Acceptance Sampling (来料验收抽样方法)

2007/8/251AcceptanceSampling(AttributeData)2007/8/252Acceptancesampling,SPC,DOE„„年來2007/8/253„Acceptancesamplingsentencelots,nottoestimatethequality.„Donotprovideanydirectformofqualitycontrol.„Notto“inspectqualityintotheproducts,”butratherasanaudittooltoensurethattheoutputofaprocessconformstorequirements.2007/8/254Whentouseacceptancesampling?„Whentestingisdestructive.„Whenthecostof100%inspectionishigh.„When100%inspectionisnottechnologicallyfeasibleorwouldrequiresomuchcalendartime.„Whentherearemanyitemstobeinspectedandtheinspectionerrorrateishigh.„Whenthevendorhasanexcellentqualityhistory,andsomereductionininspectionfrom100%isdesired.„Whentherearepotentiallyseriousproductliabilityrisks.2007/8/255Acceptancesampling„Lessexpensivebecauseoflessinspection.„Thereislesshandlingoftheproduct.„Itisapplicabletodestructivetesting.„Fewerpersonnelareinvolvedininspectionactivities.„Itoftengreatlyreducestheamountofinspectionerror.„Therejectionofentirelotsoftenprovidesastrongermotivationtothevendorforqualityimprovement.2007/8/256„Risksofaccepting”bad”lotsandrejecting“good”lots.„Lessinformationisusuallygenerated.„Acceptancesamplingrequiresplanninganddocumentationoftheacceptancesamplingprocedurewhereas100%inspectiondoesnot.2007/8/257料兩AcceptthelotsRejectthelotsAcceptableO.K.Producers'sRiskRejectableConsumerQualityDecision料AttributeData良劣兩VariableData度度參Liberman,G.J.,andG.J.Resnikiff(1955).”SamplingplansforInspectionbyvariables”JournalofQualityTechnology,Vol.29,No.2.臨列兩論2007/8/258AcceptancesamplingPlans類„Singlesamplingplan.„Doublesamplingplan.„Multiplesamplingplan.„Sequentialsamplingplan.2007/8/259SinglesamplingplanIncomingmaterialTotalnumberNTheproportionofdefects:PInspection(n,c)AcceptiffSncRejectiffSnc≤QuestionHowtodeterminen,cWhereSnn數2007/8/2510OC-Curve[]理OC-CurvePOC(P)10OC-CurveP)|(PlottheAcceptPOC(P)2007/8/2511„„列⎩⎨⎧≤−≥⇒⎩⎨⎧≤≤βαβα)(1)(''21POCPOCrisksConsumerrisksproducerP1P2不良率]|Pr[)(pcSpOCn≤=2007/8/2512∑=−−=cxNnpNxnNpxCCCpOC0)1()(∑=−−=cxxnxnxppCpOC0)1()(∑=−=cxnpxxenppOC0!)()(∞→NAsε∞→npnAs2007/8/2513„„2007/8/2514„利連兩利數n數c),(p;)-1,(p21βα2007/8/2515„利數,⎪⎪⎩⎪⎪⎨⎧===−===∑∑∑∑==−−==−−cxcxxnpxcxcxxnpxxexenppOCxexenppOC0022200111!)(!)()(1!)(!)()(2211βλαλλλ21λλαβ⎟⎟⎠⎞⎜⎜⎝⎛21λλ⎟⎟⎠⎞⎜⎜⎝⎛≈⎟⎟⎠⎞⎜⎜⎝⎛1212PPλλor2211⎟⎟⎠⎞⎜⎜⎝⎛⎟⎟⎠⎞⎜⎜⎝⎛≈PPλλ2007/8/2516Example1„不良率率不良率率不列列IlikesolutionIlikesolution了2007/8/2517RectifyingInspectionTotalnumberNTheproportionofdefects:PInspection(n,c)AcceptiffSncRejectiffSnc≤--來--100不良RectifyingInspection2007/8/2518„不良率„數⎪⎩⎪⎨⎧≤=otherwise0SifNn)-p(N)(ncpAOQ⇒⎩⎨⎧≤=cNcpTInnSifSifn)(AOQLMAX{AOQ(p)})]|Pr(1)[()|Pr()(pcSnNnpcSnNnATInn≤−−+=−+=2007/8/2519Example2„N10000n=89c=2不良率p1Example1OC-CurvepaPr[Acceptthelot|p=1%]0.93970093.01000089)-(1000001.00.9397Nn)-p(Np)(a=××==pAOQ68789)-0000.9397)(10-(189)1)(()|Pr()(=+=−−+=−+=anpnNnpcSnNnATI2007/8/2520Example2„„2007/8/2521Dodge-RomigSamplingplan„Dodge-RomigAOQLSamplingplanDetermine(n,c)suchthatATIattainminimumsubjecttowhereATI=n+(N-n)Pr[Snc|p].„Dodge-RomigLTPDSamplingplanDetermine(n,c)suchthatATIattainminimumsubjecttowhereATI=n+(N-n)Pr[Snc|p].pecified)AOQL(prespAOQ(p)∀≤pecified)LTPD(prespOC(p)∀≤兩AOQLLTPD2007/8/2522Example3QSupposethatweareinspectingLSImemoryelementsforapersonalcomputerandthattheelementsareshippedinlotsofsizeN=5000.Thevendor’sprocessaveragefalloutis1%nonconforming.Howtofindasingle-samplingplanwithanAOQL=3%.Sol裡2007/8/2523Example4QSupposethatweareinspectingLSImemoryelementsforapersonalcomputerandthattheelementsareshippedinlotsofsizeN=5000.Thevendor’sprocessaveragefalloutis0.25%nonconforming.Howtofindasingle-samplingplanwithanLTPD=1%.Sol裡2007/8/2524DoubleSamplingplan„不兩„若若若„若若–≤≤≤Remarkn2=n1orn2=2n1.2007/8/2525DoubleSamplingplan„2007/8/2526OC-CurveinDoublesamplingplan∑+=+=×=≤+≤=2111211121]Pr[]|Pr[]|Pr[)(ccxnnnnnxSxScSpcSpOC∑∑∑=−+=−=−−××+×=1212010!}!{!)(cxxccxxcyyxxeyexepOCλλλλλλWhere.np=λQuestionHowtodetermine(n1,n2,c1,c2)whichsatisfiesthatOC(P1)=0.95andOC(P2)=0.12007/8/2527數„Recallthesecondmethodthatweusedinsinglesamplingplan.Nowweusethesimilarmethodtoobtaintheanswerthatwewant.,21λλαβ⎟⎟⎠⎞⎜⎜⎝⎛21λλ⎟⎟⎠⎞⎜⎜⎝⎛≈⎟⎟⎠⎞⎜⎜⎝⎛1212PPλλor2211⎟⎟⎠⎞⎜⎜⎝⎛⎟⎟⎠⎞⎜⎜⎝⎛≈PPλλ2007/8/2528Example5.)(1)(,,nn0.10.05;;9%P1%P212112121planSamplingpOCpOCccnQ⎩⎨⎧=−======βαβαSol:裡2007/8/2529類„來„類不„參””2007/8/2530References„DouglasC.Montgomery(2001)“Introductiontostatisticalqualitycontrol(4-thedition)”„Dodge,H.F.A(1943)“SamplingplanforContinuousProduction”AnnalsofMathematicalStatistics,Vol14.„Dodge,H.F.A(1955)“ChainSamplingInspectionplan”IndustrialQualityControl,Vol,11.2007/8/2531THEENDThanksforyourlistening!!2007/8/2532Solution1„利連n,c90,3了2007/8/2533Solution2„利數COC(p1)=0.951=n*p1OC(p2)=0.12=n*p22/100.05123.0344.8410.3553.8910.9620.8185.3226.5131.3666.6814.89藍數89,2OCP(n,c)OC(p1)OC(p2)(82,2)95%10%(89,2)95%10%(137,3)95%10%(112,3)95%10%藍2007/8/2534LTPD2007/8/2535AOQL2007/8/2536Solutionforexample3不良率良2007/8/2537Solutionforexample4不良率2007/8/2538Solutionforexample5c2c1lamda0lamda1lamda1/lamda0n1n2010.20652.489412.0552058120.6527.66120.52623.92677.46237172252.6243.63020.42912.9166.79561873742.9132.4130.7609