【正文】 al Distribution常態(tài)分佈 26 第一個屬性 : 只要知道下面兩項就可以完全描述常態(tài)分配 : 均值 標準差 常態(tài)分配 的好處 簡化 第一個分佈 第二個分佈 第三個分佈 這三個分佈有什麼不同 ? 27 常態(tài)曲線和其概率 4 3 2 1 0 1 2 3 4 40% 30% 20% 10% 0% % 第二個屬性 : 曲線下方的面積可以用於估計某“事件”發(fā)生的累積概率 95% 68% 樣本值的概率 距離均值的標準偏差數(shù) 得到兩值之間的值的累積概率 28 常態(tài)概率圖 1 3 0 1 2 0 1 1 0 1 0 0 9 0 8 0 7 0 6 0 3 0 0 2 0 0 1 0 0 0 C 2 常態(tài)概率圖 頻率 1 1 0 1 0 0 9 0 8 0 7 0 6 0 5 0 4 0 3 0 2 0 1 0 0 5 0 0 C 1 常態(tài)概率圖 頻率 8 0 7 0 6 0 5 0 4 0 3 0 2 0 1 0 0 3 0 0 2 0 0 1 0 0 0 C 3 常態(tài)概率圖 頻率 1 3 0 1 2 0 1 1 0 1 0 0 9 0 8 0 7 0 6 0 . 9 9 9 . 9 9 . 9 5 . 8 0 . 5 0 . 2 0 . 0 5 . 0 1 . 0 0 1 平均： 70 標準偏差： 10 資料個數(shù)： 500 AndersonDarling常態(tài)測試 A平方 : P值 : 正偏斜分佈 概率 正偏斜 1 0 6 9 6 8 6 7 6 6 6 5 6 4 6 3 6 2 6 . 9 9 9 . 9 9 . 9 5 . 8 0 . 5 0 . 2 0 . 0 5 . 0 1 . 0 0 1 常態(tài)分配 常態(tài) 概率 平均值： 70 標準偏差 :10 資料個數(shù)： 500 AndersonDarling常態(tài)測試 A平方 : P值 : 我們可以用常態(tài)概率圖檢驗一組給定的資料是否可以描述爲“常態(tài)” 如果一個分佈接近常態(tài)分配，則常態(tài)概率圖將爲一條直線。 8 07 06 05 04 03 02 0100.9 9 9. 9 9. 9 5. 8 0. 5 0. 2 0. 0 5.0 1. 0 0 1負偏斜分佈負偏斜平均： 70標準偏差： 10資料個數(shù)： 500Anderson Darling 常態(tài)測試A 平方： P 值 :概率負偏斜分佈負偏斜平均：標準偏差：資料個數(shù)：常態(tài)測試平方：值概率29 資料收集時的重點 How the data are collected affects the statistical appropriateness and analysis of a data set(資料如何收集可影響統(tǒng)計的適切性 ). Conclusions from properly collected data can be applied more generally to the process and output. Inappropriately collected data CANNOT be used to draw valid conclusions about a process. Some aspects of proper data collection that must be accounted for are: The manufacturing environment(製程環(huán)境 )from which the data are collected. When products are manufactured in batches or lots, the data must be collected from several batches or lots. Randomization(隨機 ). When the data collection is not randomized, statistical analysis may lead to faulty conclusions. 30 Continuous Manufacturing (連續(xù) )occurs when an operation is performed on one unit of product at a time. An assembly line is typical of a continuous manufacturing environment, where each unit of product is worked on individually and a continuous stream of finished products roll off the line. The automotive industry is one example of Continuous Manufacturing. Other examples of continuously manufactured product are: ? television sets, ? fast food hamburgers, ? puters. Lot/Batch Manufacturing (批次 ) occurs occurs when operations are performed on products in batches, groups, or lots. The final product es off the line in lots, instead of a stream of individual parts. Product within the same lot are processed together, and receive the same treatment while inprocess. Lot/Batch Manufacturing is typical of the semiconductor industry and many of its suppliers. Other examples of lot/batch manufactured product include: ? chemicals, ? semiconductor packages, ? cookies. 生產製造環(huán)境 31 In Continuous Manufacturing the most important variation is between parts In Lot/Batch Manufacturing, the variation can occur between the parts in a lot and between the lots: ? Product within the same lot is manufactured together. ? Product from different lots are manufactured separately. Because of this, each lot has a different distribution. This is important because Continuous Manufacturing is a basic assumption for many of the standard statistical methods found in most textbooks or QC handbooks. These methods are not appropriate for Lot/Batch Manufacturing. Different statistical methods need to be used to take into account the several sources of variation in Lot/Batch Manufacturing. 要注意 : 連續(xù)和批量生產所用的統(tǒng)計方法有些不同 32 With Lot/Batch Manufacturing, each lot has a different mean. Due to random processing fluctuations, these lots will vary even though the process may be stable. This results in several “l(fā)evels” of distributions, each level with its own variance and mean: ? A distribution of units of product within the same lot. ? A distribution of the means of different lots. ? The total distribution of all units of product across all lots. Lot X 1 2 3 4 5 * * * * * * * * * * Distribution of Individual Lot Distribution of Lot Means Overall Distribution of Combined Lots Variation Within Each Lot Variation Between Lots Total Variation 33 2 2 2 2 2 2 2 X 1 2 X 2 2 1 2 1 2 1 , , 。 X 。 X 。 X X X X s + = + = = = = 總總 總 6s原則 變異數(shù)可相加 , 標準差則不能相加 輸入變數(shù)變異數(shù)相加計算輸出中的總變異數(shù) 所以 那麼 引起的變異數(shù)輸入變數(shù) 引起的變異數(shù)輸入變數(shù) 過程輸出的變異數(shù) 如果 s s s s s s s s 34 1 2 3 4 5 6 Lot sWithin is small sLot is large process has small withinlot variation and large lottolot variation (which is very mon), data values from the same lot will be highly correlated, while data from different lots will be independent: 35 實用品質統(tǒng)計工具 直方圖 (Histograms) 柏拉圖 (Pareto Diagrams) 散佈圖 (Scatterplots) 趨勢圖 (Trend Charts) 36 品質統(tǒng)計圖表 直方圖 (Histograms) Histograms provide a visual description of the distribution of a set of data. A histogram should be used in conjunction with summary statistics such as and s. A histogram can be used to: ? Display the distribution of the data(現(xiàn)示數(shù)據(jù)的分佈 ).