六西格瑪黑帶培訓教材(共72頁).ppt

1、Information, the way you want it(Measure Phase)2Information, the way you want it 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(Expone

2、ntial Distribution) Reject Rate(Binomial Distribution) Defect Rate(Poisson Distribution)3Information, the way you want itProcess Variation is the inevitable differences among individual measurements or units produced by a process.Sources of Variationwithin unit(positional variation)between units(uni

3、t-unit variation)between lots(lot-lot variation)between lines(line-line variation)across time(time-time variation)measurement error(repeatability & reproducibility)4Information, the way you want itInherent or Natural VariationDue to the cumulative effect of many small unavoidable causesA process

4、 operating with only chance causes of variation present is said to be “in statistical control” 5Information, the way you want itSpecial or Assignable VariationMay be due to a) improperly adjusted machine b) operator error c) defective raw materialA process operating in the presence of assignable cau

5、ses of variation is said to be “out-of-control”6Information, the way you want itProcess 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.Capabi

6、lity 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)7Information, the way you want itProcess Capability studies

7、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 competitor8Information, the way you want ita)b)c)a) Process is highly capableb) Process is marginally capablec) Process is not capable9Inform

8、ation, the way you want itSpecification 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 characteristicCont

9、rol Limits (LCL and UCL)measures the variation of a sample statistic (mean, variance, proportion, etc)10Information, the way you want itDistribution of Individual ValuesDistribution of Sample Averages11Information, the way you want itTwo measures of process capability Process Potential Cp Process Pe

10、rformance Cpu Cpl Cpk12Information, the way you want itThe Cp index assesses whether the natural tolerance (6) of a process is within the specification limits.6LSLUSLToleranceNaturalTolerancegEngineerinCp13Information, the way you want itA Cp of 1.0 indicates that a process is judged to be “capable”

11、, i.e. if the process is centered within its engineering tolerance, 0.27% of parts produced will be beyond specification limits. Cp Reject Rate1.000.270 %1.330.007 %1.506.8 ppm2.002.0 ppb14Information, the way you want ita)b)c)a) Process is highly capable (Cp2)b) Process is capable (Cp=1 to 2)c) Pro

12、cess 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 119Information, the way you want itSpecification Limits:4 to 16 gMachineMeanStd Dev(a) 10 4(b) 10 2(c) 7 2(d) 13 1Determine the corresponding Cp and Cpk for each m

13、achine.20Information, the way you want it 5 . 0464166LSLUSLCp 5 . 043410;431016Min3LSL;3USLMinCpk21Information, the way you want it 0 . 1264166LSLUSLCp 0 . 123410;231016Min3LSL;3USLMinCpk22Information, the way you want it 0 . 1264166LSLUSLCp 5 . 02347;23716Min3LSL;3USLMinCpk23Information, the way yo

14、u want it 0 . 2164166LSLUSLCp 0 . 113413;131316Min3LSL;3USLMinCpk24Information, the way you want itFor 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

15、SLLSLZ1ZLSLUSL LSLZLSLxPrxF USLZ1USLxPrxF25Information, the way you want itSpecification Limits:4 to 16 gMachineMeanStd Dev(a) 10 4(b) 10 2(c) 7 2(d) 13 1Determine the defective rate for each machine.26Information, the way you want itMean Std Dev ZLSL ZUSL F(xUSL) F(x) 10 4 -1.51.5 66,807 66,807133,

16、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 g27Information, the way you want it(a) Poor Process Potential(b) Poor Process PerformanceLSLUSLLSLUSLExperimental Design to reduce variationExperimental Design to cent

17、er mean to reduce variation28Information, the way you want it 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 1.4 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

18、dependent on the actual combination of Cp and Cpk.29Information, the way you want ita)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 Perf

19、ormanceObserved LT PerformanceOverall (LT) CapabilityProcess Data53Information, the way you want itStat Quality Tools Capability Sixpack (Weibull)54Information, the way you want it4003002001000241680Individual and MR ChartObser.Individual ValueMean=3.34UCL=10.46LCL=-3.779241680Mov.RangeR=2.677UCL=8.

20、746LCL=0400390380Last 25 Observations9630Observation NumberValues7Overall (LT)Shape: 1.00Scale: 3.34Pp: *Ppk: 0.39Capability PlotProcess ToleranceSpecificationsIIII10.001.000.100.01Weibull Prob Plot20100Capability HistogramProcess Capability for Complaint Closure55Information, the way you want itFor

21、 a Normal Distribution, the proportion of parts produced beyond a specification limit is )Z(F1USLZPr1USLZPrUSLXPrReject Rate56Information, the way you want itThus, for every reject rate there is an accompanying Z-Score, whereRecall thatHence3NSLPpkLimitSpecScoreZ3ScoreZPpk57Information, the way you

22、want itEstimation of Ppk for Reject Rate Determine the long-term reject rate (p) Determine 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-Score58Information, the way you want itA sales manag

23、er 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 day number of unanswered calls per days59Information, the way you want itStat Quality Tools Capability Anal

24、ysis (Binomial)60Information, the way you want it201000.260.250.240.230.220.210.200.19Sample NumberProportionP=0.2264UCL=0.2555LCL=0.1973201023.522.521.5Sample Number%Defective2624222020501950185026252423222120%DefectiveSample SizeProcess Capability for Telephone SalesSummary StatsCumulative %Defect

25、iveDist 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 = 0.2561Information, the way you want itOther applications, approximating a Poisson Distribution :

26、error rates particle count chemical concentration62Information, the way you want itEstimation 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= expDPU63Information, the way yo

27、u want itEstimation 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 magn

28、itude of the returned value Sigma-Capability = Z-Score + 1.564Information, the way you want itThe 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 b

29、y means of a test voltage. The number of weak spots and the length of each piece of wire are recorded. 65Information, the way you want itStat Quality Tools Capability Analysis (Poisson)66Information, the way you want it10090807060504030201000.080.070.060.050.040.030.020.010.00Sample NumberSample Cou

30、ntU=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 StatsCumulative DPUDist of DPUU ChartDefect Rate(denotes 95% C.I.)Mean DPU:M

31、in 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 = 0.0267Information, the way you want it150140130120110100LengthBoxplot of LengthDefine1 Inspection Unit= 125 unit length of

32、wirei.e.Units= Length 12568Information, the way you want itStat Quality Tools Capability Analysis (Poisson)69Information, the way you want it10090807060504030201001050Sample NumberSample CountU=3.315UCL=8.630LCL=01009080706050403020103.53.02.52.0Sample NumberDPU9630Target1.21.11.00.90.8109876543210D

33、PUSample 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 = 0.0270Information, the way you want it10090807060504030201001050Sample NumberSample CountU=3.315UCL=8.630LCL=01009080706050403020103.53.02.52.0Sample NumberDPU9630Target1.21.11.00.90.8109876543210DPUSample SizeProcess Capability for Wire Ins