3水平与6水平比较30302.0 X 10-92.7 X 10-3生产控制方式由过去的3c控制方式改为6c控制方式。3c控制方式下的稳态不合格品率为2.7×10-366控制方式下的稳态不合格品率为2.0×10-9后者比前者降低了：2.7X10-3/2.0×10-9=1.35X106即-百三十五万倍！
3σ水平与6σ水平比较 生产控制方式由过去的3控制方式改为6控制方式。 3控制方式下的稳态不合格品率为2.7 X 10-3 , 6控制方式下的稳态不合格品率为2.0 X 10-9 后者比前者降低了：2.7 X 10-3 / 2.0 X 10-9=1.35 X106即一 百三十五万倍!
正态分布N(u、2)V标准正态分布Z～N（O，1）1.随机变量具有均值为0，标准差为1的正态分布2．任何一个一般的正态分布，可通过下面的线性变换转化为标准正态分布X-μ~ N(0,1)Zc3.标准正态分布的概率密度函数+212p(x)8<x<+82元4.标准正态分布的分布函数12Φ(x)= f (x)dt =dt212元
= ~ N(0,1) σ X μ Z - ✓ 标准正态分布Z～N (0，1 ) 1. 随机变量具有均值为0，标准差为1的正态分布 2. 任何一个一般的正态分布，可通过下面的线性变换转化为标 准正态分布 3. 标准正态分布的概率密度函数 4. 标准正态分布的分布函数 ∞ ∞ - e , < < + 2π 1 ( ) = 2 2 x x x ∫ -∞ ∫-∞ x t x x x t e dt 2π 1 Φ( ) = ( )d = 2 - 2 ◼ 正态分布N (μ、σ 2 )
标准正态分布表β(x) x0.000.010.020.030.040.050.060.070.080.090.00.51200.52790.53190.50000.50400.50800.51600.51990.52390.53590.10.55170.55960.53980.54380.54780.55570.56360.56750.57140.57530.20.58710.59100.59480.59870.60260.60640.57930.58320.61030.61410.30.61790.62170.62550.62930.63310.63680.64060.64430.64800.65170.40.65540.66280.66640.67000.67360.68440.68790.65910.67720.68080.50.70190.69150.69500.69850.70540.70880.71230.71570.71900.72240.60.73890.75490.72570.72910.73240.73570.74220.74540.74860.75170.70.76110.77640.75800.76420.76730.77030.77340.77940.78230.78520.80.78810.79100.79390.79670.79950.80230.80510.80780.81060.81330.90.81590.81860.82120.82380.82640.82890.83150.83400.83650.83891.00.84130.84380.84610.84850.85080.85310.85540.85770.85990.86211.10.86430.87490.86650.86860.87080.87290.87700.87900.88100.88301.20.88490.88690.88880.89070.89250.89440.89620.89800.89970.90151.30.91310.91470.91620.90320.90490.90660.90820.90990.91150.91771.40.91920.92070.92220.92360.92510.92650.92780.92920.93060.93191.50.93320.93450.93570.93700.93820.93940.94060.94180.94300.94411.60.94520.94630.94740.94840.94950.95050.95150.95250.95350.95451.70.95540.95640.95730.95820.95910.95990.96080.96160.96250.96331.80.96410.96480.96560.96640.96710.96780.96860.96930.97000.97061.90.97380.97440.97130.97190.97260.97320.97500.97560.97620.97672.00.97720.97780.97830.97880.97930.97980.98030.98080.98120.98172.10.98210.98260.98300.98340.98380.98420.98460.98500.98540.98572.20.98610.98640.98680.98710.98740.98780.98810.98840.98870.98902.30.98930.98960.98980.99010.99040.99060.99090.99110.99130.99162.40.99220.99250.99270.99290.99310.99320.99180.99200.99340.99362.50.99400.99410.99430.99450.99460.99480.99490.99380.99510.99522.60.99530.99550.99560.99570.99590.99600.99610.99620.99630.99642.70.99650.99660.99670.99680.99690.99700.99710.99720.99730.99742.80.99740.99750.99760.99770.99770.99780.99790.99790.99800.99812.90.99820.99810.99820.99830.99840.99840.99850.99850.99860.99863.00.99900.99981.00000.99870.99930.99950.99970.99980.99990.9999
标准正态分布表 φ(x) x 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 0.5000 0.5398 0.5793 0.6179 0.6554 0.6915 0.7257 0.7580 0.7881 0.8159 0.8413 0.8643 0.8849 0.9032 0.9192 0.9332 0.9452 0.9554 0.9641 0.9713 0.9772 0.9821 0.9861 0.9893 0.9918 0.9938 0.9953 0.9965 0.9974 0.9981 0.5040 0.5438 0.5832 0.6217 0.6591 0.6950 0.7291 0.7611 0.7910 0.8186 0.8438 0.8665 0.8869 0.9049 0.9207 0.9345 0.9463 0.9564 0.9648 0.9719 0.9778 0.9826 0.9864 0.9896 0.9920 0.9940 0.9955 0.9966 0.9975 0.9982 0.5080 0.5478 0.5871 0.6255 0.6628 0.6985 0.7324 0.7642 0.7939 0.8212 0.8461 0.8686 0.8888 0.9066 0.9222 0.9357 0.9474 0.9573 0.9656 0.9726 0.9783 0.9830 0.9868 0.9898 0.9922 0.9941 0.9956 0.9967 0.9976 0.9982 0.5120 0.5517 0.5910 0.6293 0.6664 0.7019 0.7357 0.7673 0.7967 0.8238 0.8485 0.8708 0.8907 0.9082 0.9236 0.9370 0.9484 0.9582 0.9664 0.9732 0.9788 0.9834 0.9871 0.9901 0.9925 0.9943 0.9957 0.9968 0.9977 0.9983 0.5160 0.5557 0.5948 0.6331 0.6700 0.7054 0.7389 0.7703 0.7995 0.8264 0.8508 0.8729 0.8925 0.9099 0.9251 0.9382 0.9495 0.9591 0.9671 0.9738 0.9793 0.9838 0.9874 0.9904 0.9927 0.9945 0.9959 0.9969 0.9977 0.9984 0.5199 0.5596 0.5987 0.6368 0.6736 0.7088 0.7422 0.7734 0.8023 0.8289 0.8531 0.8749 0.8944 0.9115 0.9265 0.9394 0.9505 0.9599 0.9678 0.9744 0.9798 0.9842 0.9878 0.9906 0.9929 0.9946 0.9960 0.9970 0.9978 0.9984 0.5239 0.5636 0.6026 0.6406 0.6772 0.7123 0.7454 0.7764 0.8051 0.8315 0.8554 0.8770 0.8962 0.9131 0.9278 0.9406 0.9515 0.9608 0.9686 0.9750 0.9803 0.9846 0.9881 0.9909 0.9931 0.9948 0.9961 0.9971 0.9979 0.9985 0.5279 0.5675 0.6064 0.6443 0.6808 0.7157 0.7486 0.7794 0.8078 0.8340 0.8577 0.8790 0.8980 0.9147 0.9292 0.9418 0.9525 0.9616 0.9693 0.9756 0.9808 0.9850 0.9884 0.9911 0.9932 0.9949 0.9962 0.9972 0.9979 0.9985 0.5319 0.5714 0.6103 0.6480 0.6844 0.7190 0.7517 0.7823 0.8106 0.8365 0.8599 0.8810 0.8997 0.9162 0.9306 0.9430 0.9535 0.9625 0.9700 0.9762 0.9812 0.9854 0.9887 0.9913 0.9934 0.9951 0.9963 0.9973 0.9980 0.9986 0.5359 0.5753 0.6141 0.6517 0.6879 0.7224 0.7549 0.7852 0.8133 0.8389 0.8621 0.8830 0.9015 0.9177 0.9319 0.9441 0.9545 0.9633 0.9706 0.9767 0.9817 0.9857 0.9890 0.9916 0.9936 0.9952 0.9964 0.9974 0.9981 0.9986 3.0 0.9987 0.9990 0.9993 0.9995 0.9997 0.9998 0.9998 0.9999 0.9999 1.0000
二项式分布（B（n，p））V二项分布B（n，p）满足条件(3项）>一次试验只有两种可能结果用“成功”代表所关心的结果，相反的结果为“失败”>每次试验中“成功”的概率都是p>n次试验相互独立。所以该实验又称n重贝努利试验
✓二项分布B(n,p)满足条件(3项) ➢ 一次试验只有两种可能结果 用“成功”代表所关心的结果，相反的结果为 “失败” ➢ 每次试验中“成功”的概率都是 p ➢ n 次试验相互独立。 所以该实验又称n重贝努利试验 ◼ 二项式分布（B（n，p））
二项式分布（B（n，p））二项分布的概率函数在n重贝努里试验中，“成功”的次数x服从参数为n、p的二项分布，记为X～B(n，p)n-xP(X = x) = Crp*(1 - p)（二项分布的数学期望和方差：E(X)=μ=np,D(X)=α"=np(1-p)
✓ 二项分布的概率函数 在n重贝努里试验中，“成功”的次数X服从参数为n、p的二 项分布，记为 X ～B(n , p) ✓ 二项分布的数学期望和方差： ( ) , ( ) (1 ) 2 E X ＝＝np D X ＝ ＝np − p x x n x n P X x C p p − ( = ) = (1− ) ◼ 二项式分布（B（n，p））