工艺能力研究基础课件.pptx
Learning Objectives,Brief 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 ObjectivesBrief Revis,Revision,Revision,Process Capability,Process 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 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 Capa,Process Capability,Process Capability studies can indicate the consistency of the process outputindicate the degree to which the output meets specificationsbe used for comparison with another process or competitor,Process CapabilityProcess Capa,Process Capability Indices,Two measures of process capabilityProcess PotentialCpProcess PerformanceCpuCplCpk,Process Capability IndicesTwo,Process Potential,The Cp index assesses whether the natural tolerance (6) of a process is within the specification limits.,Process PotentialThe Cp index,Process Performance,The Cpk index relates the scaled distance between the process mean and the nearest specification limit.,Process PerformanceThe Cpk ind,Process Potential vs Process Performance,Cp Cpk Missed Opportunity,Process Potential vs Process P,Within vs Overall Capability,Within 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 sources of variation in addition to the short-term variability.,Within vs Overall CapabilityWi,Within vs Overall Capability,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 Ppk,Within vs Overall Capability,Within CapabilityOverall CapabilityThe key difference between the two sets of indices lies in the estimates for Within and Overall .,Within vs Overall Capability,Within CapabilityOverall C,Introduction toZ-SCORES,Introduction toZ-SCORES,13,Assuming Normality.,USL,Z is Normally distributed with Mean = 0 and SD = 1,LSL,Z score,Z Scores,13Assuming Normality.USLZ is,14,ZLSL, ZUSL,USL,LSL,ZLSL,ZUSL,14ZLSL, ZUSLUSLLSLZLSLZUSL,A ?s Process,USL,Z-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,?s,0.001ppm,USL,T,m,A Six Sigma Process,25,000ppm,USL,T,m,A Two Sigma Process,A ?s ProcessUSLZ-Score interp,Basic Instructions for MinitabComputing Standard Normal Probabilities,Basic Instructions for Minitab,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”.,Computing Percent Fallout,Cumulative Distribution FunctionNormal with mean = 11.0000 and standard deviation = 1.00000 x P( X = x) 12.0000 0.8413,Select “Calc”, “Probability Di,Minitab Output,USL = 12,T,m =11,A One Sigma Process,DPPM = (1-0.8413) x 1,000,000 = 158700,Cumulative Distribution FunctionNormal with mean = 11.0000 and standard deviation = 1.00000 x P( X = x) 12.0000 0.8413,Minitab OutputUSL = 12Tm =11A,Computing Z-Score From Percent Fallout,Select “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 “OK”.,p = 0.8413,Inverse Cumulative Distribution FunctionNormal with mean = 0 and standard deviation = 1.00000 P( X = x) x 0.8413 0.9998,Computing Z-Score From Percent,s = 1,LSL =9,USL = 12,T,m = 11,Determine the DPPMZLSL, ZUSL and the Z score,Exercise,s = 1LSL =9USL = 12Tm = 11Dete,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) 12.0000 0.8413,Solution: Minitab,Select “Calc”, “Probability Di,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) 9.0000 0.0228,DPPM =( (0.0228) +(1-0.8413) x 1,000,000 = 181500,Solution: Minitab,ZLSL = (9 - 11) / 1,Select “Cumulative probability,Select “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 “OK”.,p = 1-(0.0228) +(1-0.8413) = 1-0.1815 = 0.8185,Inverse Cumulative Distribution FunctionNormal with mean = 0 and standard deviation = 1.00000 P( X = x) x 0.8185 0.9097,Solution: Minitab,Select “Inverse Cumulative pro,Process Capability for Non-Normal Data,Process Capability for Non-No,Process Capability for Non-Normal Data,Not 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 RatePoisson,Process Capability for Non-Nor,Alternatives for Non-Normal Data,When 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 defective. 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 Da,Process Capability for Cycle Time,The 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 T,At =1, the Weibull Distribution is reduced toFor an Exponential Distribution,The Exponential Distribution is thus a Weibull Distribution with =1.,Process Capability for Cycle Time,Weibull (x; =1, ),Exponential (x; ),At =1, the Weibull Distributi,A 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 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 Time,A customer service manager wan,Stat Quality Tools Capability Analysis (Weibull),Example of Process Capability Study for Cycle Time,Stat Quality Tools Capabil,Example of Process Capability Study on Cycle Time,Example of Process Capability,Process Capability for Reject Rate,For a Normal Distribution, the proportion of parts produced beyond a specification limit is,Reject Rate,Process Capability for Reject,Process Capability for Reject Rate,Thus, for every reject rate there is an accompanying Z-Score, whereRecall thatHence,Process Capability for Reject,Process Capability for Reject Rate,Estimation 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-Score,Process Capability for Reject,Example of Process Capability Study for Reject Rate,A 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 days,Example of Process Capability,Stat Quality Tools Capability Analysis (Binomial),Example of Process Capability Study for Reject Rate,Stat Quality Tools Capabil,Example of Process Capability Study for Reject Rate,Ppk = 0.25Example of Process C,Process Capability for Defect Rate,Other applications, approximating a Poisson Distribution :error ratesparticle countchemical concentration,Process Capability for Defect,Process Capability for Defect Rate,Estimation 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 the returned valuePpk is one-third of the Z-Score,Process Capability for Defect,Example of Process Capability Study for Defect Rate,The 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 their insulation by means of a test voltage. The number of weak spots and the length of each piece of wire are recorded.,Example of Process Capability,Stat Quality Tools Capability Analysis (Poisson),Example of Process Capability Study for Defect Rate,Stat Quality Tools Capabil,Example of Process Capability Study for Defect Rate,Opportunities per UnitExample,End of TopicAny question,End of TopicAny question,Reading Reference,Introduction to Statistical Quality Control, Douglas C. Montgomery, John Wiley & Sons, ISBN 0-471-30353-4,Reading ReferenceIntroduct,
