国外著名咨询公司培训教材之四：过程能力分析

1、0 1 2 3 4 5 CPK = Min CPL, CPUCPL = X-LSL 3P CPU = USL-X 3P PPL = X-LSL 3T PPU = USL-X 3T PPK = Min PPL, PPU 6 7 8 第第 2 步步 第第 3 步步 第第 4 步步 9 010203040 70 78 86 94 Individual and MR Chart Obser. Individual Value 1 X=84.00 3.0SL=93.21 -3.0SL=74.79 0 5 10 15 Mov.Range 1 1 1 1 R=3.462 3.0SL=11.31 -3.0SL

2、=0.00E+00 203040 Last 25 Observations 75 80 85 90 Observation Number Values 8090 Ppk: 0.27 Pp: 0.34 StDev: 4.88816 Overall (LT) Cpk: 0.43 Cp: 0.54 StDev: 3.06874 Potential (ST) Capability Plot Process Tolerance Specifications III III III ST LT 708090 Normal Prob Plot 708090 Capability Histogram Proc

3、ess Capability Sixpack for Process 1 10 第第 1 1 步步 StatQuality StatQuality ToolsCapability ToolsCapability Analysis NormalAnalysis Normal 11 第第 2 步步 第第 3 步步 第第 4 步步 12 707580859095100 LSLUSL Process Capability Analysis for Process 1 USL Target LSL Mean Sample N StDev (ST) StDev (LT) Cp CPU CPL Cpk Cp

4、m Pp PPU PPL Ppk PPM USL PPM Total PPM USL PPM Total PPM USL PPM Total 90 * 80 84 40 3.06874 4.88816 0.54 0.65 0.43 0.43 * 0.34 0.41 0.27 0.27 200000.00 125000.00 325000.00 96207.74 25279.73 121487.47 206591.77 109825.59 316417.36 Process Data Potential (ST) Capability Overall (LT) CapabilityObserve

5、d PerformanceExpected ST PerformanceExpected LT Performance ST LT 13 14 15 535251504948474645 Upper SpecLower Spec 16 17 18 19 Z U S L o r Z L S L U L 20 USLT + 3 能力能力 Z = 3 1 2 3 当偏差减小，缺陷 概率降低， 所以能力增加 我们希望我们希望 小小 Z大大 z + 6 能力能力 Z = 6 1 2 3 4 5 6 TUSL 21 22 Z = (U S L -) Z = (L S L -) 23 24 Z Z0.00

6、0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.005.00e-0014.96e-0014.92e-0014.88e-0014.84e-0014.80e-0014.76e-0014.72e-0014.68e-0014.64e-001 0.104.60e-0014.56e-0014.52e-0014.48e-0014.44e-0014.40e-0014.36e-0014.33e-0014.29e-0014.25e-001 0.204.21e-0014.17e-0014.13e-0014.09e-0014.05e-0014.01e-0013.97e-0

7、013.94e-0013.90e-0013.86e-001 0.303.82e-0013.78e-0013.74e-0013.71e-0013.67e-0013.63e-0013.59e-0013.56e-0013.52e-0013.48e-001 0.403.45e-0013.41e-0013.37e-0013.34e-0013.30e-0013.26e-0013.23e-0013.19e-0013.16e-0013.12e-001 0.503.09e-0013.05e-0013.02e-0012.98e-0012.95e-0012.91e-0012.88e-0012.84e-0012.81

8、e-0012.78e-001 0.602.74e-0012.71e-0012.68e-0012.64e-0012.61e-0012.58e-0012.55e-0012.51e-0012.48e-0012.45e-001 0.702.42e-0012.39e-0012.36e-0012.33e-0012.30e-0012.27e-0012.24e-0012.21e-0012.18e-0012.15e-001 0.802.12e-0012.09e-0012.06e-0012.03e-0012.00e-0011.98e-0011.95e-0011.92e-0011.89e-0011.87e-001

9、0.901.84e-0011.81e-0011.79e-0011.76e-0011.74e-0011.71e-0011.69e-0011.66e-0011.64e-0011.61e-001 1.001.59e-0011.56e-0011.54e-0011.52e-0011.49e-0011.47e-0011.45e-0011.42e-0011.40e-0011.38e-001 1.101.36e-0011.33e-0011.31e-0011.29e-0011.27e-0011.25e-0011.23e-0011.21e-0011.19e-0011.17e-001 1.201.15e-0011.

10、13e-0011.11e-0011.09e-0011.07e-0011.06e-0011.04e-0011.02e-0011.00e-0019.85e-002 1.309.68e-0029.51e-0029.34e-0029.18e-0029.01e-0028.85e-0028.69e-0028.53e-0028.38e-0028.23e-002 1.408.08e-0027.93e-0027.78e-0027.64e-0027.49e-0027.35e-0027.21e-0027.08e-0026.94e-0026.81e-002 1.506.68e-0026.55e-0026.43e-00

11、26.30e-0026.18e-0026.06e-0025.94e-0025.82e-0025.71e-0025.59e-002 1.605.48e-0025.37e-0025.26e-0025.16e-0025.05e-0024.95e-0024.85e-0024.75e-0024.65e-0024.55e-002 1.704.46e-0024.36e-0024.27e-0024.18e-0024.09e-0024.01e-0023.92e-0023.84e-0023.75e-0023.67e-002 1.803.59e-0023.51e-0023.44e-0023.36e-0023.29e

12、-0023.22e-0023.14e-0023.07e-0023.01e-0022.94e-002 1.902.87e-0022.81e-0022.74e-0022.68e-0022.62e-0022.56e-0022.50e-0022.44e-0022.39e-0022.33e-002 2.002.28e-0022.22e-0022.17e-0022.12e-0022.07e-0022.02e-0021.97e-0021.92e-0021.88e-0021.83e-002 2.101.79e-0021.74e-0021.70e-0021.66e-0021.62e-0021.58e-0021.

13、54e-0021.50e-0021.46e-0021.43e-002 2.201.39e-0021.36e-0021.32e-0021.29e-0021.25e-0021.22e-0021.19e-0021.16e-0021.13e-0021.10e-002 2.301.07e-0021.04e-0021.02e-0029.90e-0039.64e-0039.39e-0039.14e-0038.89e-0038.66e-0038.42e-003 2.408.20e-0037.98e-0037.76e-0037.55e-0037.34e-0037.14e-0036.95e-0036.76e-00

14、36.57e-0036.39e-003 2.506.21e-0036.04e-0035.87e-0035.70e-0035.54e-0035.39e-0035.23e-0035.08e-0034.94e-0034.80e-003 2.604.66e-0034.53e-0034.40e-0034.27e-0034.15e-0034.02e-0033.91e-0033.79e-0033.68e-0033.57e-003 2.703.47e-0033.36e-0033.26e-0033.17e-0033.07e-0032.98e-0032.89e-0032.80e-0032.72e-0032.64e

15、-003 2.802.56e-0032.48e-0032.40e-0032.33e-0032.26e-0032.19e-0032.12e-0032.05e-0031.99e-0031.93e-003 2.901.87e-0031.81e-0031.75e-0031.69e-0031.64e-0031.59e-0031.54e-0031.49e-0031.44e-0031.39e-003 25 Z0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 3.001.35e-0031.31e-0031.26e-0031.22e-0031.18e-0031.

16、14e-0031.11e-0031.07e-0031.04e-0031.00e-003 3.109.68e-0049.35e-0049.04e-0048.74e-0048.45e-0048.16e-0047.89e-0047.62e-0047.36e-0047.11e-004 3.206.87e-0046.64e-0046.41e-0046.19e-0045.98e-0045.77e-0045.57e-0045.38e-0045.19e-0045.01e-004 3.304.83e-0044.66e-0044.50e-0044.34e-0044.19e-0044.04e-0043.90e-00

17、43.76e-0043.62e-0043.49e-004 3.403.37e-0043.25e-0043.13e-0043.02e-0042.91e-0042.80e-0042.70e-0042.60e-0042.51e-0042.42e-004 3.502.33e-0042.24e-0042.16e-0042.08e-0042.00e-0041.93e-0041.85e-0041.78e-0041.72e-0041.65e-004 3.601.59e-0041.53e-0041.47e-0041.42e-0041.36e-0041.31e-0041.26e-0041.21e-0041.17e

18、-0041.12e-004 3.701.08e-0041.04e-0049.96e-0059.57e-0059.20e-0058.84e-0058.50e-0058.16e-0057.84e-0057.53e-005 3.807.23e-0056.95e-0056.67e-0056.41e-0056.15e-0055.91e-0055.67e-0055.44e-0055.22e-0055.01e-005 3.904.81e-0054.61e-0054.43e-0054.25e-0054.07e-0053.91e-0053.75e-0053.59e-0053.45e-0053.30e-005 4

19、.003.17e-0053.04e-0052.91e-0052.79e-0052.67e-0052.56e-0052.45e-0052.35e-0052.25e-0052.16e-005 4.102.07e-0051.98e-0051.89e-0051.81e-0051.74e-0051.66e-0051.59e-0051.52e-0051.46e-0051.39e-005 4.201.33e-0051.28e-0051.22e-0051.17e-0051.12e-0051.07e-0051.02e-0059.77e-0069.34e-0068.93e-006 4.308.54e-0068.1

20、6e-0067.80e-0067.46e-0067.12e-0066.81e-0066.50e-0066.21e-0065.93e-0065.67e-006 4.405.41e-0065.17e-0064.94e-0064.71e-0064.50e-0064.29e-0064.10e-0063.91e-0063.73e-0063.56e-006 4.503.40e-0063.24e-0063.09e-0062.95e-0062.81e-0062.68e-0062.56e-0062.44e-0062.32e-0062.22e-006 4.602.11e-0062.01e-0061.92e-006

21、1.83e-0061.74e-0061.66e-0061.58e-0061.51e-0061.43e-0061.37e-006 4.701.30e-0061.24e-0061.18e-0061.12e-0061.07e-0061.02e-0069.68e-0079.21e-0078.76e-0078.34e-007 4.807.93e-0077.55e-0077.18e-0076.83e-0076.49e-0076.17e-0075.87e-0075.58e-0075.30e-0075.04e-007 4.904.79e-0074.55e-0074.33e-0074.11e-0073.91e-

22、0073.71e-0073.52e-0073.35e-0073.18e-0073.02e-007 5.002.87e-0072.72e-0072.58e-0072.45e-0072.33e-0072.21e-0072.10e-0071.99e-0071.89e-0071.79e-007 5.101.70e-0071.61e-0071.53e-0071.45e-0071.37e-0071.30e-0071.23e-0071.17e-0071.11e-0071.05e-007 5.209.96e-0089.44e-0088.95e-0088.48e-0088.03e-0087.60e-0087.2

23、0e-0086.82e-0086.46e-0086.12e-008 5.305.79e-0085.48e-0085.19e-0084.91e-0084.65e-0084.40e-0084.16e-0083.94e-0083.72e-0083.52e-008 5.403.33e-0083.15e-0082.98e-0082.82e-0082.66e-0082.52e-0082.38e-0082.25e-0082.13e-0082.01e-008 5.501.90e-0081.79e-0081.69e-0081.60e-0081.51e-0081.43e-0081.35e-0081.27e-008

24、1.20e-0081.14e-008 5.601.07e-0081.01e-0089.55e-0099.01e-0098.50e-0098.02e-0097.57e-0097.14e-0096.73e-0096.35e-009 5.705.99e-0095.65e-0095.33e-0095.02e-0094.73e-0094.46e-0094.21e-0093.96e-0093.74e-0093.52e-009 5.803.32e-0093.12e-0092.94e-0092.77e-0092.61e-0092.46e-0092.31e-0092.18e-0092.05e-0091.93e-

25、009 5.901.82e-0091.71e-0091.61e-0091.51e-0091.43e-0091.34e-0091.26e-0091.19e-0091.12e-0091.05e-009 Z 26 Z0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 6.009.87e-0109.28e-0108.72e-0108.20e-0107.71e-0107.24e-0106.81e-0106.40e-0106.01e-0105.65e-010 6.105.30e-0104.98e-0104.68e-0104.39e-0104.13e-0103

26、.87e-0103.64e-0103.41e-0103.21e-0103.01e-010 6.202.82e-0102.65e-0102.49e-0102.33e-0102.19e-0102.05e-0101.92e-0101.81e-0101.69e-0101.59e-010 6.301.49e-0101.40e-0101.31e-0101.23e-0101.15e-0101.08e-0101.01e-0109.45e-0118.85e-0118.29e-011 6.407.77e-0117.28e-0116.81e-0116.38e-0115.97e-0115.59e-0115.24e-0

27、114.90e-0114.59e-0114.29e-011 6.504.02e-0113.76e-0113.52e-0113.29e-0113.08e-0112.88e-0112.69e-0112.52e-0112.35e-0112.20e-011 6.602.06e-0111.92e-0111.80e-0111.68e-0111.57e-0111.47e-0111.37e-0111.28e-0111.19e-0111.12e-011 6.701.04e-0119.73e-0129.09e-0128.48e-0127.92e-0127.39e-0126.90e-0126.44e-0126.01

28、e-0125.61e-012 6.805.23e-0124.88e-0124.55e-0124.25e-0123.96e-0123.69e-0123.44e-0123.21e-0122.99e-0122.79e-012 6.902.60e-0122.42e-0122.26e-0122.10e-0121.96e-0121.83e-0121.70e-0121.58e-0121.48e-0121.37e-012 7.001.28e-0121.19e-0121.11e-0121.03e-0129.61e-0138.95e-0138.33e-0137.75e-0137.21e-0136.71e-013

29、7.106.24e-0135.80e-0135.40e-0135.02e-0134.67e-0134.34e-0134.03e-0133.75e-0133.49e-0133.24e-013 7.203.01e-0132.80e-0132.60e-0132.41e-0132.24e-0132.08e-0131.94e-0131.80e-0131.67e-0131.55e-013 7.301.44e-0131.34e-0131.24e-0131.15e-0131.07e-0139.91e-0149.20e-0148.53e-0147.91e-0147.34e-014 7.406.81e-0146.

30、31e-0145.86e-0145.43e-0145.03e-0144.67e-0144.33e-0144.01e-0143.72e-0143.44e-014 7.503.19e-0142.96e-0142.74e-0142.54e-0142.35e-0142.18e-0142.02e-0141.87e-0141.73e-0141.60e-014 7.601.48e-0141.37e-0141.27e-0141.17e-0141.09e-0141.00e-0149.30e-0158.60e-0157.95e-0157.36e-015 7.706.80e-0156.29e-0155.82e-01

31、55.38e-0154.97e-0154.59e-0154.25e-0153.92e-0153.63e-0153.35e-015 7.803.10e-0152.86e-0152.64e-0152.44e-0152.25e-0152.08e-0151.92e-0151.77e-0151.64e-0151.51e-015 7.901.39e-0151.29e-0151.19e-0151.10e-0151.01e-0159.33e-0168.60e-0167.93e-0167.32e-0166.75e-016 8.006.22e-0165.74e-0165.29e-0164.87e-0164.49e

32、-0164.14e-0163.81e-0163.51e-0163.24e-0162.98e-016 8.102.75e-0162.53e-0162.33e-0162.15e-0161.98e-0161.82e-0161.68e-0161.54e-0161.42e-0161.31e-016 8.201.20e-0161.11e-0161.02e-0169.36e-0178.61e-0177.92e-0177.28e-0176.70e-0176.16e-0175.66e-017 8.305.21e-0174.79e-0174.40e-0174.04e-0173.71e-0173.41e-0173.

33、14e-0172.88e-0172.65e-0172.43e-017 8.402.23e-0172.05e-0171.88e-0171.73e-0171.59e-0171.46e-0171.34e-0171.23e-0171.13e-0171.03e-017 8.509.48e-0188.70e-0187.98e-0187.32e-0186.71e-0186.15e-0185.64e-0185.17e-0184.74e-0184.35e-018 8.603.99e-0183.65e-0183.35e-0183.07e-0182.81e-0182.57e-0182.36e-0182.16e-01

34、81.98e-0181.81e-018 8.701.66e-0181.52e-0181.39e-0181.27e-0181.17e-0181.07e-0189.76e-0198.93e-0198.17e-0197.48e-019 8.806.84e-0196.26e-0195.72e-0195.23e-0194.79e-0194.38e-0194.00e-0193.66e-0193.34e-0193.06e-019 8.902.79e-0192.55e-0192.33e-0192.13e-0191.95e-0191.78e-0191.62e-0191.48e-0191.35e-0191.24e

35、-019 Z 27 Z0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 9.001.13e-0191.03e-0199.40e-0208.58e-0207.83e-0207.15e-0206.52e-020 5.95e-020 5.43e-0204.95e-020 9.104.52e-0204.12e-0203.76e-0203.42e-0203.12e-0202.85e-0202.59e-020 2.37e-020 2.16e-0201.96e-020 9.201.79e-0201.63e-0201.49e-0201.35e-0201.23e

36、-0201.12e-0201.02e-020 9.31e-021 8.47e-0217.71e-021 9.307.02e-0216.39e-0215.82e-0215.29e-0214.82e-0214.38e-0213.99e-021 3.63e-021 3.30e-0213.00e-021 9.402.73e-0212.48e-0212.26e-0212.05e-0211.86e-0211.69e-0211.54e-021 1.40e-021 1.27e-0211.16e-021 9.501.05e-0219.53e-0228.66e-0227.86e-0227.14e-0226.48e

37、-0225.89e-022 5.35e-022 4.85e-0224.40e-022 9.604.00e-0223.63e-0223.29e-0222.99e-0222.71e-0222.46e-0222.23e-022 2.02e-022 1.83e-0221.66e-022 9.701.51e-0221.37e-0221.24e-0221.12e-0221.02e-0229.22e-0238.36e-023 7.57e-023 6.86e-0236.21e-023 9.805.63e-0235.10e-0234.62e-0234.18e-0233.79e-0233.43e-0233.10e

38、-023 2.81e-023 2.54e-0232.30e-023 9.902.08e-0231.88e-0231.70e-0231.54e-0231.39e-0231.26e-0231.14e-023 1.03e-023 9.32e-0248.43e-024 10.007.62e-0246.89e-0246.23e-0245.63e-0245.08e-0244.59e-0244.15e-024 3.75e-024 3.39e-0243.06e-024 Z 28 例子例子: : 客户要求所有交付的灯泡都是完整的客户要求所有交付的灯泡都是完整的.没有破损的没有破损的. . 在在100100个样品

39、中有个样品中有1717 个是破损的个是破损的. . DPMODPMO是多少是多少? ? 这个发运过程的这个发运过程的 “ “sigma” sigma” 是多少是多少? ? 1) 运用规范来确定缺陷率. 缺陷是破损的灯泡. 破损率 = 17/100 = 0.17 或 17% 2) 计算 DPMO: 破损率 X 1000000 机会 = 0.17 X 1,000,000 = 170,000 DPMO 3) 将缺陷率转换为用科学记数法表示: 0.17 = 1.7E-01 29 4) 4) 从正态分布表中查找从正态分布表中查找 Z Z 值值: : 正态分布正态分布 Z Z0 00.010.010.02

40、0.020.030.030.040.040.050.050.060.060.070.070.080.080.090.09 0.05.00E-014.96E-014.92E-014.88E-014.84E-014.80E-014.76E-014.72E-014.68E-014.64E-01 0.14.60E-014.56E-014.52E-014.48E-014.44E-014.40E-014.36E-014.33E-014.29E-014.25E-01 0.24.21E-014.17E-014.13E-014.09E-014.05E-014.01E-013.97E-013.94E-013.90

41、E-013.86E-01 0.33.82E-013.78E-013.75E-013.71E-013.67E-013.63E-013.59E-013.56E-013.52E-013.48E-01 0.43.45E-013.41E-013.37E-013.34E-013.30E-013.26E-013.23E-013.19E-013.16E-013.12E-01 0.53.09E-013.05E-013.02E-012.98E-012.95E-012.91E-012.88E-012.84E-012.81E-012.78E-01 0.62.74E-012.71E-012.68E-012.64E-01

42、2.61E-012.58E-012.55E-012.51E-012.48E-012.45E-01 0.72.42E-012.39E-012.36E-012.33E-012.30E-012.27E-012.24E-012.21E-012.18E-012.15E-01 0.82.12E-012.09E-012.06E-012.03E-012.01E-011.98E-011.95E-011.92E-011.89E-011.87E-01 0.91.84E-011.81E-011.79E-011.76E-011.74E-011.71E-011.69E-011.66E-011.64E-011.61E-01

43、 Z = 0.96, Z = 0.96, 或者说或者说, , 该过程是一个该过程是一个 0.96 0.96 sigma sigma 过程过程 . . 相对于相对于 6 6 sigma sigma 的目的目 标来讲标来讲, , 不是很好不是很好. . Z 例子 - 逻辑变量 30 31 32 Z= ( x -) 33 计算计算 Z Z 值需要值需要 4 4 个条件个条件: : 1) 平均值Mean 2) 标准偏差 3) 规范 (单边 或 双边) 4) 正态分布的假定 (那么就可以使用正态表确定缺陷率) 例子例子 #1 #1A (A (单边规范极限单边规范极限): ): 等候服务台回答你的电话的平

44、均时间为5分钟. 标准偏差为2.06分钟. 规范是小于或 等于7分钟. DPMO和Z值各是多少? 1) 计算 Z 值: X = 5Zusl = USL - X = 7 - 5 = 0.97 s = 2.06 s 2.06 USL = 7 2) 确定缺陷率 (超过7分钟才被回答的电话): USL 57 超出规范上 限的缺陷! 单边规范单边规范 34 正态分布正态分布 Z Z0 00.010.010.020.020.030.030.040.040.050.050.060.060.070.070.080.080.090.09 0.05.00E-014.96E-014.92E-014.88E-014.

45、84E-014.80E-014.76E-014.72E-014.68E-014.64E-01 0.14.60E-014.56E-014.52E-014.48E-014.44E-014.40E-014.36E-014.33E-014.29E-014.25E-01 0.24.21E-014.17E-014.13E-014.09E-014.05E-014.01E-013.97E-013.94E-013.90E-013.86E-01 0.33.82E-013.78E-013.75E-013.71E-013.67E-013.63E-013.59E-013.56E-013.52E-013.48E-01 0

46、.43.45E-013.41E-013.37E-013.34E-013.30E-013.26E-013.23E-013.19E-013.16E-013.12E-01 0.53.09E-013.05E-013.02E-012.98E-012.95E-012.91E-012.88E-012.84E-012.81E-012.78E-01 0.62.74E-012.71E-012.68E-012.64E-012.61E-012.58E-012.55E-012.51E-012.48E-012.45E-01 0.72.42E-012.39E-012.36E-012.33E-012.30E-012.27E-

47、012.24E-012.21E-012.18E-012.15E-01 0.82.12E-012.09E-012.06E-012.03E-012.01E-011.98E-011.95E-011.92E-011.89E-011.87E-01 0.91.84E-011.81E-011.79E-011.76E-011.74E-011.71E-011.69E-011.66E-011.64E-011.61E-01 Z Z Z 值大于值大于0.970.97的概率是多少的概率是多少? ? 查表, 当 Z=0.97时, 概率 = 1.66E-01 科学计数转换科学计数转换: : 1.66E-01 = 0.166

48、 这表示这表示, , 电话超过电话超过7 7分钟才被回答的概率是分钟才被回答的概率是0.166, 0.166, 或者说或者说, , 缺陷率是缺陷率是0.1660.166或或16.6%.16.6%. 该过程的该过程的 “ “sigma” sigma” 是多少是多少? ? Z=.97 Z=.97 所以该过程是所以该过程是 0.97 0.97 sigmasigma过程过程相对于我们的相对于我们的 6 6 sigma sigma 目标不很好目标不很好. . 单边规范单边规范 35 30252015105 Upper SpecUpper Spec 36 65432 Low er SpecLow er S

49、pec 3.00 - 4.36 0.81 Z = -1.68 LSL - X s Z = 37 38 39 40 41 42 535251504948474645 Upper SpecLow er Spec 43 Z= (L S L - x ) = 4 6 - 4 8 .6 8 1 .1 1 = - 2 .4 2 L Z= (USL - x) = 50 - 48.68 1.11 = 1.19 U 535251504948474645 Upper SpecLow er Spec 535251504948474645 Upper SpecLow er Spec 44 45 535251504948

50、474645 U p p e r S p e cL o w e r S p e c 535251504948474645 Upper SpecLow er Spec 5 35 25 15 04 94 84 74 64 5 U p p e r S p e cL o w e r S p e c 46 LSL Z.LSL = X - LSL S =1.050 - 1.000 .015 Z.LSL = 3.33 查表查表, .0004 or ( .04% ) 超出规范超出规范 正态分布举例正态分布举例 规范为规范为 1.030” + .030 = ( 1.000, 1.060 ) 假定测量假定测量 30 个零件个零件, X = 1.050, s = .015 计算超出规范的比率计算