統計基礎及質量統計(編輯修改稿)

　

【文章內容簡介】 called nesting. Data collected from such processes usually have what is called a nested data structure. 1 1 2 1 2 3 4 5 1 2 3 4 5 LOTS 班 2 1 2 1 2 3 4 5 1 2 3 4 5 Each of the levels in the nested structure corresponds to a single variance. With a nested data set from this process, we need to take each source of variation into account when collecting data to ensure the total process variation is represented in our data set: 222Lot2Total 線班 sss ???生產線 6s 39 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 變異數可相加 , 標準差則不能相加 輸入變數變異數相加計算輸出中的總變異數 所以 那麼 引起的變異數輸入變數 引起的變異數輸入變數 過程輸出的變異數 如果 s s s s s s s s 6s 40 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: 6s 41 品質統計圖表 直方圖 (Histograms) 方框圖 (Boxplots) 柏拉圖 (Pareto Diagrams) 散佈圖 (Scatterplots) 趨勢圖 (Trend Charts) 6s 42 品質統計圖表 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(現示數據的分佈 ). ? Provide a graphical indication of the center, spread, and shape of the data distribution (較定性地顯示數據的均值 ,散佈及形狀 ). ? Clarify any numerical summary statistics (which sometimes obscure information). (顯示較模糊的統計結果 ). ? Look for outliers data points that do not fit the distribution of the rest of the data. (顯示異常點 ) x6s 43 : : . . . : . . :: : :::.:: :: . :: . : .. .:.:.:::::::::::::::.::.::::..: : . +++++加侖 /分鐘 點圖分佈 設想有一個泵流量爲 50加侖 /分鐘的計量泵 。 按照節拍對泵的實際流量進行了 100次獨立測量 。 畫出各個點，每點代表一個給定值的輸出 “ 事件 ” 。當點聚集起來時，泵的實際性能狀況可以看作泵流量的“分佈”。 6s 44 5 1 .3 5 0 . 8 5 0 . 3 4 9 . 8 4 9 . 3 4 8 . 8 4 0 3 0 2 0 1 0 0 直方圖分佈 還是這些資料，現在設想將其分組後歸入“區間”。泵流量點落入指定區間的次數決定區間條的高度。 頻率 加侖 /分鐘 6s 45 品質統計圖表 直方圖 (Histograms) 140 145 150 155 1606s 46 品質統計圖表 直方圖 (Histograms) . 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 p