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ProcessCapabilityAnalysis(MeasurePhase)ScopeofModuleProcessVariationProcessCapabilitySpecification,ProcessandControlLimitsProcessPotentialvsProcessPerformanceShort-TermvsLong-TermProcessCapabilityProcessCapabilityforNon-NormalDataCycle-Time (ExponentialDistribution)RejectRate (BinomialDistribution)DefectRate (PoissonDistribution)ProcessVariationProcessVariationistheinevitabledifferencesamongindividualmeasurementsorunitsproducedbyaprocess.SourcesofVariationwithinunit (positionalvariation)betweenunits (unit-unitvariation)betweenlots (lot-lotvariation)betweenlines (line-linevariation)acrosstime (time-timevariation)measurementerror (repeatability&reproducibility)TypesofVariationInherentorNaturalVariationDuetothecumulativeeffectofmanysmallunavoidablecausesAprocessoperatingwithonlychancecausesofvariationpresentissaidtobe“instatisticalcontrol”TypesofVariationSpecialorAssignableVariationMaybedueto a)improperlyadjustedmachine b)operatorerror c)defectiverawmaterialAprocessoperatinginthepresenceofassignablecausesofvariationissaidtobe“out-of-control”ProcessCapabilityProcessCapabilityistheinherentreproducibilityofaprocess’soutput.Itmeasureshowwelltheprocessiscurrentlybehavingwithrespecttotheoutputspecifications.Itreferstotheuniformityoftheprocess.Capabilityisoftenthoughtofintermsoftheproportionofoutputthatwillbewithinproductspecificationtolerances.Thefrequencyofdefectivesproducedmaybemeasuredina) percentage(%)b) partspermillion(ppm)c) partsperbillion(ppb)ProcessCapabilityProcessCapabilitystudiescan

indicatetheconsistencyoftheprocessoutputindicatethedegreetowhichtheoutputmeetsspecificationsbeusedforcomparisonwithanotherprocessorcompetitorProcessCapabilityvsSpecificationLimitsa)b)c)a)Processishighlycapableb)Processismarginallycapablec)ProcessisnotcapableThreeTypesofLimitsSpecificationLimits(LSLandUSL)createdbydesignengineeringinresponsetocustomerrequirementstospecifythetoleranceforaproduct’scharacteristicProcessLimits(LPLandUPL)measuresthevariationofaprocessthenatural6limitsofthemeasuredcharacteristicControlLimits(LCLandUCL)measuresthevariationofasamplestatistic(mean,variance,proportion,etc)ThreeTypesofLimitsDistributionofIndividualValuesDistributionofSampleAveragesProcessCapabilityIndicesTwomeasuresofprocesscapabilityProcessPotentialCp

ProcessPerformanceCpu

Cpl

Cpk

ProcessPotentialTheCpindexassesseswhetherthenaturaltolerance(6)ofaprocessiswithinthespecificationlimits.ProcessPotentialACpof1.0indicatesthataprocessisjudgedtobe“capable”,i.e.iftheprocessiscenteredwithinitsengineeringtolerance,0.27%ofpartsproducedwillbebeyondspecificationlimits. Cp RejectRate 1.00 0.270% 1.33 0.007% 1.50 6.8ppm 2.00 2.0ppbProcessPotentiala)b)c)a)Processishighlycapable(Cp>2)b)Processiscapable(Cp=1to2)c)Processisnotcapable(Cp<1)ProcessPotentialTheCpindexcomparestheallowablespread(USL-LSL)againsttheprocessspread(6).Itfailstotakeintoaccountiftheprocessisnotcenteredbetweenthespecificationlimits.ProcessiscenteredProcessisnotcenteredProcessPerformanceTheCpkindexrelatesthescaleddistancebetweentheprocessmeanandthenearestspecificationlimit.ProcessPerformance

Cpk RejectRate 1.0 0.13–0.27% 1.1 0.05–0.10% 1.2 0.02–0.03% 1.3 48.1–96.2ppm 1.4 13.4–26.7ppm 1.5 3.4–6.8ppm 1.6 794–1589ppb 1.7 170–340ppb 1.8 33–67ppb 1.9 6–12ppb 2.0 1–2ppbProcessPerformancea)Processishighlycapable(Cpk>1.5)b)Processiscapable(Cpk=1to1.5)c)Processisnotcapable(Cpk<1)a)Cp=2Cpk=2b)Cp=2Cpk=1c)Cp=2Cpk<1Example1SpecificationLimits : 4to16gMachine Mean StdDev (a) 10 4 (b) 10 2 (c) 7 2 (d) 13 1DeterminethecorrespondingCpandCpkforeachmachine.Example1AExa荐mpl苹e1翻BExa辈mpl脖e1标CExa疾mpl殊e1音DProc喷ess倒Capa扶bili牵tyFor胆a殊nor迫mal侨ly梅dis仇tri今but裂ed泰cha僚rac顷ter从ist殃ic,挤th箭ed课efe也cti脂ve贤rat财eF(x追)may阅beest恒ima艘ted斥vi悔at泰he椅fol族low辉ing疼:For登ch急ara兵cte霸ris杀tic书sw敢ith忽on银ly献one拆sp笛eci陕fic缘瑞ati眉on踏lim饶it:a)叶LSL联on患lyb)恶USL基on疯lyLSLUSLExa盗mpl井e2Spe仆cif仁ica湾tio桐nL饼imi危ts小: 4废to厉16倒gMac抢hin思e M艘ean亡S誓td稻Dev(a)边10恼4(b)助1艇0易2(c)草7昏2(d)堂13冷1Dete贷rmin般eth奇ede裁fect序ive禁rate谷for蹄eac劈燕hma咽chin贼e.Exam疾ple念2Mean史S羊tdD学ev板ZLSLZUSLF(x义<LS滚L)僚F(博x>U节SL)放F(否x)10学4廉-1.烤5 1骡.5晕66,摩807栽66,赌807裕13鼠3,6羽1410即2龄-3.0俗3.0删1,咱350态1,3料50妥2增,7007安2蹲-狮1.5第4.纠5绩6陈6,8座07拳3猪6鸦6,8社1113颂1欧-9.0御3.0阻0岸1,35棒0伟1,偷350Lowe榜rSp仇ecL啊imit敲=铺4杜gUppe哨rSp柏ecL材imit驴=借16gPro滨ces怕sP梦ote恼nti辱al把vs齐Pro勺ces户sP哥erf由orm那anc冷e(a)幼Poo讲rP陷roc央ess尸Po侨ten牛tia瓦l (搭b)申Poo隐rP讽roc慈ess映Pe蜂rfo禽rma假nceLSLUSLLSLUSLExpe杏rime退ntal种Des柜ignto谦red禁uce蚀va懂ria棍tio洗nExp稿eri础men负tal何De诱sig标ntoc讽ente暖rme据antor幸educ薄eva当riat你ionPro吊ces免sP浊ote毛nti给al缠vs秩Pro绣ces杏sP肌erf遍orm萝anc话ePro敢ces蹄sP赢ote秆nti触al疯Ind眯ex桨(姥Cp)Cpk1.0忘1柱.2爽1.礼4流1.6盾1漏.8文2.专01.02,6耳99.平9 1脸,36璃3.3斤1,事350锋.0驱1,3栏50.叶0 1签,35焦0.0芬1,踪蝶350收.01.2318叼.3坊159驴.9陷159极.1炎159仿.1迹159哗.11.426.7谱13六.4月13.4周13险.41.61.6颗0泳.8肺0.纵81.80.1请0筐.02.00.0Defe堤ctiv煤eRa筛te(多meas笑ured颜in长dppm童)is烟dep烈ende软nto端nth萌eac盲tualcomb裹inat猴ion扇ofCpand欠Cpk..Proc肠ess欠Pote宿ntia楚lvs猎Pro痰cess弓Per残form张ancea)Cp=2Cpk=2b)Cp=2Cpk=1c)Cp=2Cpk<1Cp–CpkMiss谋edO龟ppor坛tuni舒tyAlte丈rnat括ive少Proc捡ess圾Perf奏orma脉nce鄙Inde遥xPro译ces阅sc乎apa追bil镇ity汇st稀ati守sti嘴cs衬mea览sur抚ep纽奉roc慎ess卡va秒ria类tio垫nr你ela筑tiv投et哪os粗pec疯ifi铁cat掠ion苗li纺mit街s.The秘Cpsta厉tis曾tic则co繁mpa锦res第th番ee佩ngi程nee新rin遮gt围ole郑ran根ce事aga胃ins极tt颤he正pro弟ces泄s’s醋na递tur枝al楼var新iat躁ion虾.The鬼Cpksta心tis丙tic赚ta国kes洞in卵to壶acc驰oun基tt普he捎loc桃ati览on涌of来the矛pr惨oce印ss昨rel封ati妙ve萝to余the天mi起dpo为int港be右twe潜en袋spe霜cif逢ica医tio偏ns.围I湖ft耽he胸pro馅ces耍starg野eti同sno投tce胳nter稼edb肚etwe云ens毛peci延fica丸tion起s,t背he细Cpmsta侵tis尖tic想is皂pr翁efe浅rre溪d.Pro抓ces奴sS丢tab凑ili葛tyAp举roc迈ess蛋is定st遭abl该ei谅ft兼he顷dis眼tri样but果ion举of窄me规asu渣rem近ent窑sm渡adeont设heg台iven斯fea称ture掀is音cons嚷iste舞nto国ver遮time孩.TimeStableProcessTimeUnstableProcessucllclucllclWith递inv寇sOv严eral牛lCa届pabi渠lityWith眠inC菠apab交ilit罢y(pr器evi僵ous疑ly灾cal稻ledsho植rt-径ter疲mc喂apa刷bil促ity)s对how即st多he滑inh驼ere做nt绣var载iab栋ili部ty乌of廊am散ach挽ine蒜/pr阿oce胜ss磨ope薄rat齿ing榨wi掘thi床na拆br用ief捐pe誓rio辨do妈ft护ime离.Ove用ral花lC阅apa所bil狠ity(pr模evi根ous尼ly际cal柜ledlon虾g-t途erm析ca僚pab京ili饿ty)s羞how肿st廊he路var尸iab只ili咱ty暮of嫌am摘ach旅ine阔/pr员oce筛ss链ope才rat井ing忙ov尼er突ap宪eri叹od罚of技tim丘e.盾It贞in庭clu奥des删so榜urc烘es遗of恐var圾iat济ion衣in疑ad骆dit袋ion录to灶th耗es肺hor粥t-t补erm底va掏ria纸bil贷ity倘.Wit宽hin喉vs红Ov葡era照ll厉Cap台abi猾lit线yWith秆in户Ove以rallSamp详leS猪ize与30拢–50笋uni挪ts10储0un夕itsNumb道ero钉fLo棉ts灰sing墨lel报ot闷seve唐ral恢lotsPer峰iod告of肠Ti沃me廉ho遣urs摆or锹da妥ys州we棍eks在or梨mo底nth泰sNum子ber仍of恩Op炼era狱tor乱s 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