ProcessCapability(Cp/Cpk/Pp/Ppk)

GlobalTrainingMaterialCreator :GlobalMechanicsProcessManagerFunction :MechanicsApprover :GaryBradley/GlobalProcessTeamDocumentID :DMT00018-ENVersion/Status :V.1.0/ApprovedLocation :Notes:\\…\NMP\DOCMANR4\PCP\PCProcessLibraryDocManChangeHistory:Issue Date HandledBy Comments1.0 21stDec’01 JimChristy&S?renLundsfryd ApprovedforGlobalUseNOTE–Allcommentsandimprovementsshouldbeaddressedtothecreatorofthisdocument.ContentsSection Heading/Description Page1 Variation,TolerancesandDimensionalControl 4 2 Population,SampleandNormalDistribution 153 CpandCpkConcept 284 UseoftheNMPDataCollectionSpreadsheet 445 ConfidenceofCpk 52 ProcessCapability-EvaluatingManufacturingVariationAcknowledgementsBennyMatthiassen (NMPCMT,Copenhagen,Denmark)FrankAdler (NMPAlliance,Dallas,USA)JoniLaakso (NMPR&D,Salo,Finland)JimChristy (NMPSRC,Southwood,UK)Section1Variation,TolerancesandDimensionalControlTwoTypesofProductCharacteristicsVariable:Acharacteristicmeasuredinphysicalunits,limetres,volts,amps,decibelandseconds.ONOFFAttribute:Acharacteristicthatbycomparisontosomestandardisjudged“good”or“bad”,e.g.freefromscratches(visualquality).InthistrainingwedealwithvariablesonlyTheSourcesofProcess/SystemVariationMethodsOperatorsCustomerSatisfactionMaterialEnvironmentEquipmentProcessTwoTypesofProcessesAllprocesseshave:Natural(random)variability

=>duetocommoncausesStableProcess:

AprocessinwhichvariationinoutcomesarisesonlyfromcommoncausesUnstableProcess:

AprocessinwhichvariationisaresultofbothcommonandspecialcausesUSLLSLnominalvalueDefectUSLLSLnominalvalue

Unnaturalvariability=>duetospecialcausesShewhart(1931)TheTwoCausesofVariationCommonCauses:Causesthatareimplementedintheprocessduetothedesignoftheprocess,andaffectalloutcomesoftheprocessIdentifyingthesetypesofcausesrequiresmethodssuchasDesignofExperiment(DOE),etc.

SpecialCauses:Causesthatarenotpresentintheprocessallthetimeanddonotaffectalloutcomes,butarisebecauseofspecificcircumstancesSpecialcausescanbeidentifiedusingStatisticalProcessControl(SPC)USLLSLNominal

valueDefectUSLLSLnominal

valueTolerancesLSL(lowerspecificationlimit)10,7USL(upperspecificationlimit)10,9AcceptablepartRejectedPartRejectedProductNominal10,80,1RejectedPartAtoleranceisaallowedmaximumvariationofadimension.MeasurementReportInmostcaseswemeasureonlyonepartpercavityformeasurementreportExampleofCapabilityAnalysisDataForsomecriticaldimensionsweneedtomeasuremorethan1partForcapabilitydataweusuallymeasure5pcs2times/hour=100pcs(butsamplingplanneedstobemadeonthebasisofproductionquantity,rundurationandcycletime)ProcessCapability-Whatisit?ProcessCapabilityisameasureoftheinherentcapabilityofamanufacturingprocesstobeabletoconsistentlyproducecomponentsthatmeettherequireddesignspecificationsProcessCapabilityisdesignatedbyCpandCpkProcessPerformanceisameasureoftheperformanceofaprocesstobeabletoconsistentlyproducecomponentsthatmeettherequireddesignspecifications.ProcessPerformanceincludesspecialcausesofvariationnotpresentinProcessCapabilityProcessPerformanceisdesignatedPpandPpkWhyMakeProcessCapabilityStudiesLSL(lowerspecificationlimit)10,7USL(upperspecificationlimit)10,9Nominal10,80,1Thispartiswithinspec.ThetoolwouldbeapprovedifonlythispartwasmeasuredThesepartsareoutofspecandcouldbeapprovedifonlyonegoodpartwasmeasuredAprocesscapabilitystudywouldrevealthatthetoolshouldnotbeacceptedWhenadimensionneedstobekeptproperlywithinspec,wemuststudytheprocesscapability….butstillthisisnoguaranteefortheactualperformanceoftheprocessasitisonlyaninitialcapabilitystudy

E1.5

E1

E2

E3

E4

E5TheNokiaProcessVerificationProcessBlackdiamondstobefixedbyE3(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)Section2.Population,SampleandNormalDistributionTheBellShaped(Normal)DistributionSymmetricalshapewithapeakinthemiddleoftherangeofthedata.Indicatesthattheinputvariables(X's)totheprocessarerandomlyinfluenced.“PopulationParameters”=Populationmean=PopulationstandarddeviationPopulationversusSamplePopulationAnentiregroupofobjectsthathavebeenmadeorwillbemadecontainingacharacteristicofinterestSampleThegroupofobjectsactuallymeasuredinastatisticalstudyAsampleisusuallyasubsetofthepopulationofinterestPopulationSample“SampleStatistics” x=Samplemean s=SamplestandarddeviationTheNormalDistributionWhatMeasurementsCanBeUsedtoDescribeaProcessorSystem?Example:1

=52

=73

=44

=25

=6mean(average)ordescribesthelocationofthedistributionμ(mü),ameasureofcentraltendency,isthemeanoraverageofallvaluesinthepopulation.Whenonlyasampleofthepopulationisbeingdescribed,meanismoreproperlydenotedas

(x-bar):Example:1

=52

=73

=44

=25

=6Themostsimplemeasureofvariabilityistherange.Therangeofasampleisdefinedbyasthedifferencebetweenthelargestandthesmallestobservationfromsamplesinasub-group,e.g.5consecutivepartsfromthemanufacturingprocess.WhatMeasurementsCanBeUsedtoDescribeProcessvariation?sST-oftennotatedasorsigma,isanothermeasureofdispersionorvariabilityandstandsfor““short-termstandarddeviation””,whichmeasuresthevariabilityofaprocessorsystemusing““rational””sub-grouping.where

istherangeofsubgroupj,Nthenumberofsubgroups,andd2*dependsonthenumberNofsubgroupsandthesizenofasubgroup(seenextslide)WhatMeasurementsCanBeUsedtoDescribeProcessvariation?d2*valuesforSSTWhere:N=no.ofsub-groups,n=no.ofsamplesineachsub-groupd2*d2Typical:N=20&n=5

x3

x2

x1

x10x_tExample:WhatMeasurementsCanBeUsedtoDescribeProcessvariation?TheDifferenceBetweenSSTandsLT!!meanTimeDimensionShorttermStandardDeviationLongtermStandardDeviationSubgroupsizen=5NumberofsubgroupsN=7TRENDSubgroupNo.1ThedifferencebetweenthestandarddeviationssLTandsSTgivesanindicationofhowmuchbetteronecandowhenusingappropriateproductioncontrol,likeStatisticalProcessControl(SPC).Short-termstandarddeviation:Long-termstandarddeviation:ThedifferencebetweensSTandsLTThedifferencebetweensSTandsLTThedifferencebetweensLTandsSTisonlyinthewaythatthestandarddeviationiscalculatedsLTisalwaysthesameorlargerthansSTIfsLTequalssST,thentheprocesscontroloverthelonger-termisthesameastheshort-term,andtheprocesswouldnotbenefitfromSPCIfsLTislargerthansST,thentheprocesshaslostcontroloverthelonger-term,andtheprocesswouldbenefitfromSPCThereliabilityofsLTisimprovedifthedataistakenoveralongerperiodoftime.AlternativelysLTcanbecalculatedonseveraloccasionsseparatedbytimeandtheresultscomparedtoseewhethersLTisstableExercise1:SampleDistributions1.InExcelfile"Dataexercise1.xls"youfind100measurementsbeingtheresultofacapabilitystudy.Thespecificationforthedimensionis15,16,012.Howwelldoesthesamplepopulationfitthespecification,e.g.shouldweexpectanypartsoutsidespec?3.Mentionpossibleconsequencesofhavingapartoutsidespec.4.Mentionpossiblecausesofvariationforparts.5.Calculatethesamplemeanandsamplestandarddeviationforthe100measurements.UsetheaverageandstdevfunctionsExcel.Section3.CpandCpkConceptDefiningCpandPpSamplemeanProcessvariation6*s

USL-LSLLSL

USLNominaldimThetoleranceareadividedbythetotalprocessvariation,irrespectiveofprocesscentring.DefiningCpkandPpkSamplemeanProcessvariation3sProcessvariation3sMean-LSLUSL-MeanLSL

USLNominaldimCpkandPpkIndexesaccountalsoforprocesscentring.WhatistheDifferenceBetweenCpandCpk?TheCpindexonlyaccountsforprocessvariabilityTheCpkIndexaccountsforprocessvariabilityandcenteringoftheprocessmeantothedesignnominalTherefore,CpCpkNOTE:SameappliesalsoforPpandPpkCp=Cpk(bothlow)LSLUSLMean=NominalRejectpartsRejectpartsCphigh,Cpklow

Processshouldbeoptimized!NominalLSLMeanUSLRejectpartsWhatDoTheseIndexesTellUs??Simplenumericalvaluestodescribethequalityoftheprocess>>ThehigherthenumberthebetterRequirementforCpandCpkis1.67min.RecommendationforPpandPpkis1.33min.AreweabletoimproveourprocessbyusingSPC?Ifindexislow,followingthingsshouldbegivenathought:IstheproductdesignOK?Aretolerancelimitssetcorrectly?Tootight?Istheprocesscapableofproducinggoodqualityproducts?Processvariation?DOErequired?Isthemeasuringsystemcapable?(SeeGageR&R)Cpk-Witha2-sigmasafetymargin-3sST+3sSTLCLUCLLSLUSLMeanvalue=NominalvalueorTargetRequirementforCpandCpkis1.67min.1.67isaratioof=5/3or10/6.6*standarddeviation10*standarddeviation2*standarddeviation2*standarddeviationCpk<1.67theprocessNOTCAPABLEAcceptabilityofCpkIndexCpk>=1.67theprocessisCAPABLECpk>=2.0theprocesshasreachedSixSigmalevelWhatDoTheseIndexesTellUs??IfCp=Cpk,IfPp=Ppk,IfCpk<Cp,IfPpk<Pp,IfCp=Pp,IfCpk=Ppk,IfPp<Cp,IfPpk<Cpk,…thenprocessisaffectedbyspecialcauses.InvestigateX-bar/R-chartforout-of-controlconditions.SPCmaybeeffective…thenprocessisnotaffectedbyspecialcausesduringthestudyrun.SPCwouldnotbeeffectiveinthiscase…thenprocessperfectlycentred…thenprocessnotcentred(checkprocessmeanagainstdesignnominal)CpandCpkIndicesandDefects(bothtailsofthenormaldistribution)Pp=Ppk=1,3363ppmdefects=0,006%Cp=Cpk=1,670,6ppmdefects=0,00006%Note:PpmrejectratescalculatedfromCp&CpkarebasedontheshorttermvariationwhichmaynotrepresentthelongtermrejectrateTheEffectsofCpkandCponFFRExercise2:CpandCpkCalculateCpandCpkforthe100measurementsinthefile"Dataexercise1.xls"DeterminetheapproximateCpandCpkforthe4samplepopulationsonthefollowingpageShouldactionsbemadetoimprovetheseprocesses.Ifyes,which?EstimateCpandCpk?Thewidthofthenormaldistributionsshowninclude±3*sLSLUSLA)LSLUSLB)LSLUSLC)USLLSLD)EstimateCpandCpk?-A)LSLUSLA)MeanandnominalUSL-LSL6*sUSL-MeanMean-LSL3*sEstimateCpandCpk?-B)LSLUSLB)NominalMeanUSL-LSL6*sUSL-MeanMean-LSL3*sEstimateCpandCpk?-C)LSLUSLC)NominalMeanUSL-LSL6*sUSL-MeanMean-LSL3*sEstimateCpandCpk?-DUSLLSLD)NominalMeanUSL-LSL6*sUSL-MeanMean-LSL3*sSection4.UseoftheNMPDataCollectionSpreadsheetExampleofhowtoCollectData1. Runinandstabiliseprocess2. Notethemainparametersforreference3. Whentheprocessisstablerunthetoolfor10hours3. Take5partsoutfromeachcavityeveryhalfhourandmarkthemwithtime,dateandcavity.Total20setsof5partsfromeachcavitymustbemade,oraccordingtoagreement.4. Afterthelastsamplelotnotethemainprocessparametersforreference5. Measureandrecordthemainfunctionalcharacteristics(whitediamonds)6. FilldataintotheNMPdatacollectionspreadsheet7. Analyse!SeeDMY00019-ENClassificationandMarkingofFunctionalCharacteristicsTimeDimensionSubgroup