6s黑带培训教材1（英文）.pptx

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1、Process Capability AnalysisMeasure PhaseScope of ModuleProcess VariationProcess CapabilitySpecification,Process and Control LimitsProcess Potential vs Process PerformanceShort-Term vs Long-Term Process CapabilityProcess Capability for Non-Normal DataCycle-TimeExponential DistributionReject RateBinom

2、ial DistributionDefect RatePoisson DistributionProcess VariationProcess Variation is the inevitable differences among individual measurements or units produced by a process.Sources of Variationwithin unitpositional variationbetween unitsunit-unit variationbetween lotslot-lot variationbetween linesli

3、ne-line variationacross timetime-time variationmeasurement errorrepeatability&reproducibilityTypes of VariationInherent 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 contr

4、ol Types of VariationSpecial or Assignable VariationMay be due 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-controlProcess CapabilityProcess Capability is the inherent reproducibil

5、ity 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

6、of defectives produced may be measured inapercentage%bparts per million ppmcparts per billion ppbProcess CapabilityProcess Capability studies can indicate the consistency of the process outputindicate the degree to which the output meets specificationsbe used for parison with another process or peti

7、torProcess Capability vs Specification Limitsa)b)c)a Process is highly capableb Process is marginally capablec Process is not capableThree Types of LimitsSpecification Limits LSL and USL created by design engineering in response to customer requirements to specify the tolerance for a products charac

8、teristicProcess Limits LPL and UPLmeasures the variation of a processthe natural 6 limits of the measured characteristicControl Limits LCL and UCLmeasures the variation of a sample statistic mean,variance,proportion,etcThree Types of LimitsDistribution of Individual ValuesDistribution of Sample Aver

9、agesProcess Capability IndicesTwo measures of process capabilityProcess PotentialCpProcess PerformanceCpuCplCpkProcess PotentialThe Cp index assesses whether the natural tolerance 6 of a process is within the specification limits.Process PotentialA Cp of 1.0 indicates that a process is judged to be“

10、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 Potentiala)b)c)a Process is highly capable Cp2b Process is capable Cp=1 to 2c Process is not capable Cp1.

11、5b Process is capable Cpk=1 to 1.5c Process is not capable Cpk1a)Cp=2Cpk=2b)Cp=2Cpk=1c)Cp=2Cpk 1Example 1Specification Limits:4 to 16 gMachineMeanStd Deva 10 4b 10 2c 7 2d 13 1Determine the corresponding Cp and Cpk for each machine.Example 1AExample 1BExample 1CExample 1DProcess CapabilityFor a norm

12、ally distributed characteristic,the defective rate Fx may be estimated via the following:For characteristics with only one specification limit:aLSL onlybUSL onlyLSLUSLExample 2Specification Limits:4 to 16 gMachineMeanStd Deva 10 4b 10 2c 7 2d 13 1Determine the defective rate for each machine.Example

13、 2Mean Std Dev ZLSL ZUSL FxUSL Fx 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 Potential vs Process Performancea Poor Process Potential b Poor Process PerformanceLSLUSLLSLUSLExp

14、erimental Design to reduce variationExperimental Design to center mean to reduce variationProcess Potential vs Process Performance Process Potential Index Cp Cpk 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

15、.6 0.8 0.8 1.8 0.1 0.0 2.0 0.0Defective Rate measured in dppm is dependent on the actual bination of Cp and Cpk.Process Potential vs Process Performancea)Cp=2Cpk=2b)Cp=2Cpk=1c)Cp=2Cpk 1Cp Cpk Missed OpportunityAlternative Process Performance IndexProcess capability statistics measure process variati

16、on relative to specification limits.The Cp statistic pares 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,th

17、e Cpm statistic is preferred.Process StabilityA process is stable if the distribution of measurements made on the given feature is consistent over time.TimeStable ProcessTimeUnstable ProcessucllclucllclWithin vs Overall CapabilityWithin Capability previously called short-term capability shows the in

18、herent 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 sources of variation in addition to the short-term variability.Within vs Ov

19、erall CapabilityWithinOverallSample Size30 50 units 100 unitsNumber of Lotssingle lotseveral lotsPeriod of Timehours or daysweeks or monthsNumber of Operatorssingle operatordifferent operatorsProcess Potential Cp PpProcess Performance Cpk PpkWithin vs Overall CapabilityWithin CapabilityOverall Capab

20、ilityThe key difference between the two sets of indices lies in the estimates for Within and Overall.Estimating 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 varia

21、tion Overall is estimated byEstimating Within and OverallThe within variation Within may be estimated by one of the following:aR-bar Methodwhered2 is a Shewhart constant=kbS-bar Methodwherec4 is a Shewhart constant=kcPooled Standard Deviation MethodIn MiniTab,the Pooled Standard Deviation is the def

22、ault method.Estimating 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 eitherathe Average Moving Range:bthe Median Moving Range:Example 3The length of a camshaft for an autom

23、obile 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 capability for this supplier.The data is available in Process Capability Analysis.MTW.Example 3Stat Quality Tools Capabili

24、ty Analysis NormalExample 3Example 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 re mendation

25、s?Example 3AStat Quality Tools Capability SixpackNormalExample 3AExample 3AWhats Six 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 t

26、han 3.4 dppm rejects.66Shift1.54.5Whats 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 dppmProcess Capability for Non-Normal DataNot every measured characteristic is no

27、rmally distributed.CharacteristicDistributionCycle TimeExponential Reject RateBinomialDefect RatePoissonProcess Capability for Cycle TimeThe Weibull Distribution is a general family of distribution withwherescale parameter is the value at which CDF=68.17%,andshape parameter determines the shape of t

28、he PDF.Process Capability for Cycle TimeAt=1,the Weibull Distribution is reduced toFor an Exponential Distribution,The Exponential Distribution is thus a Weibull Distribution with=1.Weibull(x;=1,)Exponential(x;)Example 4A customer service manager wants to determine the process capability for his dep

29、artment.A primary performance index is the time taken to close a customer plaint.The goal for this index is to close a plaint within one calendar week.Performance over the last 400 plaints was reviewed.Example 4Stat Quality Tools Capability Analysis WeibullExample 4Example 4AStat Quality Tools Capab

30、ility Sixpack WeibullExample 4AProcess Capability for Reject RateFor a Normal Distribution,the proportion of parts produced beyond a specification limit is Reject RateProcess Capability for Reject RateThus,for every reject rate there is an ac panying Z-Score,whereRecall thatHenceProcess Capability f

31、or Reject RateEstimation of Ppk for Reject RateDetermine the long-term reject rate pDetermine 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-ScoreExample 5A sales manager plans to assess the p

32、rocess capability of his telephone sales departments handling of in ing calls.The following data was collected over a period of 20 days:number of in ing calls per daynumber of unanswered calls per daysExample 5Stat Quality Tools Capability Analysis BinomialExample 5Ppk=0.25Process Capability for Def

33、ect RateOther applications,approximating a Poisson Distribution:error ratesparticle countchemical concentrationProcess Capability for Defect RateEstimation of Ytp for Defect RateDefine size of an inspection unitDetermine the long-term defects per unit DPUDPU=Total Defects Total UnitsDetermine the th

34、roughput yield YtpYtp=expDPUProcess Capability for Defect RateEstimation of Sigma-Capability for Defect RateDetermine the opportunities per unitDetermine the long-term defects per opportunity dd=defects per unit opportunities per unitDetermine the inverse cumulative probability for d,using Calc Prob

35、ability Distribution NormalZ-Score is the magnitude of the returned valueSigma-Capability =Z-Score +1.5Example 6The process manager for a wire manufacturer is concerned about the effectiveness of the wire insulation process.Random lengths of electrical wiring are taken and tested for weak spots in t

36、heir insulation by means of a test voltage.The number of weak spots and the length of each piece of wire are recorded.Example 6Stat Quality Tools Capability Analysis PoissonExample 6Defects per Unit =0.0265194Throughput Yield =expDPU =exp0.0265194 =0.9738c.f.First-Time Yield =2/100 =0.02Example 6Def

37、ine1 Inspection Unit=125 unit length of wirei.e.Units=Length 125Example 6AStat Quality Tools Capability Analysis PoissonExample 6ADefects per Unit =3.31493Throughput Yield =expDPU =exp3.31493 =0.0363c.f.First-Time Yield =2/100 =0.02Example 6BDefects per Unit =3.31493Opportunities per Unit =1Defects

38、per Opportunity =3.31493Z-Score=?Example 6B1 inspection unit =1 unit length of wireOpportunities per Unit =1 Defects per Opportunity =329 12,406 =0.0265Z-Score =Abs10.0265 =1.935Sigma-Capability =Z-Score+1.5 =3.435Choice of Six Sigma Metric9、静夜四无邻，荒居旧业贫。4月-234月-23Monday,April 17,202310、雨中黄叶树，灯下白头人。1

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