Cpk.docx

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