工藝能力研究基礎(chǔ)課件

1、Learning ObjectivesBrief Revision on Process Potential vs Process PerformanceWithin vs Overall Process CapabilityIntroduction to Z-scoreProcess Capability for Non-Normal DataCycle-Time (Exponential Distribution)Reject Rate (Binomial Distribution)Defect Rate (Poisson Distribution)Learning ObjectivesB

2、rief RevisRevisionRevisionProcess CapabilityProcess Capability is the inherent reproducibility 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

3、 the proportion of output that will be within product specification tolerances. The frequency of defectives produced may be measured ina)percentage (%)b)parts per million (ppm)c)parts per billion (ppb)Process CapabilityProcess CapaProcess CapabilityProcess Capability studies can indicate the consist

4、ency of the process outputindicate the degree to which the output meets specificationsbe used for comparison with another process or competitorProcess CapabilityProcess CapaProcess Capability IndicesTwo measures of process capabilityProcess PotentialCpProcess PerformanceCpuCplCpkProcess Capability I

5、ndicesTwo Process PotentialThe Cp index assesses whether the natural tolerance (6) of a process is within the specification limits.Process PotentialThe Cp index Process PerformanceThe Cpk index relates the scaled distance between the process mean and the nearest specification limit.Process Performan

6、ceThe Cpk indProcess Potential vs Process Performancea)Cp = 2Cpk = 2b)Cp = 2Cpk = 1c)Cp = 2Cpk 1Cp Cpk Missed OpportunityProcess Potential vs Process PWithin vs Overall CapabilityWithin Capability (previously called short-term capability) shows the inherent variability of a machine/process operating

7、 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 Overall CapabilityWiWithin vs Overall Capability

8、WithinOverallSample 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 CapabilityThe key dif

9、ference between the two sets of indices lies in the estimates for Within and Overall .Within vs Overall CapabilityWithin CapabilityOverall CIntroduction toZ-SCORESIntroduction toZ-SCORES13Assuming Normality.USLZ is Normally distributed with Mean = 0 and SD = 1LSLZ scoreZ Scores13Assuming Normality.U

10、SLZ is14ZLSL, ZUSLUSLLSLZLSLZUSL14ZLSL, ZUSLUSLLSLZLSLZUSLA ?s ProcessUSLZ-Score interpretation: How many standard deviations, s or s-hats, is the mean, x-bar, from some specified value, x.Lets assume there is only an USL?s0.001ppmUSLTmA Six Sigma Process25,000ppmUSLTmA Two Sigma ProcessA ?s Process

11、USLZ-Score interpBasic Instructions for MinitabComputing Standard Normal ProbabilitiesBasic Instructions for MinitabSelect “Calc”, “Probability Distributions” and “Normal”.Select “Cumulative Probability”, enter the “Mean” and “Standard Deviation”, click on “Input constant”, enter the value and click

12、 on “OK”.Computing Percent FalloutCumulative Distribution FunctionNormal with mean = 11.0000 and standard deviation = 1.00000 x P( X = x) 12.0000 0.8413Select “Calc”, “Probability DiMinitab OutputUSL = 12Tm =11A One Sigma ProcessDPPM = (1-0.8413) x 1,000,000 = 158700Cumulative Distribution FunctionN

13、ormal with mean = 11.0000 and standard deviation = 1.00000 x P( X = x) 12.0000 0.8413Minitab OutputUSL = 12Tm =11A Computing Z-Score From Percent FalloutSelect “Inverse Cumulative probability”, set the “Mean” = 0 and “Standard Deviation” =1, click on “Input constant”, enter the total area associated

14、 with fallout and click on “OK”. p = 0.8413Inverse Cumulative Distribution FunctionNormal with mean = 0 and standard deviation = 1.00000 P( X = x) x 0.8413 0.9998Computing Z-Score From Percents = 1LSL =9USL = 12Tm = 11Determine the DPPMZLSL, ZUSL and the Z scoreExercises = 1LSL =9USL = 12Tm = 11Dete

15、Select “Calc”, “Probability Distributions” and “Normal”.Select “Cumulative probability”, enter the “Mean” and “Standard Deviation”, click on “Input constant”, enter the value and click on “OK”.Cumulative Distribution FunctionNormal with mean = 11.0000 and standard deviation = 1.00000 x P( X = x) 12.

16、0000 0.8413Solution: MinitabSelect “Calc”, “Probability DiSelect “Cumulative probability”, enter the “Mean” and “Standard Deviation”, click on “Input constant”, enter the value and click on “OK”.Cumulative Distribution FunctionNormal with mean = 11.0000 and standard deviation = 1.00000 x P( X = x) 9

17、.0000 0.0228DPPM =( (0.0228) +(1-0.8413) x 1,000,000 = 181500Solution: MinitabZLSL = (9 - 11) / 1Select “Cumulative probabilitySelect “Inverse Cumulative probability”, set the “Mean” = 0 and “Standard Deviation” =1, click on “Input constant”, enter the total area associated with fallout and click on

18、 “OK”. p = 1-(0.0228) +(1-0.8413) = 1-0.1815 = 0.8185Inverse Cumulative Distribution FunctionNormal with mean = 0 and standard deviation = 1.00000 P( X = x) x 0.8185 0.9097Solution: MinitabSelect “Inverse Cumulative proProcess Capability for Non-Normal DataProcess Capability for Non-NoProcess Capabi

19、lity for Non-Normal DataNot every measured characteristic is normally distributed. Some data follows distributions that are known, and these may be able to have their capability measured accurately using that knowledgeCharacteristicDistributionCycle TimeWeibull (Exponential)Reject RateBinomialDefect

20、 RatePoissonProcess Capability for Non-NorAlternatives for Non-Normal DataWhen all other methods fail, it may be necessary to fall back on a simple assessment of the total amount out of specifications. Simply count the number of defective units and divide by the total to compute the fraction defecti

21、ve. Another standard metric for this is the DPPM.If a Capability Index must be reported, the DPPM can be converted back into a Z value, and then either Ppk = Z/3 or Cpk = Z/3 depending upon whether the data is long term or short term.Alternatives for Non-Normal DaProcess Capability for Cycle TimeThe

22、 Weibull Distribution is a general family of distribution withWhere scale parameter is the value at which CDF=68.17%, and shape parameter determines the shape of the PDF.Process Capability for Cycle TAt =1, the Weibull Distribution is reduced toFor an Exponential Distribution,The Exponential Distrib

23、ution is thus a Weibull Distribution with =1.Process Capability for Cycle TimeWeibull (x; =1, )Exponential (x; )At =1, the Weibull DistributiA customer service manager wants to determine the process capability for his department. A primary performance index is the time taken to close a customer comp

24、laint. The goal for this index is to close a complaint within one calendar week.Performance over the last 400 complaints was reviewed.Example of Process Capability Study for Cycle TimeA customer service manager wanStat Quality Tools Capability Analysis (Weibull)Example of Process Capability Study fo

25、r Cycle TimeStat Quality Tools CapabilExample of Process Capability Study on Cycle TimeExample of Process Capability Process Capability for Reject RateFor a Normal Distribution, the proportion of parts produced beyond a specification limit isReject RateProcess Capability for Reject Process Capabilit

26、y for Reject RateThus, for every reject rate there is an accompanying Z-Score, whereRecall thatHenceProcess Capability for Reject Process Capability for Reject RateEstimation of Ppk for Reject RateDetermine the long-term reject rate (p)Determine the inverse cumulative probability for p, using Calc P

27、robability Distribution NormalZ-Score is the magnitude of the returned valuePpk is one-third of the Z-ScoreProcess Capability for Reject Example of Process Capability Study for Reject RateA sales manager plans to assess the process capability of his telephone sales departments handling of incoming c

28、alls. The following data was collected over a period of 20 days:number of incoming calls per daynumber of unanswered calls per daysExample of Process Capability Stat Quality Tools Capability Analysis (Binomial)Example of Process Capability Study for Reject RateStat Quality Tools CapabilPpk = 0.25Exa

29、mple of Process Capability Study for Reject RatePpk = 0.25Example of Process CProcess Capability for Defect RateOther applications, approximating a Poisson Distribution :error ratesparticle countchemical concentrationProcess Capability for Defect Process Capability for Defect RateEstimation of Ppk for Defect RateDetermine the long-term defects per opportunity (d)d = defects per unit opportunities per unitDetermine the inverse cumulative probability for d, using Calc Probability Distribution NormalZ-Score is the magnitude of