統計基礎及質量統計(文件)

　

【正文】 . 0 4 0 . 0 4 5 . 0 5 0 . 0 5 5 . 0 6 0 . 0 6 5 . 0 7 0 . 0 7 50 2 4 6 8 10. 0 0 0 . 0 2 5 . 0 5 0 . 0 7 5 . 1 0 0 . 1 2 5? MultiModal Shape(雙峰 ): ? Skewed Shape(偏一邊 ): Data can be rightskewed or leftskewed. This data is rightskewed – the right tail is longer than the left tail. Outliers:特異點 6s 47 練習 6s 48 品質統計圖表 方框圖 (Boxplots) Boxplots are a graphical tool valuable for paring the distributions of two or more groups (., different lots, shifts, operators, etc.). Each distribution on this chart consists of the following: ? A “box” representing the middle 50% of the data values. The length of the “box” is called the “Interquartile Range” (IQR). Inside the “box” is a line representing the median (50th percentile) of the data. ? Two “tails” which extend out to the minimum and maximum data values (assuming there are no outliers in the data). ? If the distance between the a data point and the nearer quartile is greater than , the data point is labeled as an outlier, and the “tail” on that side of the boxplot is shortened to the outermost data value within from the quartile. 6s 49 品質統計圖表 方框圖 (Boxplots) Median Maximum Data Value 75th Percentile 25th Percentile Outermost data values within of the 75th and 25th Percentiles. Outlier NO OUTLIERS IQR OUTLIERS Minimum Data Value Outlier 6s 50 品質統計圖表 方框圖 (Boxplots) EXAMPLE : Creating a Boxplot The figure below is a boxplot of the 100 plating thickness measurements. The histogram for the same data set is displayed for parison. 140 145 150 155 160 95 % Co nf i de nce In te r v al f or M ea n “ S ho rte s t Ha lf” De nses t r eg i on o f d at a, ( c on ta i ns 50 % o f d at a). 6s 51 品質統計圖表 方框圖 (Boxplots) Lot 1 Lot 2 Lot 3 Lot 4 Lot 5 Lot 6 Lot 7 130135140145150155160165170L o t 1 L o t 2 L o t 3 L o t 4 L o t 5 L o t 6 L o t 7L o t No .Plating thickness measurements collected from 7 lots of product. 6s 52 品質統計圖表 方框圖 (Boxplots) . 0 4 0 . 0 4 5 . 0 5 0 . 0 5 5 . 0 6 0 . 0 6 5 . 0 7 0 . 0 7 50 2 4 6 8 10.... . .90 95 100 105? MultiModal Shape: ? Skewed Shape: Outliers: 6s 53 練習 6s 54 品質統計圖表 柏拉圖 (Pareto Diagrams) While histograms are used to display the distribution of a set of continuous (measured) data, Pareto diagrams are used to display the distribution of discrete (counted) data, such as different types of defects. Pareto diagrams can also be used with continuous (measured) data, particularly in displaying variance ponents analysis results, as we will see later in this course. Pareto diagrams are a useful tool for determining which problems or types of problems are most severe or occur most frequently, hence should be given high priority for process improvement efforts. Pareto diagrams separate the significant vital few problems from the trivial many to help determine which problems to address first (and which to address later). 重點中找重點 ! 6s 55 Pareto圖分析 Pareto 圖 根據 frequency 欄的內容判斷各個缺陷影響的大小，並按從大到小的次序排列。 畫出各個點，每點代表一個給定值的輸出 “ 事件 ” 。 X 。 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： 500Anderson Darling 常態測試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：常態測試平方：值概率6s 32 神秘分佈 以寸 爲的神秘變數畫 的 常態概率圖 。 即使在資料不完全符合常態分配時 ， 分析結果也很接近 。 比例尺規 通常用來表示等距類別的數位資訊，但在測量範圍內有絕對零點。 設備 應用 環境 材料 油漆粘 附性差 應用表 從每一組中選擇一項 國籍 婚姻狀態 職業 責任人列表 有權使用數位相機 6s 8 順序 型衡量工具 順序尺規根據特性給名義型資料排序 (合格或不合格 )。 ? 示例中的名義尺規包括魚骨圖上的 “ 原因 ” , 是 /否 , 合格 /不合格 , 等等。 刻度盤位於表座的頂端，用來作差異對比等。 樣本通常爲所關心母體的子集 “ 母體參數 ” “ 樣本統計量 ” m = 母體均值 s = 樣本標準偏差 母體 s = 母體標準偏差 ~ 6s 21 ? 均值 : 一 組 值的算 術 平均 均值 : 反映所有值的影響 受極值影響嚴重 ? 中位數 : 反應 50% 的序一組數排序後居中的數 在計算中不必包含所有值 相對於極值具有 “可靠性 ” ? 眾數值 : 在一組資料中最常發生的值 nnn nxx??? 1Median (Mean平均 ) (Median中數 ) 眾數 Center(中心 ) 50% 50% 6s 22 1n)X(Xn1i2i?????s1n)X(Xn1i2i2?????s全距 : 在一組資料中，最高值和最低值 間的數值距離 變異 (s2): 每個資料點與均值的平均平方偏差 標準偏差 (s): 變異數的平方根 . 量化變動最常用的量 全距＝最大值－最小值 Spread(散佈 ) 6s 6s 23 The s Rule states how m and s can be used to describe the entire distribution: ? Roughly 6075% of the data are within ?1s of m. ? Roughly 9098% of the data are within ?2s of m. ? Roughly 99100% of the data are within ?3s of m. 6075% 9098% 99100% m m s m 2 s m + s m + 2 s m + 3 s m 3 s Spread(散佈 ) 6s 24 The shape of a distribution can be described by skewness 歪斜 (denoted by ?1) and by kurtosis凹擊平坦 (denoted by ?2). ?1 0 ?1 = 0 ?1 0 ?2 0 ?2 = 0 ?2 0 歪斜 凹擊平坦 Shape (形狀 ) 6s 25 N)(Xn1i2i2????msNX= 1i??Nimnx=xn1=ii?N) (X= N1=i2i??ms ? ?1 21?????nxxniis母體均值 樣本均值 母體標準偏差 樣本標準偏差 常用 計算公式 ~ 母體 變異 樣本 變異 1n)X(Xn1i2i2?????s~ 6s 26 The most important and useful distribution shape is called the Normal distribution, which is symmetric(對稱 ), unimodal(單峰 ), and free of outliers (沒有特異點 ): Normal Distribution常態分佈 “ 常態 ” 分佈是具有某些一致屬性的資料的分佈 這些屬性對理解基礎過程 （ 資料從該過程中收集 ） 的特徵非常有用 . 大多數自然現象和人爲過程都符合常態分配 ， 可以用常態分配表示 , 故大部份統計都假設是常態分佈 。 6s 27 A Normal probability plot is a cumulative distribution plot where the vertical scale is changed in such a way that data