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1、ProcessCapabilityAnalyProcessCapabilityAnalysissisProcess VariationProcess VariationProcess Variation is the inevitable differences is the inevitable differences among individual measurements or units produced by among individual measurements or units produced by a process.a process.Sources of Varia
2、tionSources of Variationn nwithin unitwithin unit(positional variation)(positional variation)n nbetween unitsbetween units(unit-unit variation)(unit-unit variation)n nbetween lotsbetween lots(lot-lot variation)(lot-lot variation)n nbetween linesbetween lines(line-line variation)(line-line variation)
3、n nacross timeacross time(time-time variation)(time-time variation)n nmeasurement errormeasurement error(repeatability & reproducibility)(repeatability & reproducibility)2 2Natural VariationInherent or Natural VariationInherent or Natural Variationn nDue to the cumulative effect of many small unavoi
4、dable causesDue to the cumulative effect of many small unavoidable causesn nA process operating with only chance causes of variation A process operating with only chance causes of variation present is said to be “in statistical control” present is said to be “in statistical control” 3 3Assignable Va
5、riationSpecial or Assignable VariationSpecial or Assignable Variationn nMay be due toMay be due to a) improperly adjusted machine a) improperly adjusted machine b) operator error b) operator error c) defective raw material c) defective raw materialn nA process operating in the presence of assignable
6、 causes of variation is A process operating in the presence of assignable causes of variation is said to be “out-of-control”said to be “out-of-control”4 4Process CapabilityProcess Capability studies can n nindicate the consistency of the process outputindicate the consistency of the process outputn
7、nindicate the degree to which the output meets indicate the degree to which the output meets specificationsspecificationsn nbe used for comparison with another process or be used for comparison with another process or competitorcompetitor5 5Process Capability & Spec Limitsa)b)c)a) Process is highly
8、capableb) Process is marginally capablec) Process is not capable6 6Process Capability IndexTwo measures of process capabilityTwo measures of process capabilityn nProcess PotentialProcess Potentialn nC Cp pn nProcess PerformanceProcess Performancen nC Cpupun nC Cplpln nC Cpkpk7 7Process PotentialThe
9、CThe Cp p index assesses whether the natural tolerance index assesses whether the natural tolerance (6(6 ) of a process is within the specification limits.) of a process is within the specification limits.8 8Process PotentialA CA Cp p of 1.0 indicates that a process is judged to be of 1.0 indicates
10、that a process is judged to be “capable”, i.e. if the process is centered within its “capable”, i.e. if the process is centered within its engineering tolerance, 0.27% of parts produced engineering tolerance, 0.27% of parts produced will be beyond specification limits.will be beyond specification li
11、mits. C Cp p Reject Rate Reject Rate1.001.000.270 %0.270 %1.331.330.007 %0.007 %1.501.506.8 ppm6.8 ppm2.002.002.0 ppb2.0 ppb9 9Process PerformanceThe CThe Cpkpk index relates the scaled distance between the index relates the scaled distance between the process mean and the nearest specification limi
12、t.process mean and the nearest specification limit.1010Process PerformanceC CpkpkReject RateReject Rate1.01.00.13 0.27 %0.13 0.27 %1.11.10.05 0.10 %0.05 0.10 %1.21.20.02 0.03 % 0.02 0.03 % 1.31.348.1 96.2 ppm48.1 96.2 ppm1.41.413.4 26.7 ppm13.4 26.7 ppm1.51.5 3.4 6.8 ppm 3.4 6.8 ppm1.61.6 794 1589 p
13、pb 794 1589 ppb1.71.7 170 340 ppb 170 340 ppb1.81.8 33 67 ppb 33 67 ppb1.91.9 6 12 ppb 6 12 ppb2.02.0 1 2 ppb 1 2 ppb1111Process Performancea) Process is highly capable (Cpk1.5)b) Process is capable (Cpk=1 to 1.5)c) Process is not capable (Cpk1)a)Cp = 2Cpk = 2b)Cp = 2Cpk = 1c)Cp = 2Cpk 11212Process
14、CapabilityFor a normally distributed characteristic, the defective rate For a normally distributed characteristic, the defective rate F(x)F(x) may may be estimated via the following:be estimated via the following:For characteristics with only one specification limit:For characteristics with only one
15、 specification limit:a)a)LSL onlyLSL onlyb)b)USL onlyUSL onlyLSLUSL1313Process Potential vs Process Performance(a) Poor Process Potential(a) Poor Process Potential (b) Poor Process Performance(b) Poor Process PerformanceLSLUSLLSLUSLExperimental Design to reduce variationExperimental Design to center
16、 mean to reduce variation1414Process Potential vs Process Performance Process Potential Index (CProcess Potential Index (Cp p) ) C Cpkpk 1.01.0 1.2 1.2 1.4 1.4 1.6 1.6 1.8 1.8 2.0 2.0 1.01.02,699.92,699.9 1,363.31,363.3 1,350.01,350.0 1,350.01,350.0 1,350.01,350.0 1,350.01,350.0 1.21.2 318.3 318.3 1
17、59.9 159.9 159.1 159.1 159.1 159.1 159.1 159.1 1.41.4 26.7 26.7 13.4 13.4 13.4 13.4 13.4 13.4 1.61.6 1.6 1.6 0.8 0.8 0.8 0.8 1.81.8 0.1 0.1 0.0 0.0 2.02.0 0.0 0.0Defective Rate (measured in dppm) is dependent Defective Rate (measured in dppm) is dependent on the actual combination of Con the actual
18、combination of Cp p and C and Cpkpk. .1515Process Potential vs Process Performancea)Cp = 2Cpk = 2b)Cp = 2Cpk = 1c)Cp = 2Cpk tat QQuality Tools Capability uality Tools Capability A Analysis (Normal)nalysis (Normal)2222Example2323ExampleS Stat tat QQuality Tools Capability uality Tools Capability S Si
19、xpack (Normal)ixpack (Normal)2424Example2525Exercise The upper coil height of X15-36LP is recorded. The upper coil height of X15-36LP is recorded. The The specification is .348” max.specification is .348” max. The coil height is critical The coil height is critical to the actuator not rubbing on the
20、 VCM. Each to the actuator not rubbing on the VCM. Each subgroup consists of 5 actuator.subgroup consists of 5 actuator.Please find the data from provided Please find the data from provided 4. Process Capability 4. Process Capability Analysis.Analysis. Using the given data, find out the Cpk & Ppk of
21、 Using the given data, find out the Cpk & Ppk of the actuator.the actuator.2626Six Sigma Quality - PastOriginal Definition by Motorola:Original Definition by Motorola:n nif the specification limits are at least 6if the specification limits are at least 6 away from away from the process mean the proc
22、ess mean , i.e. C, i.e. Cp p 2, 2,n nand the process shifts by less than 1.5and the process shifts by less than 1.5 , i.e. C, i.e. Cpkpk 1.5,1.5,n nthen the process will yield less than 3.4 dppm rejects.then the process will yield less than 3.4 dppm rejects.66Shift1.54.52727Six Sigma Quality NowMike
23、l J Harry claims that the process mean between lots Mikel J Harry claims that the process mean between lots will vary, with an average process shift of will vary, with an average process shift of 1.51.5 . .k = z + 1.5 k = z + 1.5 Shift1.5zNote:Sigma Capability = (dpmo) (dppm)2828Process Capability f
24、or non-normal dataNot every measured characteristic is normally distributed.CharacteristicDistributionReject RateBinomialDefect RatePoisson2929Capability for reject rateFor a For a Normal DistributionNormal Distribution, the proportion of parts , the proportion of parts produced beyond a specificati
25、on limit isproduced beyond a specification limit is Reject Rate3030Capability for reject rateThus, for every reject rate there is an accompanying Z-Score, whereRecall thatHence3131Capability for reject rateEstimation of Ppk for Reject Raten nDetermine the long-term Determine the long-term reject rat
26、ereject rate ( (p p) )n nDetermine the Determine the inverse cumulative probability inverse cumulative probability for for p p, ,using using C Calc alc Probability Probability D Distribution istribution NNormalormaln nZ-Score Z-Score is the magnitude of the returned valueis the magnitude of the retu
27、rned valuen nP Ppkpk is one-third of the is one-third of the Z-ScoreZ-Score3232Example for reject rate capabilityn nAn engineer wants to evaluate the process capability of coil height screening stage. The engineer capture 1 month data of April. n nPlease calculate its Cpk & Ppk of the process.3333Ex
28、ample for reject rate capabilityn nS Stat tat QQuality Tools uality Tools Capability Analysis (Bi Capability Analysis (Bin nomial)omial)3434Example for reject rate capabilityPpk = z-score / 3= 2.016 / 3 =0.672ZST = ZLT + 1.5, thusCpk = ?3535Example for reject rate capabilityn nSigma Shiftn nAccordin
29、g to experience, 1.5 Z-score shift According to experience, 1.5 Z-score shift from Zfrom ZSTST to Z to ZLT LT & vice versa.& vice versa.ZSTZSTZLTWant to know:ZLTCollected:Add1.5Subtract1.5ZLT = ZST - 1.53636Capability of defect rateEstimation of Sigma-Capability for Defect Estimation of Sigma-Capabi
30、lity for Defect RateRaten nDetermine the Determine the opportunities per unitopportunities per unitn nDetermine the long-term Determine the long-term defects per opportunitydefects per opportunity ( (d d) )d d= defects per unit = defects per unit opportunities per unit opportunities per unitn nDeter
31、mine the Determine the inverse cumulative probability inverse cumulative probability for for d d, ,using using C Calc alc Probability Probability D Distribution istribution NNormalormaln nZ-Score Z-Score is the magnitude of the returned valueis the magnitude of the returned valuen nSigma-Capability
32、Sigma-Capability = = Z-ScoreZ-Score + 1.5 + 1.53737Example of capability of defect rateThe process manager for a wire manufacturer is concerned The process manager for a wire manufacturer is concerned about the effectiveness of the wire insulation process. about the effectiveness of the wire insulat
33、ion process. Random lengths of electrical wiring are taken and tested Random lengths of electrical wiring are taken and tested for weak spots in their insulation by means of a test for weak spots in their insulation by means of a test voltage. voltage. The number of weak spots and the length of each
34、 piece of The number of weak spots and the length of each piece of wire are recorded. wire are recorded. 3838Example of capability of defect rateS Stat tat QQuality Tools uality Tools Capability Analysis (Poiss Capability Analysis (Poisso on)n)3939Example of capability of defect rateDefects per Unit = 0.0265194Throughput Yield = expDPU = exp0.0265194 = 0.9738c.f. First-Time Yield = 2 / 100 = 0.024040End of PresentationRev 1 26 Apr 02Rev 1 26 Apr 02
