6s黑带培训教材1英文

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1、Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,Process Capability Analysis,,73,ProcessCapabilityAnalysis,,(,MeasurePhase),ScopeofModule,ProcessVariation,ProcessCapability,Specification,ProcessandControlLimits,ProcessPotentialvsProc

2、essPerformance,Short-TermvsLong-TermProcessCapability,ProcessCapabilityforNon-NormalData,Cycle-Time(ExponentialDistribution),RejectRate(BinomialDistribution),DefectRate(PoissonDistribution),ProcessVariation,ProcessVariation,istheinevitabledifferencesamongindividual,measurementsorunitsproducedbyaproc

3、ess.,,SourcesofVariation,withinunit(positionalvariation),betweenunits(unit-unitvariation),betweenlots(lot-lotvariation),betweenlines(line-linevariation),acrosstime(time-timevariation),measurementerror(repeatability&reproducibility),TypesofVariation,InherentorNaturalVariation,,Duetothecumulativeeffec

4、tofmanysmallunavoidablecauses,Aprocessoperatingwithonlychancecausesofvariationpresentissaidtobe,“,“instatisticalcontrol,”,”,TypesofVariation,SpecialorAssignableVariation,,Maybeduetoa)improperlyadjustedmachine,b)operatorerror,c)defectiverawmaterial,Aprocessoperatinginthepresenceofassignablecausesofva

5、riationissaidtobe,“,“out-of-control”,ProcessCapability,ProcessCapability,istheinherentreproducibilityofaprocess,’,’s,output.Itmeasureshowwelltheprocessiscurrentlybehaving,withrespecttotheoutputspecifications.Itreferstotheuniformity,of the process.,,Capability is oftenthoughtof in termsof the proport

6、ion ofoutput,thatwill bewithinproductspecification tolerances. The frequency,of defectives produced may be measured in,a) percentage (%),b) partspermillion(ppm),c) partsperbillion(ppb),ProcessCapability,ProcessCapability,studiescan,,indicatetheconsistencyoftheprocessoutput,,indicatethedegreeto whic

7、htheoutputmeets specifications,,be usedforcomparison withanotherprocessor competitor,ProcessCapability vs SpecificationLimits,a),b),c),,a) Process is highlycapable,b) Process is marginallycapable,c) Process is not capable,,Three Typesof Limits,Specification Limits(LSLandUSL),createdby design enginee

8、ring inresponse tocustomer requirements to specify the tolerancefora product’scharacteristic,,ProcessLimits(LPL and UPL),measuresthevariation of aprocess,thenatural6, limitsofthemeasuredcharacteristic,,ControlLimits(LCL and UCL),measuresthevariation of asample statistic(mean,variance, proportion, e

9、tc),Three Typesof Limits,,DistributionofIndividual Values,,DistributionofSample Averages,ProcessCapability Indices,Twomeasuresofprocesscapability,,ProcessPotential,C,p,,ProcessPerformance,C,pu,C,pl,C,pk,ProcessPotential,TheC,p,index assesses whether the natural tolerance(6,,) ofa,processis within t

10、he specificationlimits.,,ProcessPotential,A C,p,of 1.0 indicatesthat aprocessis judged tobe,“,“capable,”,”,,i.e.iftheprocessis centeredwithin its engineering tolerance,,0.27% ofparts producedwillbebeyond specificationlimits.,,C,p,Reject Rate,1.000.270%,1.330.007%,1.506.8 ppm,2.002.0 ppb,ProcessPoten

11、tial,a),b),c),,a) Process is highlycapable(C,p,>2),b) Process is capable (C,p,=1 to 2),c) Process is not capable (C,p,<1),,ProcessPotential,TheC,p,index compares the allowablespread(USL-LSL) against,theprocessspread (6,).Itfails totake into account if the process,is not centeredbetweenthespecificat

12、ion limits.,Process is centered,Process is not centered,ProcessPerformance,TheC,pk,index relates the scaleddistance between the process,meanandthenearestspecification limit.,,ProcessPerformance,C,pk,Reject Rate,1.00.13 –0.27%,1.10.05 –0.10%,1.20.02 –0.03%,1.348.1 –96.2ppm,1.413.4 –26.7ppm,1.53.4 –6.

13、8 ppm,1.6794 –1589ppb,1.7170 –340 ppb,1.833 –67ppb,1.96,–,–12ppb,2.01,–,–2 ppb,ProcessPerformance,,a) Process is highlycapable(C,pk,>1.5),b) Process is capable (C,pk,=1 to 1.5),c) Process is not capable (C,pk,<1),,a),C,p,= 2,C,pk,= 2,b),C,p,= 2,C,pk,= 1,c),C,p,= 2,C,pk,< 1,Example1,Specification Lim

14、its: 4to16 g,,MachineMeanStd Dev,(a)104,(b)102,(c)72,(d)131,,Determine the correspondingC,p,andC,pk,foreachmachine.,Example1A,Example1B,Example1C,Example1D,ProcessCapability,Fora normally distributed characteristic, the defectiverate,F(x),may be,estimatedvia the following:,,,,,,For characteristicswi

15、thonlyone specification limit:,a) LSL only,b) USL only,LSL,USL,Example 2,Specification Limits: 4to 16g,,Machine Mean Std Dev,(a)104,(b)102,(c)72,(d)131,,Determinethe defective rate for each machine.,Example 2,MeanStdDevZ,LSL,Z,USL,F(xUSL)F(x),,104-1.5 1.566,80766,807 133,614,,102-3.0 3.01,3501,3502

16、,700,,72-1.54.566,807366,811,,131-9.0 3.001,3501,350,,LowerSpecLimit =4 g,UpperSpecLimit =16 g,Process Potential vsProcess Performance,(,a) Poor ProcessPotential(b)PoorProcess Performance,LSL,USL,LSL,USL,Experimental Design,to reducevariation,Experimental Design,to centermean,to reducevariation,Proc

17、ess Potential vsProcess Performance,Process Potential Index(C,p,),C,pk,1.01.21.41.61.82.0,,1.0,2,699.9 1,363.31,350.0 1,350.0 1,350.01,350.0,,1.2,318.3159.9159.1159.1159.1,,1.4,26.713.413.413.4,,1.6,1.60.80.8,,1.8,0.10.0,,2.0,0.0,,DefectiveRate(measuredin dppm) is dependent onthe actual,combination

18、ofC,p,and C,pk,..,Process Potential vsProcess Performance,a),C,p,= 2,C,pk,= 2,b),C,p,= 2,C,pk,= 1,c),C,p,= 2,C,pk,< 1,,C,p,– C,pk,,Missed Opportunity,,Alternative ProcessPerformance Index,Process capability statisticsmeasure processvariationrelativeto specification limits.,,The C,p,statisticcompare

19、s the engineeringtoleranceagainst the process’s naturalvariation.,,The C,pk,statistictakesintoaccount the location ofthe process relativeto the midpoint betweenspecifications.Ifthe process,target isnot centered betweenspecifications,, theC,pm,statisticis preferred.,Process Stability,A processis stab

20、leif the distributionof measurementsmade,on the given featureis consistentovertime.,Time,Stable Process,Time,Unstable Process,ucl,lcl,ucl,lcl,Within vsOverall Capability,Within Capability,(previously called,short-termcapability,) shows the inherentvariability ofa machine/process operating withina br

21、ief periodof time.,,Overall Capability,(previously called,long-termcapability,) shows the variability of a machine/processoperatingovera period of time. It includessources of variation inaddition to theshort-term variability.,Within vsOverall Capability,Within Overall,,Sample Size 30,–,– 50units

22、, 100units,,Number ofLotssingle lot severallots,,Period ofTimehours ordaysweeks ormonths,,Number ofOperatorssingle operatordifferent operators,,Process PotentialC,p,P,p,,Process PerformanceC,pk,P,pk,Within vsOverall Capability,Within CapabilityOverall Capability,,The key difference between thetwos

23、etsof indicesliesin the estimates for,,Within,and ,Overall,.,Estimating,,Within,and ,Overall,Consider the following observationsfroma ControlChart:,,S/N X,1,X,2,…X,k,MeanRangeStdDev,,1 x,1,1,x,2,1,…x,k,1,X,1,R,1,S,1,2 x,1,2,x,2,2,…x,k,2,X,2,R,2,S,2,: ::::::,m x,1,m,x,2,m,…x,k,m,X,m,R,m,S,m,,Th

24、e overall variation,,Overall,is estimated by,–,–,–,Estimating,,Within,and ,Overall,The withinvariation,,Within,may be estimated byone of thefollowing:,(a) R-barMethod,,whered,2,is aShewhart constant =,(k),,(b) S-barMethod,,wherec,4,is aShewhart constant =,(k),,(c) PooledStandardDeviationMethod

25、,,In MiniTab, the,Pooled StandardDeviation,is the defaultmethod.,Estimating,,Within,and ,Overall,In cases wherethereis only 1observation per sub-group (i.e. k=1),,the,Moving Range Method,is used, where.,,The,within variation,,Within,is then estimated using either,,a) the,Average MovingRange,:,,b)

26、 the,Median Moving Range,:,Example 3,The lengthof acamshaftfor an automobile engineis specified,at 600 ±2mm.Control ofthelength ofthe camshaft iscritical,to avoid scrap/rework.,,The camshaft isprovidedby anexternalsupplier.Assess the,process capability for this supplier.,,The data is available in,Pr

27、ocess Capability Analysis.MTW,.,Example 3,S,tat,,Q,uality Tools Capability,A,nalysis (Normal),Example 3,Example 3A,Histogramof camshaft length suggests mixed populations.,Further investigation revealedthatthere aretwosuppliersfor,the camshaft.Datawas collected over camshafts from both,sources.,,Ar

28、e the two suppliers similarin performance?,If not, what are your recommendations?,Example 3A,S,tat,,Q,uality Tools Capability,S,ixpack(Normal),Example3A,Example3A,What,’,’sSixSigmaQuality,—,—Then,OriginalDefinitionbyMotorola:,ifthespecificationlimitsareatleast,±,±6,awayfromtheprocessmean,,,i.e.

29、C,p,2,,andtheprocessshiftsbylessthan1.5,,,i.e.C,pk,1.5,,thentheprocesswillyieldlessthan3.4dppmrejects.,6,,6,,Shift,1.5,,4.5,,What,’,’sSixSigmaQuality,—,—Now,MikelJHarryclaimsthattheprocessmeanbetweenlotswillvary,withanaverageprocessshiftof,1.5,,.,k, =,z, + 1.5,k, =,z, + 1.5,Shift,1

30、.5,,z,,Note:,SigmaCapability=,ƒ,ƒ(dpmo),,ƒ(dppm),ProcessCapabilityforNon-NormalData,Noteverymeasuredcharacteristicisnormallydistributed.,,CharacteristicDistribution,CycleTimeExponential,RejectRateBinomial,DefectRatePoisson,ProcessCapabilityforCycleTime,The,WeibullDistribution,isageneralfamilyofdi

31、stributionwith,,where,scaleparameter,isthevalueatwhichCDF=68.17%,,and,shapeparameter,determinestheshapeofthePDF.,ProcessCapabilityforCycleTime,At,=1,the,WeibullDistribution,isreducedto,,Foran,ExponentialDistribution,,,,The,ExponentialDistribution,is thus a,Weibull Distribution,with,,=1.,Weibull

32、 (x;,=1, ),Exponential (x;,),Example 4,A customerservice manager wants todeterminetheprocess,capabilityforhis department.A primary performance index,is the time taken toclose a customer complaint.The goal for,thisindexis to close acomplaintwithin onecalendarweek.,,Performance over thelast400compl

33、aintswasreviewed.,Example 4,S,tat,,Q,uality Tools Capability,A,nalysis (Weibull),Example 4,Example 4A,S,tat,,Q,uality Tools CapabilitySixpack (Wei,b,ull),Example 4A,Process Capability for RejectRate,For a,Normal Distribution,, theproportion ofpartsproducedbeyond a,specification limitis,,Reject

34、Rate,Process Capability for RejectRate,Thus,foreveryreject rate there is anaccompanying Z-Score,,,where,,Recall that,,Hence,Process Capability for RejectRate,Estimationof P,pk,for RejectRate,,Determinethe long-term,reject rate,(,p,),,Determinethe,inverse cumulative probability,for,p,,,using,C,alc,P

35、robability,D,istribution,,,N,ormal,,Z-Score,isthemagnitudeofthereturnedvalue,,P,pk,isone-thirdofthe,Z-Score,Example5,Asalesmanagerplanstoassesstheprocesscapabilityofhis,telephonesalesdepartment,’,’shandlingofincomingcalls.,,Thefollowingdatawascollectedoveraperiodof20days:,numberofincomingcallsperd

36、ay,numberofunansweredcallsperdays,Example5,S,tat,,Q,ualityTools,,CapabilityAnalysis(Bi,n,omial),Example5,P,pk,= 0.25,,ProcessCapabilityforDefectRate,Otherapplications,approximatinga,PoissonDistribution,:,,errorrates,,particlecount,,chemicalconcentration,ProcessCapabilityforDefectRate,Estimationof

37、Y,tp,forDefectRate,,Definesizeofaninspectionunit,,Determinethelong-term,defectsperunit,(,DPU,),DPU=TotalDefects,TotalUnits,,Determinethe,throughputyield,(,Y,tp,),Y,tp,=exp{,–,–DPU},ProcessCapabilityforDefectRate,EstimationofSigma-CapabilityforDefectRate,,Determinethe,opportunitiesperunit,,Determine

38、thelong-term,defectsperopportunity,(,d,),d=defectsperunit,,opportunitiesperunit,,Determinethe,inversecumulativeprobability,for,d,,,using,C,alc,Probability,D,istribution,,,N,ormal,,Z-Score,isthemagnitudeofthereturnedvalue,,Sigma-Capability,=,Z-Score,+1.5,Example6,Theprocessmanagerforawiremanufact

39、urerisconcerned,abouttheeffectivenessofthewireinsulationprocess.,,Random lengths of electricalwiringaretaken and testedfor,weakspots in theirinsulation by meansof atest voltage.,,Thenumber of weak spotsandthelengthof eachpiece of,wirearerecorded.,Example6,S,tat,,Q,uality Tools,, Capability Analys

40、is (Poiss,o,n),Example6,DefectsperUnit,=0.0265194,,Throughput Yield,=exp{,–,–DPU},=exp{,–,–0.0265194},=0.9738,,c.f.First-Time Yield,=2 /100,=0.02,Example6,Define,1 InspectionUnit =125unit lengthofwire,i.e.,Units,=,Length, 125,Example6A,S,tat,,Q,uality Tools,, Capability Analysis (Poiss,o,n),Exam

41、ple6A,DefectsperUnit,=3.31493,,Throughput Yield,=exp{,–,–DPU},=exp{,–,–3.31493},=0.0363,,c.f.First-Time Yield,=2 /100,=0.02,Example6B,DefectsperUnit,=3.31493,,Opportunities per Unit,=1,,DefectsperOpportunity,= 3.31493,,Z-Score= ???,Example6B,1,inspection unit,=1 unit length ofwire,,Opportunities pe

42、r Unit,=1,,DefectsperOpportunity,=329, 12,406,=0.0265,,Z-Score,=Abs{,,–,1,(0.0265)},=1.935,,Sigma-Capability,=Z-Score+ 1.5,=3.435,DPU,Z-Score,s,Choice of Six SigmaMetric,9,、静夜,四,四无邻,，,，荒居,旧,旧业贫,。,。。11月-2211月-22,Friday, November 4, 2022,10,、雨中黄叶,树,树，灯下白,头,头人。。20:07:1820:07:1820:07,11/4/20228:07:18

43、PM,11,、以我独沈,久,久，愧君相,见,见频。。11月-2220:07:1820:07,Nov-2204-Nov-22,12,、故,人,人江,海,海别,，,，几,度,度隔,山,山川,。,。。20:07:1820:07:1820:07,Friday,November4,2022,13,、乍见翻疑,梦,梦，相悲各,问,问年。。11月-2211月-2220:07:1820:07:18,November 4, 2022,14,、,他,他,乡,乡,生,生,白,白,发,发,，,，,旧,旧,国,国,见,见,青,青,山,山,。,。,。,。04,十,十,一,一,月,月20228:07:18,下,下,午,午2

44、0:07:1811,月,月-22,15,、比不了得,就,就不比，得,不,不到的就不,要,要。。。十一月 228:07,下,下午11月-2220:07,November 4, 2022,16,、行动出,成,成果，工,作,作出财富,。,。。2022/11/4 20:07:1820:07:18,04 November2022,17,、,做,做,前,前,，,，,能,能,够,够,环,环,视,视,四,四,周,周,；,；,做,做,时,时,，,，,你,你,只,只,能,能,或,或,者,者,最,最,好,好,沿,沿,着,着,以,以,脚,脚,为,为,起,起,点,点,的,的,射,射,线,线,向,向,前,前,。,。,。,

45、。8:07:18,下,下,午,午8:07,下,下,午,午20:07:1811,月,月-22,9,、没,有,有失,败,败，,只,只有,暂,暂时,停,停止,成,成功,！,！。11,月,月-2211,月,月-22,Friday,November4,2022,10,、很,多,多事,情,情努,力,力了,未,未必,有,有结,果,果，,但,但是,不,不努,力,力却,什,什么,改,改变,也,也没,有,有。,。,。20:07:1820:07:1820:07,11/4/20228:07:18PM,11,、成功,就,就是日,复,复一日,那,那一点,点,点小小,努,努力的,积,积累。,。,。11月-2220:07:1

46、820:07,Nov-2204-Nov-22,12,、世间成事,，,，不求其绝,对,对圆满，留,一,一份不足，,可,可得无限完,美,美。。20:07:1820:07:1820:07,Friday, November 4,2022,13,、不,知,知香,积,积寺,，,，数,里,里入,云,云峰,。,。。11,月,月-2211,月,月-2220:07:1820:07:18,November4,2022,14,、,意,意,志,志,坚,坚,强,强,的,的,人,人,能,能,把,把,世,世,界,界,放,放,在,在,手,手,中,中,像,像,泥,泥,块,块,一,一,样,样,任,任,意,意,揉,揉,捏,捏,。,。

47、04,十,十,一,一,月,月20228:07:18,下,下,午,午20:07:1811,月,月-22,15,、楚塞三,湘,湘接，荆,门,门九派通,。,。。。十一月228:07,下,下午11月-2220:07,November4,2022,16,、少年十,五,五二十时,，,，步行夺,得,得胡马骑,。,。。2022/11/4 20:07:1820:07:18,04 November2022,17,、空山新雨,后,后，天气晚,来,来秋。。8:07:18 下午8:07,下,下午20:07:1811月-22,9,、,杨,杨,柳,柳,散,散,和,和,风,风,，,，,青,青,山,山,澹,澹,吾,吾,虑,虑,

48、。,。,。,。11,月,月-2211,月,月-22,Friday,November4,2022,10,、阅读,一,一切好,书,书如同,和,和过去,最,最杰出,的,的人谈,话,话。20:07:1820:07:1820:07,11/4/20228:07:18PM,11,、越是没,有,有本领的,就,就越加自,命,命不凡。11月-2220:07:1820:07,Nov-2204-Nov-22,12,、越是无能,的,的人，越喜,欢,欢挑剔别人,的,的错儿。20:07:1820:07:1820:07,Friday, November 4,2022,13,、,知,知,人,人,者,者,智,智,，,，,自,自,

49、知,知,者,者,明,明,。,。,胜,胜,人,人,者,者,有,有,力,力,，,，,自,自,胜,胜,者,者,强,强,。,。11,月,月-2211,月,月-2220:07:1820:07:18,November4,2022,14,、意志坚强,的,的人能把世,界,界放在手中,像,像泥块一样,任,任意揉捏。04 十一,月,月 20228:07:18 下午20:07:1811月-22,15,、最,具,具挑,战,战性,的,的挑,战,战莫,过,过于,提,提升,自,自我,。,。。十一,月,月228:07,下,下,午,午11,月,月-2220:07,November4,2022,16,、业,余,余生,活,活要,有

50、,有意,义,义，,不,不要,越,越轨,。,。2022/11/420:07:1920:07:19,04November2022,17,、一,个,个人,即,即使,已,已登,上,上顶,峰,峰，,也,也仍,要,要自,强,强不,息,息。8:07:19,下,下午8:07,下,下,午,午20:07:1911,月,月-22,,MOMODA POWERPOINT,Lorem ipsum dolor sit amet, consectetur adipiscing elit. Fusce id urna blandit, eleifend nulla ac, fringilla purus. Nulla iaculis tempor felis ut cursus.,感谢,您,您的,下,下载,观,观看,专家,告,告诉,