6s黑带培训教材1（英文）(共72页).ppt

1、Process Capability Analysis(Measure Phase)Scope of Module Process Variation Process Capability Specification, Process and Control Limits Process Potential vs Process Performance Short-Term vs Long-Term Process Capability Process Capability for Non-Normal Data Cycle-Time(Exponential Distribution) Rej

2、ect Rate(Binomial Distribution) Defect Rate (Poisson Distribution)Process VariationProcess Variation is the inevitable differences among individual measurements or units produced by a process.Sources of Variation within unit(positional variation) between units(unit-unit variation) between lots(lot-l

3、ot variation) between lines(line-line variation) across time(time-time variation) measurement error(repeatability & reproducibility)Types of VariationInherent or Natural Variation Due to the cumulative effect of many small unavoidable causes A process operating with only chance causes of variati

4、on present is said to be “in statistical control” Types of VariationSpecial or Assignable Variation May be due to a) improperly adjusted machine b) operator error c) defective raw material A process operating in the presence of assignable causes of variation is said to be “out-of-control”Process Cap

5、abilityProcess 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 b

6、e 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 Capability studies can indicate the consistency of the process output indicate the degree to which the output

7、meets specifications be used for comparison with another process or competitorProcess 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

8、response to customer requirements to specify the tolerance for a products characteristicProcess Limits (LPL and UPL) measures the variation of a process the natural 6 limits of the measured characteristicControl Limits (LCL and UCL) measures the variation of a sample statistic (mean, variance, propo

9、rtion, etc)Three Types of LimitsDistribution of Individual ValuesDistribution of Sample AveragesProcess Capability IndicesTwo measures of process capability Process Potential Cp Process Performance Cpu Cpl CpkProcess PotentialThe Cp index assesses whether the natural tolerance (6) of a process is wi

10、thin the specification limits.6LSLUSLToleranceNaturalTolerancegEngineerinCpProcess 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 Rate1.0

11、00.270 %1.330.007 %1.506.8 ppm2.002.0 ppbProcess 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 1Example 1Specification Li

12、mits :4 to 16 gMachine MeanStd Dev(a) 10 4(b) 10 2(c) 7 2(d) 13 1Determine the corresponding Cp and Cpk for each machine.Example 1A 5 . 0464166LSLUSLCp 5 . 043410;431016Min3LSL;3USLMinCpkExample 1B 0 . 1264166LSLUSLCp 0 . 123410;231016Min3LSL;3USLMinCpkExample 1C 0 . 1264166LSLUSLCp 5 . 02347;23716M

13、in3LSL;3USLMinCpkExample 1D 0 . 2164166LSLUSLCp 0 . 113413;131316Min3LSL;3USLMinCpkProcess CapabilityFor a normally distributed characteristic, the defective rate F(x) may be estimated via the following:For characteristics with only one specification limit:a)LSL onlyb)USL only USLxPrLSLxPrxFUSL1LSLU

14、SLLSLZ1ZLSLUSL LSLZLSLxPrxF USLZ1USLxPrxFExample 2Specification Limits :4 to 16 gMachine MeanStd Dev(a) 10 4(b) 10 2(c) 7 2(d) 13 1Determine the defective rate for each machine.Example 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 6

15、6,807 3 66,811 13 1 -9.03.0 0 1,350 1,350Lower Spec Limit = 4 gUpper Spec Limit = 16 gProcess Potential vs Process Performance(a) Poor Process Potential(b) Poor Process PerformanceLSLUSLLSLUSLExperimental Design to reduce variationExperimental Design to center mean to reduce variationProcess Potenti

16、al vs Process Performance Process Potential Index (Cp) Cpk 1.0 1.2 1.4 1.6 1.8 2.0 1.0 2,699.91,363.31,350.01,350.01,350.01,350.0 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 C

17、p and Cpk.Process Potential vs Process Performancea)Cp = 2Cpk = 2b)Cp = 2Cpk = 1c)Cp = 2Cpk USLPPM USLPPM USLPPM USLPPM USLPPM LSLPpkPPLPPUPpScaleShapeSample NMeanLSLTargetUSL122970.80122970.80 * 75000.00 75000.00 *0.39 *0.39 *3.341.004003.34 * *7.00Expected LT PerformanceObserved LT PerformanceOver

18、all (LT) CapabilityProcess DataExample 4AStat Quality Tools Capability Sixpack (Weibull)Example 4A4003002001000241680Individual and MR ChartObser.Individual ValueMean=3.34UCL=10.46LCL=-3.779241680Mov.RangeR=2.677UCL=8.746LCL=0400390380Last 25 Observations9630Observation NumberValues7Overall (LT)Shap

19、e: 1.00Scale: 3.34Pp: *Ppk: 0.39Capability PlotProcess ToleranceSpecificationsIIII10.001.000.100.01Weibull Prob Plot20100Capability HistogramProcess Capability for Complaint ClosureProcess Capability for Reject RateFor a Normal Distribution, the proportion of parts produced beyond a specification li

20、mit is )Z(F1USLZPr1USLZPrUSLXPrReject RateProcess Capability for Reject RateThus, for every reject rate there is an accompanying Z-Score, whereRecall thatHence3NSLPpkLimitSpecScoreZ3ScoreZPpkProcess Capability for Reject RateEstimation of Ppk for Reject Rate Determine the long-term reject rate (p) D

21、etermine the inverse cumulative probability for p,using Calc Probability Distribution Normal Z-Score is the magnitude of the returned value Ppk is one-third of the Z-ScoreExample 5A sales manager plans to assess the process capability of his telephone sales departments handling of incoming calls. Th

22、e following data was collected over a period of 20 days: number of incoming calls per day number of unanswered calls per daysExample 5Stat Quality Tools Capability Analysis (Binomial)Example 5201000.200.19Sample NumberProportionP=0.2264UCL=0.2555LCL=0.1973201023.522.521.5Samp

23、le Number%Defective2624222020501950185026252423222120%DefectiveSample SizeProcess Capability for Telephone SalesSummary StatsCumulative %DefectiveDist of %DefectiveP ChartRate of Defectives(denotes 95% C.I.)Average P:%Defective:Target:PPM Def.:Process Z:0.22642722.64302264270.751(0.2222, 0.2307)(22.

24、22, 23.07)(222241, 230654)(0.737, 0.765)Ppk = 0.25Process Capability for Defect RateOther applications, approximating a Poisson Distribution : error rates particle count chemical concentrationProcess Capability for Defect RateEstimation of Ytp for Defect Rate Define size of an inspection unit Determ

25、ine the long-term defects per unit (DPU)DPU= Total Defects Total Units Determine the throughput yield (Ytp)Ytp= expDPUProcess Capability for Defect RateEstimation of Sigma-Capability for Defect Rate Determine the opportunities per unit Determine the long-term defects per opportunity (d)d= defects pe

26、r unit opportunities per unit Determine the inverse cumulative probability for d,using Calc Probability Distribution Normal Z-Score is the magnitude of the returned value Sigma-Capability = Z-Score + 1.5Example 6The process manager for a wire manufacturer is concerned about the effectiveness of the

27、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 6Stat Quality Tools Capability Analysis (Poisson)Example 61009080706050

28、4030201000.080.070.060.050.040.030.020.010.00Sample NumberSample CountU=0.02652UCL=0.06904LCL=01009080706050403020100.0300.0250.0200.015Sample NumberDPU0.0750.0500.0250.000Target1501401301201101000.080.070.060.050.040.030.020.010.00DPUSample SizeProcess Capability for Wire InsulationSummary StatsCum

29、ulative DPUDist of DPUU ChartDefect Rate(denotes 95% C.I.)Mean DPU:Min DPU:Max DPU:Targ DPU:0.026519400.07534250(0.0237309, 0.0295455)Defects per Unit = 0.0265194Throughput Yield = expDPU = exp0.0265194 = 0.9738c.f. First-Time Yield = 2 / 100 = 0.02Example 6150140130120110100LengthBoxplot of LengthD

30、efine1 Inspection Unit= 125 unit length of wirei.e.Units= Length 125Example 6AStat Quality Tools Capability Analysis (Poisson)Example 6A10090807060504030201001050Sample NumberSample CountU=3.315UCL=8.630LCL=01009080706050403020103.53.02.52.0Sample NumberDPU9630Target0.90.8109876543210DPUSam

31、ple SizeProcess Capability for Wire InsulationSummary StatsCumulative DPUDist of DPUU ChartDefect Rate(denotes 95% C.I.)Mean DPU:Min DPU:Max DPU:Targ DPU:3.3149309.417810(2.96637, 3.69319)Defects per Unit = 3.31493Throughput Yield = expDPU = exp3.31493 = 0.0363c.f. First-Time Yield = 2 / 100 = 0.02Example 6B10090807060504030201001050Sample NumberSample CountU=3.315UCL=8.630LCL=01009080706050403020103.53.02.52.0Sample NumberDPU9630Target0.90.8109876543210DPUSample SizeProcess Capability for Wire InsulationSummary StatsCumulative DPU