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1©NOKIA2001T0001801.PPT/21-Dec-2001/JimChristyCompanyConfidentialProcessCapability(Cp/Cpk/Pp/Ppk)Globa

lTrainingMaterialCreator:GlobalMechanicsProcessManagerFunction:MechanicsApprover:GaryBradley/GlobalProcessTeamDoc

umentID:DMT00018-ENVersion/Status:V.1.0/ApprovedLocation:Notes:\\…\NMP\DOCMANR4\PCP\PCProcessLibraryDocManChangeHistory:IssueDateHandl

edByComments1.021stDec’01JimChristy&SørenLundsfrydApprovedforGlobalUseNOTE–Allcommentsandimprovementsshouldbeaddressedtothecreatorofthisdocumen

t.2©NOKIA2001T0001801.PPT/21-Dec-2001/JimChristyCompanyConfidentialContentsSectionHeading/DescriptionPage1Variation,TolerancesandDimensionalContro

l42Population,SampleandNormalDistribution153CpandCpkConcept284UseoftheNMPDataCollectionSpreadsheet445ConfidenceofCpk523©NO

KIA2001T0001801.PPT/21-Dec-2001/JimChristyCompanyConfidentialProcessCapability-EvaluatingManufacturingVariationAcknowledgements•Benny

Matthiassen(NMPCMT,Copenhagen,Denmark)•FrankAdler(NMPAlliance,Dallas,USA)•JoniLaakso(NMPR&D,Salo,Finland)•JimChristy(NMPSRC,Southwood,UK)4©

NOKIA2001T0001801.PPT/21-Dec-2001/JimChristyCompanyConfidentialSection1Variation,TolerancesandDimensionalControl5©NOKIA2001T0001801.PP

T/21-Dec-2001/JimChristyCompanyConfidentialTwoTypesofProductCharacteristicsVariable:Acharacteristicmeasuredinphy

sicalunits,e.g.millimetres,volts,amps,decibelandseconds.ONOFFAttribute:Acharacteristicthatbycomparisontosomestandardisjudged“good”or“bad”,e.g.f

reefromscratches(visualquality).6©NOKIA2001T0001801.PPT/21-Dec-2001/JimChristyCompanyConfidentialTheSourcesofProcess/SystemVariationMetho

dsOperatorsCustomerSatisfactionMaterialEnvironmentEquipmentProcess7©NOKIA2001T0001801.PPT/21-Dec-2001/JimChristyCompanyConfidentialTwoTypesofProce

sses•Allprocesseshave:–Natural(random)variability=>duetocommoncauses•StableProcess:Aprocessinwhichvariationinoutcomesarisesonlyf

romcommoncauses•UnstableProcess:AprocessinwhichvariationisaresultofbothcommonandspecialcausesUSLLSLnominalvalueDefectUSLLSLnominalvalue

–Unnaturalvariability=>duetospecialcauses8©NOKIA2001T0001801.PPT/21-Dec-2001/JimChristyCompanyConfidentialShewhart(1931)TheTw

oCausesofVariation•CommonCauses:–Causesthatareimplementedintheprocessduetothedesignoftheprocess,andaffectalloutcomesofthep

rocess–IdentifyingthesetypesofcausesrequiresmethodssuchasDesignofExperiment(DOE),etc.•SpecialCauses:–Causesthatarenotpresentintheprocessallth

etimeanddonotaffectalloutcomes,butarisebecauseofspecificcircumstances–SpecialcausescanbeidentifiedusingStat

isticalProcessControl(SPC)USLLSLNominalvalueDefectUSLLSLnominalvalue9©NOKIA2001T0001801.PPT/21-Dec-2001/JimChr

istyCompanyConfidentialTolerancesLSL(lowerspecificationlimit)10,7USL(upperspecificationlimit)10,9AcceptablepartRejectedPartRejectedProductNo

minal10,80,1RejectedPartAtoleranceisaallowedmaximumvariationofadimension.10©NOKIA2001T0001801.PPT/21-D

ec-2001/JimChristyCompanyConfidentialMeasurementReportInmostcaseswemeasureonlyonepartpercavityformeasurementreport11©NOKIA2001T000180

1.PPT/21-Dec-2001/JimChristyCompanyConfidentialExampleofCapabilityAnalysisData•Forsomecriticaldimensionsweneedtomeasuremorethan1part•F

orcapabilitydataweusuallymeasure5pcs2times/hour=100pcs(butsamplingplanneedstobemadeonthebasisofproductionquantity,rundurationandcycletime)1s

tSubgroup2ndSubgroup3rdSubgroup4thSubgroup118.53118.52118.54118.56118.54118.54118.52118.55118.51118.51118.50118.55118.53118.51118.52118.55118.51118.5

4118.54118.555thSubgroup6thSubgroup7thSubgroup8thSubgroup118.55118.54118.57118.60118.54118.56118.56118.57118.55118

.55118.57118.55118.54118.54118.55118.56118.56118.53118.54118.559thSubgroup10thSubgroup11thSubgroup12thSubgroup118.60118.6

1118.58118.60118.59118.60118.60118.63118.58118.61118.61118.63118.60118.59118.60118.61118.59118.59118.59118.6412©NOKIA2001T00018

01.PPT/21-Dec-2001/JimChristyCompanyConfidentialProcessCapability-Whatisit?•ProcessCapabilityisameasureoft

heinherentcapabilityofamanufacturingprocesstobeabletoconsistentlyproducecomponentsthatmeettherequireddesignspecificatio

ns•ProcessCapabilityisdesignatedbyCpandCpk•ProcessPerformanceisameasureoftheperformanceofaprocesstobeabletoconsistentlyproducecomponentsthatmeetthere

quireddesignspecifications.ProcessPerformanceincludesspecialcausesofvariationnotpresentinProcessCapability•ProcessPerfo

rmanceisdesignatedPpandPpk13©NOKIA2001T0001801.PPT/21-Dec-2001/JimChristyCompanyConfidentialWhyMakeProcessCapabilityStudiesLSL(lower

specificationlimit)10,7USL(upperspecificationlimit)10,9Nominal10,80,1Thispartiswithinspec.Thetoolwouldbea

pprovedifonlythispartwasmeasuredThesepartsareoutofspecandcouldbeapprovedifonlyonegoodpartwasmeasuredAproc

esscapabilitystudywouldrevealthatthetoolshouldnotbeacceptedWhenadimensionneedstobekeptproperlywithinspec,wemuststu

dytheprocesscapability….butstillthisisnoguaranteefortheactualperformanceoftheprocessasitisonlyaninitialcapabil

itystudy14©NOKIA2001T0001801.PPT/21-Dec-2001/JimChristyCompanyConfidentialE1.5E1E2E3E4E5TheNokiaProcessVerificationProcessBlackdiamonds

tobefixedbyE3(oftenachangeofawhitediamond)ProposalforblackdiamondstobediscussedwithSupplier.Max:105,85OngoingProcessControl(SPC)Tolerancesappliedtod

rawing-1part/cavitymeasuredformeasurementreportWhitediamonds(s)tobeagreedWhitediamonds(s)tobediscussedwithsupplier10parts/cavit

ymeasuredformeasurementreportCapabilitystudy:Requirement:CpandCpk>1.67byE3.Quantitiestobeagreedwithsuppli

er.Minimum5partspr1/2hourin10hoursmeasuredforeachcavity=100parts.Canvarydependingontoolcapacity,e.g.

stampedparts(seeDMY00019-EN)15©NOKIA2001T0001801.PPT/21-Dec-2001/JimChristyCompanyConfidentialSection2.Population,SampleandNorm

alDistribution16©NOKIA2001T0001801.PPT/21-Dec-2001/JimChristyCompanyConfidentialTheBellShaped(Normal)

Distribution•Symmetricalshapewithapeakinthemiddleoftherangeofthedata.•Indicatesthattheinputvariables(X's)totheprocessar

erandomlyinfluenced.17©NOKIA2001T0001801.PPT/21-Dec-2001/JimChristyCompanyConfidential“PopulationParameters”=Populationmean=P

opulationstandarddeviationPopulationversusSamplePopulation•Anentiregroupofobjectsthathavebeenmadeorwillbemadecontainingach

aracteristicofinterestSample•Thegroupofobjectsactuallymeasuredinastatisticalstudy•Asampleisusuallyasubsetofthepopulationofinterest“SampleStatis

tics”x=Samplemeans=Samplestandarddeviation18©NOKIA2001T0001801.PPT/21-Dec-2001/JimChristyCompanyConfidentialTheNormalDistribution19©NOKIA2001T00018

01.PPT/21-Dec-2001/JimChristyCompanyConfidentialWhatMeasurementsCanBeUsedtoDescribeaProcessorSystem?xxxxN

N12...Example:x1=5x2=7x3=4x4=2x5=68.4524562475x•mean(average)ordescribesthelocationofthedistributionx•µ(mü

),ameasureofcentraltendency,isthemeanoraverageofallvaluesinthepopulation.Whenonlyasampleofthepopulationisbeingdescribed,meanismoreproperlydenoteda

s(x-bar):x20©NOKIA2001T0001801.PPT/21-Dec-2001/JimChristyCompanyConfidential),...,,min(),...,,max(2121NNxxxxxxRExa

mple:x1=5x2=7x3=4x4=2x5=6527)6,2,4,7,5min()6,2,4,7,5max(R•Themostsimplemeasureofvariabilityistherange.Therangeofasam

pleisdefinedbyasthedifferencebetweenthelargestandthesmallestobservationfromsamplesinasub-group,e.g.5consecutivepartsfromthemanufacturingproc

ess.WhatMeasurementsCanBeUsedtoDescribeProcessvariation?21©NOKIA2001T0001801.PPT/21-Dec-2001/JimChristyCompanyConfidential•sST-oftennotatedaso

rsigma,isanothermeasureofdispersionorvariabilityandstandsfor“short-termstandarddeviation”,whichmeasuresthevariabilityofaprocessorsyst

emusing“rational”sub-grouping.sRNdRdSTjjN122**whereistherangeofsubgroupj,Nthenumberofsubg

roups,andd2*dependsonthenumberNofsubgroupsandthesizenofasubgroup(seenextslide)RXXjjjmaxminWhatMeasurementsCan

BeUsedtoDescribeProcessvariation?22©NOKIA2001T0001801.PPT/21-Dec-2001/JimChristyCompanyConfidentiald2*valuesforSSTWhere:N=no.ofsub-groups,n=no.ofsa

mplesineachsub-groupd2*d2Typical:N=20&n=523©NOKIA2001T0001801.PPT/21-Dec-2001/JimChristyCompanyConfidential•••••••x3•x2•x1•x10x_t1)(...)()(2

22212NxxxxxxssNLTLT92.17.315)8.46()8.42()8.44()8.47()8.45(22222LTsExample:WhatMeasurementsCanBeUsedtoDescribe

Processvariation?24©NOKIA2001T0001801.PPT/21-Dec-2001/JimChristyCompanyConfidentialTheDifferenceBetweenSSTa

ndsLT!!meanTimeDimensionShorttermStandardDeviationLongtermStandardDeviationSubgroupsizen=5NumberofsubgroupsN=7SubgroupNo.125©NOKIA2

001T0001801.PPT/21-Dec-2001/JimChristyCompanyConfidentialThedifferencebetweenthestandarddeviationssLTandsSTgivesanindicationofhowmuchbet

teronecandowhenusingappropriateproductioncontrol,likeStatisticalProcessControl(SPC).sxxxxxxNLTN()()...()

122221sRNdRdSTjjN122**Short-termstandarddeviation:Long-termstandarddeviation:ThedifferencebetweensSTandsLT26©NOKIA2001T0001801.PPT/21-De

c-2001/JimChristyCompanyConfidentialThedifferencebetweensSTandsLT•ThedifferencebetweensLTandsSTisonlyinthewaythatthestandarddeviati

oniscalculated•sLTisalwaysthesameorlargerthansST•IfsLTequalssST,thentheprocesscontroloverthelonger-termisth

esameastheshort-term,andtheprocesswouldnotbenefitfromSPC•IfsLTislargerthansST,thentheprocesshaslostcontroloverthelonger-term,andtheprocess

wouldbenefitfromSPC•ThereliabilityofsLTisimprovedifthedataistakenoveralongerperiodoftime.AlternativelysLTcanbecalculatedonseveraloccasio

nsseparatedbytimeandtheresultscomparedtoseewhethersLTisstable27©NOKIA2001T0001801.PPT/21-Dec-2001/JimChristyCompanyConfidentialExer

cise1:SampleDistributions1.InExcelfile"Dataexercise1.xls"youfind100measurementsbeingtheresultofacapabilit

ystudy.Thespecificationforthedimensionis15,16,012.Howwelldoesthesamplepopulationfitthespecification,e.g.shouldweexpectanypartso

utsidespec?3.Mentionpossibleconsequencesofhavingapartoutsidespec.4.Mentionpossiblecausesofvariationforparts.5.Calcu

latethesamplemeanandsamplestandarddeviationforthe100measurements.UsetheaverageandstdevfunctionsExcel.28©NOKIA2001T0001801.PPT/21-Dec-200

1/JimChristyCompanyConfidentialSection3.CpandCpkConcept29©NOKIA2001T0001801.PPT/21-Dec-2001/JimChristyCompanyConfidentialDefiningCpandPpSampleme

anProcessvariation6*sstpsLSLUSLC*6-USL-LSLLSLUSLNominaldimltpsLSLUSLP*6-Thetoleranceareadividedbythetotalprocessvariation,irrespectiveofpr

ocesscentring.30©NOKIA2001T0001801.PPT/21-Dec-2001/JimChristyCompanyConfidentialDefiningCpkandPpkststpksmeanUSL

sLSLmeanC*3-,*3-minSamplemeanProcessvariation3sProcessvariation3sMean-LSLUSL-MeanLSLUSLNominaldimltltpksmeanUSLsLSLmeanP*3-,*3-minCpkandPpkI

ndexesaccountalsoforprocesscentring.31©NOKIA2001T0001801.PPT/21-Dec-2001/JimChristyCompanyConfidentialWhatistheDifferenc

eBetweenCpandCpk?•TheCpindexonlyaccountsforprocessvariability•TheCpkIndexaccountsforprocessvariabilityandcenteri

ngoftheprocessmeantothedesignnominal•Therefore,CpCpk•NOTE:SameappliesalsoforPpandPpkCp=Cpk(bothlow)LSLUSLMean=NominalRejectpartsRejectpar

tsCphigh,CpklowProcessshouldbeoptimized!NominalLSLMeanUSLRejectparts32©NOKIA2001T0001801.PPT/21-Dec-2001/JimChristyCompanyConf

identialWhatDoTheseIndexesTellUs??•Simplenumericalvaluestodescribethequalityoftheprocess>>Thehigherthenumberthebetter•RequirementforC

pandCpkis1.67min.•RecommendationforPpandPpkis1.33min.•Thisleavesussomespaceforthevariation,i.e.asafetymargin•Ar

eweabletoimproveourprocessbyusingSPC?•Ifindexislow,followingthingsshouldbegivenathought:•IstheproductdesignOK?

•Aretolerancelimitssetcorrectly?•Tootight?•Istheprocesscapableofproducinggoodqualityproducts?Processvariation?DOErequired?•Isthemeasuringsystemcapa

ble?(SeeGageR&R)33©NOKIA2001T0001801.PPT/21-Dec-2001/JimChristyCompanyConfidentialCpk-Witha2-sigmasafetymargin-3sST+3sSTLCLUCLLS

LUSLMeanvalue=NominalvalueorTarget•RequirementforCpandCpkis1.67min.1.67isaratioof=5/3or10/6.6*standarddeviation10*standarddeviation2*standarddev

iation2*standarddeviation34©NOKIA2001T0001801.PPT/21-Dec-2001/JimChristyCompanyConfidential•Cpk<1.67thepro

cessNOTCAPABLEAcceptabilityofCpkIndex•Cpk>=1.67theprocessisCAPABLE•Cpk>=2.0theprocesshasreachedSixSigmalevel

35©NOKIA2001T0001801.PPT/21-Dec-2001/JimChristyCompanyConfidentialWhatDoTheseIndexesTellUs??•IfCp=Cpk,•IfP

p=Ppk,•IfCpk<Cp,•IfPpk<Pp,•IfCp=Pp,•IfCpk=Ppk,•IfPp<Cp,•IfPpk<Cpk,…thenprocessisaffectedbyspecialcauses.InvestigateX-bar

/R-chartforout-of-controlconditions.SPCmaybeeffective…thenprocessisnotaffectedbyspecialcausesduringthestudyrun.SPCwouldnotbeeffectiveinthisc

ase…thenprocessperfectlycentred…thenprocessnotcentred(checkprocessmeanagainstdesignnominal)36©NOKIA2001T0001801.PPT/21-Dec-2001/JimChristyCompanyC

onfidentialCpandCpkIndicesandDefects(bothtailsofthenormaldistribution)Cpk/PpkCp/Pp0.10.20.30.40.50.60.70.80.91.01.11.21.33

1.41.51.672.02.53.04.0%/PPM0.176.4256.6144.8940.0038.5638.2638.2138.2138.2138.2138.2138.2138.2138.2138.2138.2138.2138.2138.2138.21%0.254.8638.9331.

0228.2527.5627.4427.4327.4327.4327.4327.4327.4327.4327.4327.4327.4327.4327.4327.43%0.336.8125.0920.1918.7518.4518.4118.4118.4118.4118.411

8.4118.4118.4118.4118.4118.4118.4118.41%0.423.0115.1012.3311.6411.5211.5111.5111.5111.5111.5111.5111.5111.5111.5111.5111.5111.51%0.513.368

.477.036.736.696.686.686.686.686.686.686.686.686.686.686.68%0.67.194.413.733.613.593.593.593.593.593.593.593.593.593.

593.59%0.73.572.131.831.791.791.791.791.791.791.791.791.791.791.79%0.81.640.950.840.820.820.820.820.820.820.820.820.820.82%0.90.690.400.350

.350.350.350.350.350.350.350.350.35%1.027001509136313501350135013501350135013501350PPM1.1967532485484483483483483483483PPM1.231816

5160159159159159159159PPM1.336338333332323232PPM1.427141313131313PPM1.5733333PPM1.670.60.30.30.30.3PPM2.00.00

.00.00.0PPM2.50.00.00.0PPM3.00.00.0PPM4.00.0PPMPp=Ppk=1,3363ppmdefects=0,006%Cp=Cpk=1,670,6ppmdefects=0,00006%Note:Ppmrejectratesc

alculatedfromCp&Cpkarebasedontheshorttermvariationwhichmaynotrepresentthelongtermrejectrate37©NOKIA2001T0001801.PPT/21-Dec-2001/Ji

mChristyCompanyConfidentialTheEffectsofCpkandCponFFRCpkCpPpmdefectsTotalnumberofdefectsfor50,000,000parts

Totalnumberofdefectsifphonehas10oftheseparts0.81.338,200410,0004,100,00011.331,35067,500675,0001.331.33633,15031,5001.331.67331,65016

,5001.501.5073503,5001.671.671303002.002.0000138©NOKIA2001T0001801.PPT/21-Dec-2001/JimChristyCompanyConfidentialExercise2:CpandCpk•Calcul

ateCpandCpkforthe100measurementsinthefile"Dataexercise1.xls"•DeterminetheapproximateCpandCpkforthe4samplepopula

tionsonthefollowingpage•Shouldactionsbemadetoimprovetheseprocesses.Ifyes,which?39©NOKIA2001T0001801.PPT/21-Dec-2001/JimChristyCompan

yConfidentialEstimateCpandCpk?Thewidthofthenormaldistributionsshowninclude±3*sLSLUSLA)LSLUSLB)LSLUSLC)USLLS

LD)40©NOKIA2001T0001801.PPT/21-Dec-2001/JimChristyCompanyConfidentialEstimateCpandCpk?-A)LSLUSLA)Meanandnomi

nalUSL-LSL6*sUSL-MeanMean-LSL3*s41©NOKIA2001T0001801.PPT/21-Dec-2001/JimChristyCompanyConfidentialEstimateCp

andCpk?-B)LSLUSLB)NominalMeanUSL-LSL6*sUSL-MeanMean-LSL3*s42©NOKIA2001T0001801.PPT/21-Dec-2001/JimChristyCompanyConfidentialEst

imateCpandCpk?-C)LSLUSLC)NominalMeanUSL-LSL6*sUSL-MeanMean-LSL3*s43©NOKIA2001T0001801.PPT/21-Dec-2001/JimChristy

CompanyConfidentialEstimateCpandCpk?-DUSLLSLD)NominalMeanUSL-LSL6*sUSL-MeanMean-LSL3*s44©NOKIA2001T0001801.

PPT/21-Dec-2001/JimChristyCompanyConfidentialSection4.UseoftheNMPDataCollectionSpreadsheet45©NOKIA2001T0001801.PPT/21-Dec-200

1/JimChristyCompanyConfidentialExampleofhowtoCollectData1.Runinandstabiliseprocess2.Notethemainparame

tersforreference3.Whentheprocessisstablerunthetoolfor10hours3.Take5partsoutfromeachcavityeveryhalfhourandmarkthemwithtime,dateandcavit

y.Total20setsof5partsfromeachcavitymustbemade,oraccordingtoagreement.4.Afterthelastsamplelotnotethemainprocessparametersforreference5.Measur

eandrecordthemainfunctionalcharacteristics(whitediamonds)6.FilldataintotheNMPdatacollectionspreadsheet7.Analyse!TimeDimensionSubgroupsizen=

5NumberofsubgroupsN=200,5hoursbetweensamplestakenNote:Forclarity,only6subgroupsareshown46©NOKIA2001T0001801.PP

T/21-Dec-2001/JimChristyCompanyConfidentialDataCollectionSheet(DMM00024-EN-5.0)47©NOKIA2001T0001801.PPT/21-Dec-

2001/JimChristyCompanyConfidentialDataCollectionSheet(DMM00024-EN-5.0)48©NOKIA2001T0001801.PPT/21-Dec-2001/JimCh

ristyCompanyConfidentialGraphicalPresentation:Histogram•Whatkindofdistribution?LocationversustoleranceareaWidth(deviation)•Example:Cp2.59Pp1.

86•Cpk0.88Ppk0.6349©NOKIA2001T0001801.PPT/21-Dec-2001/JimChristyCompanyConfidentialGraphicalPresentation:X-barandR-Cha

rtX-BarChartR-Chart50©NOKIA2001T0001801.PPT/21-Dec-2001/JimChristyCompanyConfidentialGraphicalPresentation-TimeS

eriesPlotSomethinghappenedhere!!!51©NOKIA2001T0001801.PPT/21-Dec-2001/JimChristyCompanyConfidentialExercise3:CpkDataSpreadsh

eet•Openspreadsheet"Dataexercice3.xls".Dim13isidenticaltothedatafromthepreviousexercises.•Verifytheresultsfromthepreviousexercis

esfordimension13.•Analysetheremainingdatasetsancommenttheprocess,shouldanyactionsbemade?Remembertocreateandlookatthecharts.52©NOKI

A2001T0001801.PPT/21-Dec-2001/JimChristyCompanyConfidentialSection5.ConfidenceofCpk53©NOKIA2001T0001801.PPT/21-Dec-2001/

JimChristyCompanyConfidentialConfidenceofCpk•Cpkvaluesarenotdefinitenumbersastheyarebasedonrelativelysmallsamplesofapopula

tion.•The95%confidenceintervaldeterminestheintervalwhichincludesthetrueCpkvaluewithaprobabilityof95%,

i.e."thereisaprobabilityof5%thatCpkiseitherlowerorhigher"thanthisconfidenceinterval.95%confidenceintervalActualcpkCpkupperconfidencelimitCpklowerc

onfidencelimit54©NOKIA2001T0001801.PPT/21-Dec-2001/JimChristyCompanyConfidentialConfidenceofCpk95%ConfidenceIntervalonaCpkof1.670.0000.5001.0001.

5002.0002.5003.0003.500050100150200250SampleSizeCpkCpk.LCpk.USmallsamplesizesgiveswideconfidenceintervals55©NOKIA2001T0001801.P

PT/21-Dec-2001/JimChristyCompanyConfidentialCpkConfidenceLimitswithasamplesizeof100andanominalCpkof1.67