統計基礎及質量統計(已改無錯字)

　　

【正文】 roblems 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。 最後一組總是標有 “ 其他 ” ， 並以默認方式包括所有缺陷的分類計算 ， 這幾類缺陷非常少 ， 它們占總缺陷的 5% 以下 。 該圖右側 Y 軸表示占總缺陷的百分比 ，左側 Y 軸表示缺陷數 。 紅線 (在螢幕上可以看到 ) 表示累積百分比，而直方圖表示每類缺陷的頻率 (占總量的百分比 ) 。在圖的下方列出所有的值 百分比 缺陷的 Pareto圖 缺陷 計數 274 59 43 19 10 18 百分比 累積百分比％ 400 300 200 100 0 100 80 60 40 20 0 品質統計圖表 柏拉圖 (Pareto Diagrams) 6s 56 Pareto圖分析 : 創建一個加權的 Pareto圖 通過指定金額 /缺陷或用其他的加權方法，可以給次數加權。 列在 C1中的缺陷發生次數的價格列在 C3 (value) 中 ， 價格乘以次數等於這類缺陷的費用 (c4) 。 繪製費用（ cost） 曲線圖，而不是繪製次數（ count） 圖， 這樣可以更好地說明每個缺陷對業務的影響。 缺陷的 Pareto圖 缺陷 計數 百分比 累積百分比％ 6000 5000 4000 3000 2023 1000 0 100 80 60 40 20 0 品質統計圖表 柏拉圖 (Pareto Diagrams) 6s 57 層別 Pareto圖 : 解釋分組資料 上圖使用了一個 By Variable（ 從屬變數），所有的圖都在一頁上。 下圖使用同樣的命令，沒有從屬變數。 當選擇每頁一張圖時 ， 所有的圖的計數 (左軸 )刻度相同 。 右側的百分比只反映該圖占總體的百分比 。 這些圖表明 ， 70%的記錄缺陷是刮傷和剝落的 (下部 )， 約有一半的缺陷是夜班人員記錄的 (上右圖 )。 此外，記錄缺陷是刮傷和剝落的比例，對白班和夜班的 來說似乎也差不多。然而，晚班和周末班出現的缺陷樣式是不同的。 裂紋 Pareto圖 白班 晚班 夜班 周末班 刮傷 剝落 其他 污點 15 10 5 0 15 10 5 0 15 10 5 0 15 10 5 0 裂紋 Pareto圖 40 30 20 10 0 100 80 60 40 20 0 缺陷 計數 15 13 6 6 百分比 累積百分比％ 品質統計圖表 柏拉圖 (Pareto Diagrams) 6s 58 練習 6s 59 品質統計圖表 散佈圖 (Scatterplots) Until now, all the graphical tools we39。ve discussed have been for examining the distribution of a single process characteristic. The scatterplot is a graphical tool for examining the relationship between two process characteristics. A scatterplot is an XY plot of one variable versus another. Each unit of product usually has many characteristics, process input variables, etc. One objective might be to see whether two variables or characteristics are related to each other (., to see what happens to one of the variables when the other variable changes). This relationship between two variables is called correlation. Scatterplots can help us answer this type of question. 6s 60 品質統計圖表 散佈圖 (Scatterplots) Acid Age Etch Rate Acid Age Etch Rate Acid Age Etch Rate 13 13 15 18 30 23 18 19 31 19 7 4 12 25 21 24 29 26 28 20 9 19 6 14 9 9 27 25 30 31 051015202530350 1 2 3 4 5 6Ac i d Ag e6s 61 品質統計圖表 散佈圖 (Scatterplots) In addition to telling us whether or not two variables are related, scatterplots can tell us how they are related, and the strength of the relationship: Strong Positive Correlation 強正相關 No Correlation無關 Weak Negative Correlation 弱負相關 Weak Positive Correlation 弱正相關 Strong Negative Correlation 強負相關 6s 62 品質統計圖表 散佈圖 (Scatterplots) In addition, scatterplots are an excellent tool for determining the type of relationship between the two variables, as well as looking for outliers: Linear Relationship 線性相關 Outliers 特異 NonLinear Relationship 非線性相關 6s 63 品質統計圖表 散佈圖 (Scatterplots) Correlation and Causation We must always take care not to confuse correlation with causation. The fact that two characteristics are correlated does not prove that one causes the other. Both may be related to some other factor which is the true root cause. Number of Televisions Number of Traffic Accidents 1970 1990 But is there a causeeffect relationship between the two? ? Did the increase in TV’s cause the number of accidents to go up? (Not likely.) ? Did the increase in traffic accidents cause people to buy more TV’s? (Not likely, either.) 6s 64 練習 6s 65 品質統計圖表 趨勢圖 (Trend Charts) Trend Charts Stability: A process is stable if its mean and standard deviation are constant and predictable over time. A disadvantage of histograms and normal probability plots is that they cannot be used to determine whether the process is stable over time. A plot of the data in time order will allow us to do that. These timeordered plots, called Trend charts and Control charts are essential when examining the stability of a distribution over time. A trend chart or a control chart can detect instability if it exists. Control charts, which are a special kind of trend chart, are discussed in detail separately in a later course module. 可看出穩定性及預測性 6s 66 品質統計圖表 趨勢圖 (Trend Charts) The table below contains average plating thickness measurements taken from 21 lots of product. Below that is a trend chart of the