Cpk.docx
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Cpk
如何正确计算设备的Cpk非常重要。
在选择不同供应商设备产品时,Cpk为用户用于比较设备性能的参数,Cpk还是生产线设置、设备查错、成品率管理使用的统计学工具。
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SortyourSigmasout!
Thetheorybehindtheall-importantSigmaorCpkratingformachinesonthefactoryfloorcanbeconfusing.AStatisticalProcessControl(SPC)toolcancalculatetheanswer,butwhatifthemachineconsistentlyfallsshortofitsmanufacturer'sclaims?
EvensomemachinevendorscannotnecessarilyagreeonwhenamachinehasreachedtheHolyGrailof6-Sigmarepeatability.Mostuncertaintiescenteronhowtointerpretthedataandhowtoapplyappropriateupperandlowerlimitsofvariability.Thekeylieswiththestandarddeviationoftheprocess,which,fortunately,everyonecanagreeon.
GreaterAccuracy,MaximumRepeatability
Industrialprocesseshavealwaysdemandedtheutmostrepeatability,tomaximizeyieldwithinacceptedqualitylimits.Takeelectronicsurfacemountassembly:
asfine-pitchpackagesincluding0201passivesandCSPsentermainstreamproduction,assemblyprocessesmustdeliverthatrepeatabilitywithsignificantlyhigheraccuracy.Asmanufacturingsuccessbecomesmoredelicatelypoised,thisissuewillbecomerelevanttoagrowingaudience,includingproductdesigners,machinepurchasers,qualitymanagers,andprocessengineersfocusedoncontinuousimprovement.
Thisarticlewillexplainanddemystifythesecretslockedupinthecharminglysimple-yetobstinatelyinscrutable-expressionburiedsomewheredownamachine'sspecificationsheet. Youmayhaveseenitwrittenlikethis:
Repeatability=6-Sigma#±25 m
Thisshowsthatthemachinehasanextremelyhighprobability(6-sigma)that,eachtimeitrepeats,itwillbewithin25 mofthenominal,idealposition.
Agreatdealofanalysis,includingtheworkoftheMotorolaSixSigmaqualityprogram,amongothers,hasledto6-SigmabecomingacceptedthroughoutmanufacturingbusinessesastheGoldStandardasfarasrepeatabilityisconcerned.Amachineorprocesscapableofachieving6-Sigmaissurelybeyondreproach.Nottrue:
manydonotunderstandhowtocorrectlycalculatethevalueforsigmabasedonthemachine'sperformance.Theselectionoflimitsforthemaximumacceptablevariancefromnominalisalsocritical.Inpractice,virtuallyanymachineorprocesscanachieve6-Sigmaifthoselimitsaresetwideenough.
Thisisanimportantsubjecttograsp.UnderstandingitwillhelpyoumakemeaningfulcomparISOnsbetweentheclaimsofvariousequipmentmanufacturerswhenevaluatingcapitalpurchases,forexample.Youwillalsobeabletosetuplinesandindividualmachinesquicklyandconfidently,troubleshootandaddressyieldissues,andensurecontinuousimprovementintheemergingchipscaleassemblyera.Andyouwillhaveaclearerviewofthecapabilitiesofamachineorprocessinactionontheshopfloor,andapplyextraknowledgewhenanalyzingthedatayouarecollectingthroughaSPCtoolsuchasQC-CALC,inordertoregularlyreassessequipmentandprocessperformance.
Theaimofthisarticle,therefore,istoprovideabasicunderstandingofthesubject,andempoweralltypesofreaderstomakebetterdecisionsatalmosteveryleveloftheenterprise.
GraspitGraphically
Insteadofdivingintoastatisticaltreatise,let'stakeagraphicalviewoftheproposition.
Allprocessesvarytoonedegreeoranother.Abuyerneedstoask"istheprocessormachineaccurateandrepeatable?
And,"HowcanIbesure?
"Accuracyisdeterminedbycomparingthemachine'smovementsagainstahighlyaccurategagestandardtraceabletoastandardsorganization.
Considerthepossibilitiesofaccuracyversusrepeatability.SupposewemeasuretheX&Yoffseterror10timesandplotthetenpointsonatargetchartasseeninfigure1.Case1inthisdiagramshowsahighlyrepeatablemachinesinceallmeasurementsaretightlyclusteredand"rightontarget".Theaveragevariationbetweeneachpoint,knownasthestandarddeviation(writtenassigma,ortheGreeksymbolσ),issmall.
However,asmallstandarddeviationdoesnotguaranteeanaccuratemachine.Case2showsaveryrepeatablemachinethatisnotveryaccurate.Thiscaseisusuallycorrectablebyadjustingthemachineatinstallation.ItisthecombinationofAccuracyandRepeatabilitywestrivetoperfect.
Asimplewayofdeterminingbothaccuracyandprecisionistorepeatedlymeasurethesamethingmanytimes.WithscreenprintingmachinesthecriticalmeasurementisX&Yfiducialalignment.Theoretically,theX&Yoffsetmeasurementsshouldbeidenticalbutpracticallyweknowthemachinecannotmovetotheexactlocationeverytimeduetotheinherentvariation.Thelargerthevariationthelargerthestandarddeviation.
Aftermakingmanyrepeatedmeasurements,thelawsofnaturetakeover.Plottingallyourreadingsgraphicallywillresultinwhatisknownasthenormaldistributioncurve(thebellcurveoffigure2alsocalledGaussian).Thenormaldistributionshowshowthestandarddeviationrelatestothemachine'saccuracyandrepeatability.Aconsistentinaccuracywilldisplacethecurvetotheleftorrightofthenominalvalue,whileaperfectlyaccuratemachinewillresultinacurvecenteredonthenominal.Repeatability,ontheotherhand,isrelatedtothegradientofthecurveeithersideofthepeakvalue;asteep,narrowcurveimplieshighrepeatability.Ifthemachinewerefoundtoberepeatablebutinaccurate,thiswouldresultinanarrowcurvedisplacedtotheleftorrightofthenominal.Asapriority,machineusersneedtobesureofadequaterepeatability.Ifthiscanbeestablished,thecauseofaconsistentinaccuracycanbeidentifiedandremedied.Theremainderofthissectionwilldescribehowtogainanaccurateunderstandingofrepeatabilitybyanalyzingthenormaldistribution.
Anumberoflawsapplytoanormaldistribution,includingthefollowing:
1. 68.26%ofthemeasurementstakenwillliewithinonestandarddeviation(orsigma)eithersideofaverageormean
2. 99.73%ofthemeasurementstakenwillliewithinthreestandarddeviationseithersideofaverage
3. 99.9999998%ofthemeasurementstakenwillliewithinsixstandarddeviationseithersideofaverage
Considerthebellcurveshowninfigure2.Theprocessitdepictshasthreestandarddeviationsbetweennominaland25 m.Therefore,wecandescribetheprocessasfollows:
Repeatability=3-sigmaat±25 m
Therearetwoimportantfactstounderstandrightaway:
" Donotbeconfusedbythefactthattherearesixstandarddeviationintervalsbetweentheupperandlowerlimits,-25 mand+25 m:
thisisnota6-sigmaprocess.Thelawsgoverningthenormaldistributionsayitis3-sigma.
" Thenormaldistributioncurvecontinuestoinfinity,andthereforeexistsoutsidethe±25 mlimits.Itcontinuesto6-sigma,describedbynote3above,andevenbeyond.Simplybydrawingextrasigmazonesontothegraph,wecanillustratethatthe3-sigmaprocessat±25 machieves6-sigmarepeatabilityat±50 m.Itisthesameprocess,withthesamestandarddeviation,orvariability.
Nowconsiderwhathappensifweanalyzeamorerepeatableprocess.Clearly,asthebulkofthemeasurementsareclusteredmorecloselyaroundthetarget,thestandarddeviationbecomessmaller,andthebellcurvewillbecomenarrower.
Forexample,let'sdiscussasituationwherethemachinehasarepeatabilityof4-sigmaat±25microns,andiscenteredatanominalof0.000asshowninfigure3.Thisbellcurveshowsanadditionalsigmazonebetweennominalandthe25 mlimit.Quiteclearly,ahigherpercentageofthemeasurementsliewithinthespecifiedupperandlowerlimits.Thenarrowingofthebellcurverelativetothespecificationlimitshighlightswhatisreferredtoasthe"spread".Equipmentbuildersattempttodesignmachinesthatproducethenarrowestspreadwithinthestatedlimitsoftheequipment,increasingtheprobabilitythattheequipmentwilloperatewithinthoselimits.
Lastly,wedrawourbellcurvewith6sigmazonestoshowwhatitmeanstostatethatamachinehas±25micronaccuracyandisrepeatableto6-sigma.Youcanseehowthe6-sigmamachinehasaverymuchsmallerstandarddeviationcomparedtothe3-sigmamachine.Infact,thestandarddeviationishalved.Thismeansthe6-sigmamachinehaslessvariationandthereforeismorerepeatable.Considertheverynarrowbellcurveoffigure4inrelationtothelawsgoverningthenormaldistribution,whichstate99.9999998%ofmeasurementswillliewithin6standarddeviationsofnominal.
Atthispoint,wecansummarizeanumberofimportantpointsregardingtherepeatabilityofaprocess:
" ANYprocesscanbecalleda6-sigmaprocess,dependingontheacceptedupperandlowerlimitsofvariability
" Theterm6-sigmaalonemeansverylittle.Itmustbeaccompaniedbyanindicationofthelimitswithinwhichtheprocesswilldeliver6-sigmarepeatability
" Toimprovetherepeatabilityofaprocessfrom,say,3-sigmato6-sigmawithoutchangingthelimits,wemusthalvethestandarddeviationoftheprocess
Relationshiptoppm
Wecanalsonowseewhy6-sigmaissomuchbetterthan3-sigmaintermsofthecapabilityofaprocess.At3-sigma,99.73%ofthemeasurementsarewithinlimits.Therefore,0.27%lieoutside;butthisequatesto2700partspermillion(ppm).Thisisnotverygoodinamodernindustrialprocesssuchasscreenprinting,oranyotherSMTassemblyactivityforthatmatter.6-sigma,ontheotherhand,impliesonly0.0000002%or0.002ppm(2partsperbillion)outsidelimits.ReadersfamiliarwiththeMotorolaSixSigmaqualityprogramwillhaveexpectedtosee3.4ppmfailures.Thisisbecausethemethodologyallowsfora1.5sigma"processdrift"inmeannotincluded