirement:CpandCpk>1.67byE3.Quantitiestobeagreedwithsupplier.Minimum5partspr1/2hourin10hoursmeasuredforeachcavity=100parts.Canvarydependingontoolcapacity,e.g.stampedparts(seeDMY00019-EN)第十四頁，共五十六頁。

14Section2.Population,SampleandNormalDistribution第十五頁，共五十六頁。

15TheBellShaped(Normal)DistributionSymmetricalshapewithapeakinthemiddleoftherangeofthedata.Indicatesthattheinputvariables(X's)totheprocessarerandomlyinfluenced.第十六頁，共五十六頁。

16“PopulationParameters〞?=Populationmean?=PopulationstandarddeviationPopulationversusSamplePopulationAnentiregroupofobjectsthathavebeenmadeorwillbemadecontainingacharacteristicofinterestSampleThegroupofobjectsactuallymeasuredinastatisticalstudyAsampleisusuallyasubsetofthepopulationofinterestPopulationSample“SampleStatistics”x=Samplemeans=Samplestandarddeviation第十七頁，共五十六頁。

17TheNormalDistribution第十八頁，共五十六頁。

18WhatMeasurementsCanBeUsedtoDescribeaProcessorSystem?Example:1=52=73=44=25=6mean(average)ordescribesthelocationofthedistributionμ(mü),ameasureofcentraltendency,isthemeanoraverageofallvaluesinthepopulation.Whenonlyasampleofthepopulationisbeingdescribed,meanismoreproperlydenotedas(x-bar):第十九頁，共五十六頁。

19Example:1=52=73=44=25=6Themostsimplemeasureofvariabilityistherange.Therangeofasampleisdefinedbyasthedifferencebetweenthelargestandthesmallestobservationfromsamplesinasub-group,e.g.5consecutivepartsfromthemanufacturingprocess.WhatMeasurementsCanBeUsedtoDescribeProcessvariation?第二十頁，共五十六頁。

20sST-oftennotatedas??orsigma,isanothermeasureofdispersionorvariabilityandstandsfor“short-termstandarddeviation〞,whichmeasuresthevariabilityofaprocessorsystemusing“rational〞sub-grouping.whereistherangeofsubgroupj,Nthenumberofsubgroups,andd2*dependsonthenumberNofsubgroupsandthesizenofasubgroup(seenextslide)WhatMeasurementsCanBeUsedtoDescribeProcessvariation?第二十一頁，共五十六頁。

21d2*valuesforSSTWhere:N=no.ofsub-groups,n=no.ofsamplesineachsub-groupd2*d2Typical:N=20&n=5第二十二頁，共五十六頁。

22x3x2x1x10x_tExample:WhatMeasurementsCanBeUsedtoDescribeProcessvariation?第二十三頁，共五十六頁。

23TheDifferenceBetweenSSTandsLT!!meanTimeDimensionShorttermStandardDeviationLongtermStandardDeviationSubgroupsizen=5NumberofsubgroupsN=7TRENDSubgroupNo.1第二十四頁，共五十六頁。

24ThedifferencebetweenthestandarddeviationssLTandsSTgivesanindicationofhowmuchbetteronecandowhenusingappropriateproductioncontrol,likeStatisticalProcessControl(SPC).Short-termstandarddeviation:Long-termstandarddeviation:ThedifferencebetweensSTandsLT第二十五頁，共五十六頁。

25ThedifferencebetweensSTandsLTThedifferencebetweensLTandsSTisonlyinthewaythatthestandarddeviationiscalculatedsLTisalwaysthesameorlargerthansSTIfsLTequalssST,thentheprocesscontroloverthelonger-termisthesameastheshort-term,andtheprocesswouldnotbenefitfromSPCIfsLTislargerthansST,thentheprocesshaslostcontroloverthelonger-term,andtheprocesswouldbenefitfromSPCThereliabilityofsLTisimprovedifthedataistakenoveralongerperiodoftime.AlternativelysLTcanbecalculatedonseveraloccasionsseparatedbytimeandtheresultscomparedtoseewhethersLTisstable第二十六頁，共五十六頁。

26Exercise1:SampleDistributions1.InExcelfile"Dataexercise1.xls"youfind100measurementsbeingtheresultofacapabilitystudy.Thespecificationforthedimensionis15,16?,012.Howwelldoesthesamplepopulationfitthespecification,e.g.shouldweexpectanypartsoutsidespec?3.Mentionpossibleconsequencesofhavingapartoutsidespec.4.Mentionpossiblecausesofvariationforparts.5.Calculatethesamplemeanandsamplestandarddeviationforthe100measurements.UsetheaverageandstdevfunctionsExcel.第二十七頁，共五十六頁。

27Section3.CpandCpkConcept第二十八頁，共五十六頁。

28DefiningCpandPpSamplemeanProcessvariation6*sUSL-LSLLSLUSLNominaldimThetoleranceareadividedbythetotalprocessvariation,irrespectiveofprocesscentring.第二十九頁，共五十六頁。

29DefiningCpkandPpkSamplemeanProcessvariation3sProcessvariation3sMean-LSLUSL-MeanLSLUSLNominaldimCpkandPpkIndexesaccountalsoforprocesscentring.第三十頁，共五十六頁。

30WhatistheDifferenceBetweenCpandCpk?TheCpindexonlyaccountsforprocessvariabilityTheCpkIndexaccountsforprocessvariabilityandcenteringoftheprocessmeantothedesignnominalTherefore,Cp?CpkNOTE:SameappliesalsoforPpandPpkCp=Cpk(bothlow)LSLUSLMean=NominalRejectpartsRejectpartsCphigh,CpklowProcessshouldbeoptimized!NominalLSLMeanUSLRejectparts第三十一頁，共五十六頁。

31WhatDoTheseIndexesTellUs??Simplenumericalvaluestodescribethequalityoftheprocess>>ThehigherthenumberthebetterRequirementforCpandCpkis1.67min.RecommendationforPpandPpkis1.33min.Thisleavesussomespaceforthevariation,i.e.asafetymarginAreweabletoimproveourprocessbyusingSPC?Ifindexislow,followingthingsshouldbegivenathought:IstheproductdesignOK?Aretolerancelimitssetcorrectly?Tootight?Istheprocesscapableofproducinggoodqualityproducts?Processvariation?DOErequired?Isthemeasuringsystemcapable?(SeeGageR&R)第三十二頁，共五十六頁。

32Cpk-Witha2-sigmasafetymargin-3sST+3sSTLCLUCLLSLUSLMeanvalue=NominalvalueorTargetRequirementforCpandCpkis1.67min.1.67isaratioof=5/3or10/6.6*standarddeviation10*standarddeviation2*standarddeviation2*standarddeviation第三十三頁，共五十六頁。

33Cpk<1.67theprocessNOTCAPABLEAcceptabilityofCpkIndexCpk>=1.67theprocessisCAPABLECpk>=2.0theprocesshasreachedSixSigmalevel第三十四頁，共五十六頁。

34WhatDoTheseIndexesTellUs??IfCp=Cpk,IfPp=Ppk,IfCpk

35CpandCpkIndicesandDefects(bothtailsofthenormaldistribution)Pp=Ppk=1,33?63ppmdefects=0,006%Cp=Cpk=1,67?0,6ppmdefects=0,00006%Note:PpmrejectratescalculatedfromCp&Cpkarebasedontheshorttermvariationwhichmaynotrepresentthelongtermrejectrate第三十六頁，共五十六頁。

36TheEffectsofCpkandCponFFR第三十七頁，共五十六頁。

37Exercise2:CpandCpkCalculateCpandCpkforthe100measurementsinthefile"Dataexercise1.xls"DeterminetheapproximateCpandCpkforthe4samplepopulationsonthefollowingpageShouldactionsbemadetoimprovetheseprocesses.Ifyes,which?第三十八頁，共五十六頁。

38EstimateCpandCpk?Thewidthofthenormaldistributionsshowninclude±3*sLSLUSLA)LSLUSLB)LSLUSLC)USLLSLD)第三十九頁，共五十六頁。

39EstimateCpandCpk?-A)LSLUSLA)MeanandnominalUSL-LSL6*sUSL-MeanMean-LSL3*s第四十頁，共五十六頁。

40EstimateCpandCpk?-B)LSLUSLB)NominalMeanUSL-LSL6*sUSL-MeanMean-LSL3*s第四十一頁，共五十六頁。

41EstimateCpandCpk?-C)LSLUSLC)NominalMeanUSL-LSL6*sUSL-MeanMean-LSL3*s第四十二頁，共五十六頁。

42EstimateCpandCpk?-DUSLLSLD)NominalMeanUSL-LSL6*sUSL-MeanMean-LSL3*s第四十三頁，共五十六頁。

43Section4.UseoftheNMPDataCollectionSpreadsheet第四十四頁，共五十六頁。

44ExampleofhowtoCollectData1.Runinandstabiliseprocess2.Notethemainparametersforreference3.Whentheprocessisstablerunthetoolfor10hours3.Take5partsoutfromeachcavityeveryhalfhourandmarkthemwithtime,dateandcavity.Total20setsof5partsfromeachcavitymustbemade,oraccordingtoagreement.4.Afterthelastsamplelotnotethemainprocessparametersforreference5.Measureandrecordthemainfunctionalcharacteristics(whitediamonds)6.FilldataintotheNMPdatacollectionspreadsheet7.Analyse!SeeDMY00019-ENClassificationandMarkingofFunctionalCharacteristicsTimeDimensionSubgroupsizen=5NumberofsubgroupsN=200,5hoursbetweensamplestakenNote:Forclarity,only6subgroupsareshown第四十五頁，共五十六頁。

45DataCollectionSheet(DMM00024-EN-5.0)第四十六頁，共五十六頁。

46DataCollectionSheet(DMM00024-EN-5.0)第四十七頁，共五十六頁。

47GraphicalPresentation:HistogramWhatkindofdistribution?LocationversustoleranceareaWidth(deviation)Example:Cp2.59Pp1.86Cpk0.88Ppk0.63第四十八頁，共五十六頁。

48GraphicalPresentation:X-barandR-ChartX-BarChartR-Chart第四十九頁，共五十六頁。

49GraphicalPresentation-TimeSeriesPlotSomethinghappenedhere!!!第五十頁，共五十六頁。

50Exercise3:CpkDataSpreadsheetOpenspreadsheet"Dataexercice3.xls".Dim13isidenticaltothedatafromthepreviousexercises.Verifytheresultsfromthepreviousexercisesfordimension13.Analysetheremainingdatasetsancommenttheprocess,shouldanyactionsbemade?Remembertocreateandlookatthecharts.第五十一頁，共五十六頁。

51Section5.ConfidenceofCpk第五十二頁，共五十六頁。

52ConfidenceofCpkCpkvaluesarenotdefinitenumbersastheyarebasedonrelativelysmallsamplesofapopulation.The95%confidenceintervaldeterminestheintervalwhichincludesthetrueCpkvaluewithaprobabilityof95%,i.e."thereisaprobabilityof5%thatCpkiseitherlowerorhigher"thanthisconfidenceinterval.95%confidenceintervalActualcpkCpkupperconfidencelimitCpklowerconfidencelimit第五十三頁，共五十六頁。

53ConfidenceofCpkSmallsamplesizesgiveswideconfidenceintervals第五十四頁，共五十六頁。

54CpkConfidenceLimitswithasamplesizeof100andanominalCpkof1.67第五十五頁，共五十六頁。

55內(nèi)容(nèiróng)總結(jié)ProcessCapability(Cp/Cpk/Pp/Ppk)GlobalTrainingMaterial。IssueDateHandledByComments。Pp=Ppk=1,33。Cp=Cpk=1,67。Example:Cp2.59Pp1.86。Cpk0.88Ppk0.63第五十六頁，共五十六頁。