6s培训教材英文版

1、(Measure Phase) 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) Reject Rate(Binomial Distribution) Defect Rat

2、e(Poisson Distribution)Process Variation is the inevitable differences among individual measurements or units produced by a process.Sources of Variationwithin unit(positional variation)between units(unit-unit variation)between lots(lot-lot variation)between lines(line-line variation)across time(time

3、-time variation)measurement error(repeatability & reproducibility)Inherent 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 control” Special or Assignable VariationMay b

4、e 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-control”Process Capability is the inherent reproducibility of a processs output. It measures how well the process is currentl

5、y 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

6、per million (ppm)c) parts per billion (ppb)Process Capability studies can indicate the consistency of the process output indicate the degree to which the output meets specifications be used for comparison with another process or competitora)b)c)a) Process is highly capableb) Process is marginally ca

7、pablec) Process is not capableSpecification Limits (LSL and USL) created by design engineering in response to customer requirements to specify the tolerance for a products characteristicProcess Limits (LPL and UPL)measures the variation of a processthe natural 6 limits of the measured characteristic

8、Control Limits (LCL and UCL)measures the variation of a sample statistic (mean, variance, proportion, etc)Distribution of Individual ValuesDistribution of Sample AveragesTwo measures of process capability Process Potential Cp Process Performance Cpu Cpl CpkThe Cp index assesses whether the natural t

9、olerance (6) of a process is within the specification limits.6LSLUSLToleranceNaturalTolerancegEngineerinCpA 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

10、Reject Rate1.000.270 %1.330.007 %1.506.8 ppm2.002.0 ppba)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 1Specification Limits:4 to 16

11、 gMachineMeanStd Dev(a) 10 4(b) 10 2(c) 7 2(d) 13 1Determine the corresponding Cp and Cpk for each machine. 5 . 0464166LSLUSLCp 5 . 043410;431016Min3LSL;3USLMinCpk 0 . 1264166LSLUSLCp 0 . 123410;231016Min3LSL;3USLMinCpk 0 . 1264166LSLUSLCp 5 . 02347;23716Min3LSL;3USLMinCpk 0 . 2164166LSLUSLCp 0 . 11

12、3413;131316Min3LSL;3USLMinCpkFor 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 USLxPrLSLxPrxFUSL1LSLUSLLSLZ1ZLSLUSL LSLZLSLxPrxF USLZ1USLxPrxFSpecification Limits:4 to 16

13、gMachineMeanStd Dev(a) 10 4(b) 10 2(c) 7 2(d) 13 1Determine the defective rate for each machine.Mean 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 66,807 3 66,811 13 1 -9.03.0 0 1,350 1,350Lower Spec Limit = 4 gUpper Spec Limit = 16 g(a)

14、Poor Process Potential(b) Poor Process PerformanceLSLUSLLSLUSLExperimental Design to reduce variationExperimental Design to center mean to reduce variation 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.

15、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 Cp and Cpk.a)Cp = 2Cpk = 2b)Cp = 2Cpk = 1c)Cp = 2Cpk USLPPM USLPPM USLPPM USLPPM USLPPM LSLPpkPPLPPUPpScaleShapeSample NMeanLSLTargetUSL122970.80122970.80 * 75000.00 7

16、5000.00 *0.39 *0.39 *3.341.004003.34 * *7.00Expected LT PerformanceObserved LT PerformanceOverall (LT) CapabilityProcess DataStat Quality Tools Capability Sixpack (Weibull)4003002001000241680Individual and MR ChartObser.Individual ValueMean=3.34UCL=10.46LCL=-3.779241680Mov.RangeR=2.677UCL=8.746LCL=0

17、400390380Last 25 Observations9630Observation NumberValues7Overall (LT)Shape: 1.00Scale: 3.34Pp: *Ppk: 0.39Capability PlotProcess ToleranceSpecificationsIIII10.001.000.100.01Weibull Prob Plot20100Capability HistogramProcess Capability for Complaint ClosureFor a Normal Distribution, the proportion of

18、parts produced beyond a specification limit is )Z(F1USLZPr1USLZPrUSLXPrReject RateThus, for every reject rate there is an accompanying Z-Score, whereRecall thatHence3NSLPpkLimitSpecScoreZ3ScoreZPpkEstimation of Ppk for Reject Rate Determine the long-term reject rate (p) Determine the inverse cumulat

19、ive probability for p,using Calc Probability Distribution Normal Z-Score is the magnitude of the returned value Ppk is one-third of the Z-ScoreA sales manager plans to assess the process capability of his telephone sales departments handling of incoming calls. The following data was collected over a

20、 period of 20 days: number of incoming calls per day number of unanswered calls per daysStat Quality Tools Capability Analysis (Binomial)201000.260.250.240.230.220.210.200.19Sample NumberProportionP=0.2264UCL=0.2555LCL=0.1973201023.522.521.5Sample Number%Defective2624222020501950185026252423222120%D

21、efectiveSample 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)(22.22, 23.07)(222241, 230654)(0.737, 0.765)Ppk = 0.25Other

22、 applications, approximating a Poisson Distribution : error rates particle count chemical concentrationEstimation of Ytp for Defect Rate Define size of an inspection unit Determine the long-term defects per unit (DPU)DPU= Total Defects Total Units Determine the throughput yield (Ytp)Ytp= expDPUEstim

23、ation of Sigma-Capability for Defect Rate Determine the opportunities per unit Determine the long-term defects per opportunity (d)d= defects per unit opportunities per unit Determine the inverse cumulative probability for d,using Calc Probability Distribution Normal Z-Score is the magnitude of the r

24、eturned value Sigma-Capability = Z-Score + 1.5The 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 sp

25、ots and the length of each piece of wire are recorded. Stat Quality Tools Capability Analysis (Poisson)10090807060504030201000.080.070.060.050.040.030.020.010.00Sample NumberSample CountU=0.02652UCL=0.06904LCL=01009080706050403020100.0300.0250.0200.015Sample NumberDPU0.0750.0500.0250.000Target150140

26、1301201101000.080.070.060.050.040.030.020.010.00DPUSample SizeProcess Capability for Wire InsulationSummary StatsCumulative 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 = exp

27、DPU = exp0.0265194 = 0.9738c.f. First-Time Yield = 2 / 100 = 0.02150140130120110100LengthBoxplot of LengthDefine1 Inspection Unit= 125 unit length of wirei.e.Units= Length 125Stat Quality Tools Capability Analysis (Poisson)10090807060504030201001050Sample NumberSample CountU=3.315UCL=8.630LCL=010090

28、80706050403020103.53.02.52.0Sample NumberDPU9630Target1.21.11.00.90.8109876543210DPUSample 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 = 3.3149

29、3Throughput Yield = expDPU = exp3.31493 = 0.0363c.f. First-Time Yield = 2 / 100 = 0.0210090807060504030201001050Sample NumberSample CountU=3.315UCL=8.630LCL=01009080706050403020103.53.02.52.0Sample NumberDPU9630Target1.21.11.00.90.8109876543210DPUSample SizeProcess Capability for Wire InsulationSummary StatsCumulative DPUDist of DPUU ChartDefect Rate(denotes 95% C.I.)Mea