JB/T 3736.4-1994 质量管理中常用的统计工具 正态概率纸

Ad1中华人民共和国机械行业标准JB/T3736.1~3736.8-9质量管理中常用的统计工具1994-12-09发布1995-10-01实施中华人民共和国机械工业部发布中华人民共和国机械行业标准JB/T3736.4-9质量管理中常用的统计工具代替JB3736.4-8正态概率纸1主题内容与适用范E本标准阐述了正态概率纸的构成、绘制与应用。正态概率纸适用于推断观测值是否来自正态分布的总体,估计总体的均值、标准差与不合格品率等场合。2构成正态概率纸是按标准正态分布构造的,它是一个直角坐标系,横坐标刻度是均匀的,表示观测值;纵坐标是不均匀的,表示标准正态分布的函数值。见图1。正态概率纸的绘制方法见附录A(补充件)。3应用步骤3.1步骤收集n个观测值。b.整理数据。按观测值大小,由小到大列表,汇总每个观测值发生的频数、累积频数及累积频率。n≥30时累积频率=累积频数n<30时累积频率=中位秩[按n和i查中位秩表,见附录B(补充件)c.在正态概率纸上打点,横坐标值为观测值,纵坐标值为与其对应的累积频率值。画直线,使直线两边点数大致相等,各点离直线的偏差均值尽可能地小。d.推断观测值是否来自正态分布的总体。若各点离直线偏差不大(尤其是纵坐标为50附近的点),则可推断总体遵从正态分布,并可进行以下步骤。e.估计总体的均值μ和标准差σ。直线上纵坐标为50的点对应的横坐标值为以;直线上纵坐标值为0.135的点对应的横坐标值与p的差(取绝对值)的1/3为a。.估计总体的不合格品率P。若观测值为有规范要求的质量特性值,则总体的不合格品率的估计值为横坐标上不合格的观测值所在区间对应于纵坐标的区间长度注:观测值较多时,可对观测值分组进行如上步骤。机械工业部19941209批准1995-10-01实施JB/T3736.4-9499.99HMm輯輯辅辅辅镇宝排挂0008TIIIIIIIIHIEII99.9菲用图1正态概率纸15JB/T3736.4-943.2示例a.某种零件某一尺寸要求为10-005,测得此种48个零件的该尺寸见表1。mm10.05010.05210.04910.05310.05010.0510.05410.05210.04910.04910.05110.0490.05110.04810.04710.05010.05210.05310.05010.04610.05110.04810.05110.04910.05010.05010.04810.05210.04710.05110.05110.05010.05010.05110.04810.05010.05210.04910.05010.05410.050b.整理数据,见表2。表2观测值mm累积频数累积频率%10.04610.04710.0481347163310.04930.610.050132857.1410.05175.5110.0524285.7110.05395424610.0544897.96c.在正态概率纸上打点,画直线,见图2。d.观察图2中打的点和所画的直线,可推断观测值来自正态分布的总体e.由图2可见,均值p=10.0499mm,纵坐标值为0.135的点所对应的横坐标值为10.0444,故标准差a=10.0499-10.0440.0018(mm)。『.由图2可见,公差范围为0.045~0.055,区间以外的部分为不合格区,对应的纵坐标区间长度为总体不合格品率P=0.8%JB/T3736.4-9499.999.999.9.10.04510.c4710.04510.0510.05310.055图217JB/T3736.4-94附录正态概率纸的绘制(补充件)正态概率纸是将正态分布的测量结果在图纸上能形成一条直线的原理而设计成的。其横坐标是均匀的,表示观测值,纵坐标是不均匀的,表示标准正态分布的函数值。纵坐标值的确定方法如下:选有代表性的点a=0.01%,0.02%…,0.1%0.2%20%,22%,…,80%,81%…,99%,9.1%…,99.9%,9.91%,…,99,99%;查标准正态分布表,求出它们对应的分位数Z,列表如下(见表A1)。根据此表在纵坐标的一侧按均匀分度标出Z值,再在另侧标出与Z。值相对应的α值,此α值即为正态概率纸的纵坐标值正态概率纸的横坐标轴为均匀分度,见本标准图1。表A1标准正态分布分位数表%%210.000.1094.000.0211.001.2356.000.150.033.4312.0058.000.2013.00250.0514.0098.000.06001.00.36990.073.1916.000.9966.000.410.0817.000.950.4718.00880.2020.000,8474.000.6499.502.580.3022.00.710.402.65026.000.6028.000.5881.000.8899.900.2.4630.00082.000.920.8032.000.470.9084.001.36.001.0499.942.002.0538.000.311.0840.000.2587.001.1342,001.1744.0046,00101.281.4848,000.0591.00l.341.419.0052.00附录中位秩表(适用于观测值个数少于3时(补充件)表B1中位秩表56?|891011121314151617181920212223242526272829112.910.99.4837.46.76.15.65.214.8454.2|4.03836343.231302.82.726252.4|24231.426.42.8{01p8.o624.813.62.6.7o.90.3979.218.78.31.97.5.26.96.6646.15.9{573|50.0421|36.432128.625.923.621.78.6.416.4p5.414.613.8|13.1|12.512.01.51.010.610.29.89.49.4|68.6570.039335532429.827.5k5.623922.521.2k0.019.018.1|17.216.41.715.114.513.913.4129125173.663.6045.241.237.9k5.032.630.528.6524.223.021.9|20.920.019.2|18.4l17.?1.1J6.515.989.17.217.960.754850.046.042.539.537.04.7k327k30.929.3|27.926.625.424.323.32.421.520.7|20.019.3o.6h.971.44.558.854.00.0k65k3.5k0.8856.434.532831.329.928.627.426.325.324.42352.13550.0k46.94.2k41.839.737.735.934332931.530.329.128.127.126192683876.470.25.00.556553150.01734.842640.638.837.293385278372517.453.059255852750.042.545.3433|41.4|397381367|354341|30113986.480.074.469.563161.5582|55.252550.047.845.743.842140.539.037.636.494487.481.476.171.467.363.6|60.357.454.?|52.2|50.047.946.1|44.342.741239.84.8k8.32.6571.573.119.165.562.359.457|54352.15.049.145.34.7432289.1k83.68.874,570.7167.2164.161258656.253.951.950.048.246.665762.960.357.955.753.751850.05890.395.48].077.070.1167.164461.859.557.3553|53.41796.090.886.281.978.174.67.468.565.863.361.058.8|56.818291.386.982879.175.772.669.7671|64.662.360.219964|91.7|87.583.680076.773.7170.9|68.3|65.963.68续表B1011121314819202122232425262728297|71.969.467.096.892588.584.981.678.575672.970.496992989.085582.3|79.376.573.92397093189.486.182980.077.397.2|93.489886.683580.797.393.690.287.084.197493990.687.52797594.190997.69.3|2997.6附加说明本标准由机械工业部机械标准化研究所提出并归口。本标准由北京第一机床厂、机械工业部机械标准化研究所、沈阳第三机床厂、沈阳重型机器厂负责起草。本标准主要起草人张宝生、蒋鸿章、魏静、田井、肖泉湘、储如娅