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1、Process Capability Analysis(Measure Phase)Process Capability AnalysisProcess Capability Analysis2Scope of ModuleProcess VariationProcess CapabilitySpecification,Process and Control LimitsProcess Potential vs Process PerformanceShort-Term vs Long-Term Process CapabilityProcess Capability for Non-Norm
2、al DataCycle-Time(Exponential Distribution)Reject Rate(Binomial Distribution)Defect Rate(Poisson Distribution)Process Capability AnalysisProcess Capability Analysis3Process VariationProcess Variation is the inevitable differences among individual measurements or units produced by a process.Sources o
3、f Variationwithin unit(positional variation)between units(unit-unit variation)between lots(lot-lot variation)between lines(line-line variation)across time(time-time variation)measurement error(repeatability&reproducibility)Process Capability AnalysisProcess Capability Analysis4Types of VariationInhe
4、rent or Natural VariationDue to the cumulative effect of many small unavoidable causesA process operating with only chance causes of variation present is said to be“in statistical control”Process Capability AnalysisProcess Capability Analysis5Types of VariationSpecial or Assignable VariationMay be d
5、ue to a)improperly adjusted machine b)operator error c)defective raw materialA process operating in the presence of assignable causes of variation is said to be“out-of-control”Process Capability AnalysisProcess Capability Analysis6Process CapabilityProcess Capability is the inherent reproducibility
6、of a processs output.It measures how well the process is currently behaving with respect to the output specifications.It refers to the uniformity of the process.Capability is often thought of in terms of the proportion of output that will be within product specification tolerances.The frequency of d
7、efectives produced may be measured ina)percentage(%)b)parts per million(ppm)c)parts per billion(ppb)Process Capability AnalysisProcess Capability Analysis7Process CapabilityProcess Capability studies can indicate the consistency of the process outputindicate the degree to which the output meets spec
8、ificationsbe used for comparison with another process or competitorProcess Capability AnalysisProcess Capability Analysis8Process Capability vs Specification Limitsa)b)c)a)Process is highly capableb)Process is marginally capablec)Process is not capableProcess Capability AnalysisProcess Capability An
9、alysis9Three Types of LimitsSpecification Limits (LSL and USL)created by design engineering in response to customer requirements to specify the tolerance for a products characteristicProcess Limits (LPL and UPL)measures the variation of a processthe natural 6 limits of the measured characteristicCon
10、trol Limits (LCL and UCL)measures the variation of a sample statistic(mean,variance,proportion,etc)Process Capability AnalysisProcess Capability Analysis10Three Types of LimitsDistribution of Individual ValuesDistribution of Sample AveragesProcess Capability AnalysisProcess Capability Analysis11Proc
11、ess Capability IndicesTwo measures of process capabilityProcess PotentialCpProcess PerformanceCpuCplCpkProcess Capability AnalysisProcess Capability Analysis12Process PotentialThe Cp index assesses whether the natural tolerance(6)of a process is within the specification limits.Process Capability Ana
12、lysisProcess Capability Analysis13Process PotentialA Cp of 1.0 indicates that a process is judged to be“capable”,i.e.if the process is centered within its engineering tolerance,0.27%of parts produced will be beyond specification limits.Cp Reject Rate1.000.270%1.330.007%1.506.8 ppm2.002.0 ppbProcess
13、Capability AnalysisProcess Capability Analysis14Process Potentiala)b)c)a)Process is highly capable(Cp2)b)Process is capable(Cp=1 to 2)c)Process is not capable(Cp1.5)b)Process is capable(Cpk=1 to 1.5)c)Process is not capable(Cpk1)a)Cp=2Cpk=2b)Cp=2Cpk=1c)Cp=2Cpk 1Process Capability AnalysisProcess Cap
14、ability Analysis19Example 1Specification Limits:4 to 16 gMachineMeanStd Dev(a)10 4(b)10 2(c)7 2(d)13 1Determine the corresponding Cp and Cpk for each machine.Process Capability AnalysisProcess Capability Analysis20Example 1AProcess Capability AnalysisProcess Capability Analysis21Example 1BProcess Ca
15、pability AnalysisProcess Capability Analysis22Example 1CProcess Capability AnalysisProcess Capability Analysis23Example 1DProcess Capability AnalysisProcess Capability Analysis24Process CapabilityFor a normally distributed characteristic,the defective rate F(x)may be estimated via the following:For
16、characteristics with only one specification limit:a)LSL onlyb)USL onlyLSLUSLProcess Capability AnalysisProcess Capability Analysis25Example 2Specification Limits:4 to 16 gMachineMeanStd Dev(a)10 4(b)10 2(c)7 2(d)13 1Determine the defective rate for each machine.Process Capability AnalysisProcess Cap
17、ability Analysis26Example 2Mean Std Dev ZLSL ZUSL F(xUSL)F(x)10 4 -1.51.5 66,807 66,807133,614 10 2 -3.03.0 1,350 1,350 2,700 7 2 -1.54.5 66,807 3 66,811 13 1 -9.03.0 0 1,350 1,350Lower Spec Limit=4 gUpper Spec Limit=16 gProcess Capability AnalysisProcess Capability Analysis27Process Potential vs Pr
18、ocess Performance(a)Poor Process Potential(b)Poor Process PerformanceLSLUSLLSLUSLExperimental Design to reduce variationExperimental Design to center mean to reduce variationProcess Capability AnalysisProcess Capability Analysis28Process Potential vs Process Performance Process Potential Index (Cp)C
19、pk 1.0 1.2 1.4 1.6 1.8 2.0 1.02,699.9 1,363.3 1,350.0 1,350.0 1,350.0 1,350.0 1.2 318.3 159.9 159.1 159.1 159.1 1.4 26.7 13.4 13.4 13.4 1.6 1.6 0.8 0.8 1.8 0.1 0.0 2.0 0.0Defective Rate(measured in dppm)is dependent on the actual combination of Cp and Cpk.Process Capability AnalysisProcess Capabilit
20、y Analysis29Process Potential vs Process Performancea)Cp=2Cpk=2b)Cp=2Cpk=1c)Cp=2Cpk 1Cp Cpk Missed OpportunityProcess Capability AnalysisProcess Capability Analysis30Alternative Process Performance IndexProcess capability statistics measure process variation relative to specification limits.The Cp s
21、tatistic compares the engineering tolerance against the processs natural variation.The Cpk statistic takes into account the location of the process relative to the midpoint between specifications.If the process target is not centered between specifications,the Cpm statistic is preferred.Process Capa
22、bility AnalysisProcess Capability Analysis31Process StabilityA process is stable if the distribution of measurements made on the given feature is consistent over time.TimeStable ProcessTimeUnstable ProcessucllclucllclProcess Capability AnalysisProcess Capability Analysis32Within vs Overall Capabilit
23、yWithin Capability(previously called short-term capability)shows the inherent variability of a machine/process operating within a brief period of time.Overall Capability(previously called long-term capability)shows the variability of a machine/process operating over a period of time.It includes sour
24、ces of variation in addition to the short-term variability.Process Capability AnalysisProcess Capability Analysis33Within vs Overall CapabilityWithinOverallSample Size30 50 units 100 unitsNumber of Lotssingle lotseveral lotsPeriod of Timehours or daysweeks or monthsNumber of Operatorssingle operator
25、different operatorsProcess Potential Cp PpProcess Performance Cpk PpkProcess Capability AnalysisProcess Capability Analysis34Within vs Overall CapabilityWithin CapabilityOverall CapabilityThe key difference between the two sets of indices lies in the estimates for Within and Overall.Process Capabili
26、ty AnalysisProcess Capability Analysis35Estimating Within and OverallConsider the following observations from a Control Chart:S/NX1X2 XkMeanRangeStd Dev1x1,1x2,1 xk,1 X1 R1 S12x1,2x2,2 xk,2 X2 R2 S2:mx1,mx2,m xk,m Xm Rm SmThe overall variation Overall is estimated byProcess Capability AnalysisProces
27、s Capability Analysis36Estimating Within and OverallThe within variation Within may be estimated by one of the following:(a)R-bar Methodwhered2 is a Shewhart constant=(k)(b)S-bar Methodwherec4 is a Shewhart constant=(k)(c)Pooled Standard Deviation MethodIn MiniTab,the Pooled Standard Deviation is th
28、e default method.Process Capability AnalysisProcess Capability Analysis37Estimating Within and OverallIn cases where there is only 1 observation per sub-group(i.e.k=1),the Moving Range Method is used,where .The within variation Within is then estimated using eithera)the Average Moving Range:b)the Me
29、dian Moving Range:Process Capability AnalysisProcess Capability Analysis38Example 3The length of a camshaft for an automobile engine is specified at 600 2 mm.Control of the length of the camshaft is critical to avoid scrap/rework.The camshaft is provided by an external supplier.Assess the process ca
30、pability for this supplier.The data is available in Process Capability Analysis.MTW.Process Capability AnalysisProcess Capability Analysis39Example 3Stat Quality Tools Capability Analysis(Normal)Process Capability AnalysisProcess Capability Analysis40Example 3Process Capability AnalysisProcess Capab
31、ility Analysis41Example 3AHistogram of camshaft length suggests mixed populations.Further investigation revealed that there are two suppliers for the camshaft.Data was collected over camshafts from both sources.Are the two suppliers similar in performance?If not,what are your recommendations?Process
32、 Capability AnalysisProcess Capability Analysis42Example 3AStat Quality Tools Capability Sixpack(Normal)Process Capability AnalysisProcess Capability Analysis43Example 3AProcess Capability AnalysisProcess Capability Analysis44Example 3AProcess Capability AnalysisProcess Capability Analysis45Whats Si
33、x Sigma Quality ThenOriginal Definition by Motorola:if the specification limits are at least 6 away from the process mean,i.e.Cp 2,and the process shifts by less than 1.5,i.e.Cpk 1.5,then the process will yield less than 3.4 dppm rejects.66Shift1.54.5Process Capability AnalysisProcess Capability Ana
34、lysis46Whats Six Sigma Quality NowMikel J Harry claims that the process mean between lots will vary,with an average process shift of 1.5.k =z+1.5 k =z+1.5 Shift1.5zNote:Sigma Capability =(dpmo)(dppm)Process Capability AnalysisProcess Capability Analysis47Process Capability for Non-Normal DataNot eve
35、ry measured characteristic is normally distributed.CharacteristicDistributionCycle TimeExponential Reject RateBinomialDefect RatePoissonProcess Capability AnalysisProcess Capability Analysis48Process Capability for Cycle TimeThe Weibull Distribution is a general family of distribution withwherescale
36、 parameter is the value at which CDF=68.17%,andshape parameter determines the shape of the PDF.Process Capability AnalysisProcess Capability Analysis49Process Capability for Cycle TimeAt=1,the Weibull Distribution is reduced toFor an Exponential Distribution,The Exponential Distribution is thus a We
37、ibull Distribution with=1.Weibull(x;=1,)Exponential(x;)Process Capability AnalysisProcess Capability Analysis50Example 4A customer service manager wants to determine the process capability for his department.A primary performance index is the time taken to close a customer complaint.The goal for thi
38、s index is to close a complaint within one calendar week.Performance over the last 400 complaints was reviewed.Process Capability AnalysisProcess Capability Analysis51Example 4Stat Quality Tools Capability Analysis(Weibull)Process Capability AnalysisProcess Capability Analysis52Example 4Process Capa
39、bility AnalysisProcess Capability Analysis53Example 4AStat Quality Tools Capability Sixpack(Weibull)Process Capability AnalysisProcess Capability Analysis54Example 4AProcess Capability AnalysisProcess Capability Analysis55Process Capability for Reject RateFor a Normal Distribution,the proportion of
40、parts produced beyond a specification limit is Reject RateProcess Capability AnalysisProcess Capability Analysis56Process Capability for Reject RateThus,for every reject rate there is an accompanying Z-Score,whereRecall thatHenceProcess Capability AnalysisProcess Capability Analysis57Process Capabil
41、ity for Reject RateEstimation of Ppk for Reject RateDetermine the long-term reject rate(p)Determine the inverse cumulative probability for p,using Calc Probability Distribution NormalZ-Score is the magnitude of the returned valuePpk is one-third of the Z-ScoreProcess Capability AnalysisProcess Capab
42、ility Analysis58Example 5A sales manager plans to assess the process capability of his telephone sales departments handling of incoming calls.The following data was collected over a period of 20 days:number of incoming calls per daynumber of unanswered calls per daysProcess Capability AnalysisProces
43、s Capability Analysis59Example 5Stat Quality Tools Capability Analysis(Binomial)Process Capability AnalysisProcess Capability Analysis60Example 5Ppk=0.25Process Capability AnalysisProcess Capability Analysis61Process Capability for Defect RateOther applications,approximating a Poisson Distribution:e
44、rror ratesparticle countchemical concentrationProcess Capability AnalysisProcess Capability Analysis62Process Capability for Defect RateEstimation of Ytp for Defect RateDefine size of an inspection unitDetermine the long-term defects per unit(DPU)DPU=Total Defects Total UnitsDetermine the throughput
45、 yield(Ytp)Ytp=expDPUProcess Capability AnalysisProcess Capability Analysis63Process Capability for Defect RateEstimation of Sigma-Capability for Defect RateDetermine the opportunities per unitDetermine the long-term defects per opportunity(d)d=defects per unit opportunities per unitDetermine the in
46、verse cumulative probability for d,using Calc Probability Distribution NormalZ-Score is the magnitude of the returned valueSigma-Capability =Z-Score +1.5Process Capability AnalysisProcess Capability Analysis64Example 6The process manager for a wire manufacturer is concerned about the effectiveness o
47、f the wire insulation process.Random lengths of electrical wiring are taken and tested for weak spots in their insulation by means of a test voltage.The number of weak spots and the length of each piece of wire are recorded.Process Capability AnalysisProcess Capability Analysis65Example 6Stat Qualit
48、y Tools Capability Analysis(Poisson)Process Capability AnalysisProcess Capability Analysis66Example 6Defects per Unit =0.0265194Throughput Yield =expDPU =exp0.0265194 =0.9738c.f.First-Time Yield =2/100 =0.02Process Capability AnalysisProcess Capability Analysis67Example 6Define1 Inspection Unit=125
49、unit length of wirei.e.Units=Length 125Process Capability AnalysisProcess Capability Analysis68Example 6AStat Quality Tools Capability Analysis(Poisson)Process Capability AnalysisProcess Capability Analysis69Example 6ADefects per Unit =3.31493Throughput Yield =expDPU =exp3.31493 =0.0363c.f.First-Tim
50、e Yield =2/100 =0.02Process Capability AnalysisProcess Capability Analysis70Example 6BDefects per Unit =3.31493Opportunities per Unit =1Defects per Opportunity =3.31493Z-Score=?Process Capability AnalysisProcess Capability Analysis71Example 6B1 inspection unit =1 unit length of wireOpportunities per