统计基础知识第一讲.ppt

* Example #1 is for a 1 sided spec. In order to determine the Z value or the # of std. deviations between the mean and the spec limit I need to calculate Z by taking the (spec. - mean)/std. deviation. If I want the proportion defective or the # of calls that will take more than 7 min. to be answered I look up 0.97 (the Z value) on the normal table. If I want DPMO I multiply the probability of a defect or the proportion defective by 1,000,000 opportunities. The gray shaded area represents the proportion of defectives or calls w/greater than 7 min. response time. * Here I look under the Z column for 0.9 then I look across the top of the table for .07. The value in the cell is the probability or proportion defective. * For a 2 sided specification I have to do a little more work because I have the chance of having defects on both sides. Therefore I need to first calculate an upper and lower Z value. Use the table to find the proportion defective for both the upper and lower. Add the two together to find out the total proportion defective. Look up the total proportion defective on the Z table to determine the sigma score and/or I multiply the proportion defective by 1,000,000 to get DPMO. * Note: The first thing I should notice about this process is that the data is not centered. This average or mean value of my data is not the same as the center of the specification. In 6 Sigma we always center processes 1st and then work on reducing the variability. If this process were centered the Z score would improve to 0.47sigma from 0.37 sigma. Now I need to work on reducing the variability to improve my Z score. * 均值的计算方法 * 　　　方差和标准差的计算方法 　　 　　 * 例：离散分布 掷两颗骰子，出现的点数之和Ｙ的均值、方差和标准差： 例 * 1.常用的离散分布： 二项分布 泊松分布 超几何分布 7 常用的分布 2.常用的连续分布 正态分布 均匀分布 指数分布 对数正态分布 * 正态分布 一般，属于计量数据的特性值服从正态分布。 （1）正态分布的曲线 * 其中: -∞x∞ μ为正态均值，描述质量特性值分布的集中位置。 σ为正态方差，描述质量特性值x分布的分散程度。 记符号χ∽N（μ，σ2） 正态分布 （2）正