【正文】 直方圖 (Histograms) 柏拉圖 (Pareto Diagrams) 散佈圖 (Scatterplots) 趨勢圖 (Trend Charts) 36 品質(zhì)統(tǒng)計(jì)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 ). ? Provide a graphical indication of the center, spread, and shape of the data distribution (較定性地顯示數(shù)據(jù)的均值 ,散佈及形狀 ). ? Clarify any numerical summary statistics (which sometimes obscure information). (顯示較模糊的統(tǒng)計(jì)結(jié)果 ). ? Look for outliers data points that do not fit the distribution of the rest of the data. (顯示異常點(diǎn) ) x37 : : . . . : . . :: : :::.:: :: . :: . : .. .:.:.:::::::::::::::.::.::::..: : . +++++加侖 /分鐘 點(diǎn)圖分佈 設(shè)想有一個泵流量爲(wèi) 50加侖 /分鐘的計(jì)量泵 。 畫出各個點(diǎn)，每點(diǎn)代表一個給定值的輸出 “ 事件 ” 。 38 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(xiàn)在設(shè)想將其分組後歸入“區(qū)間”。 頻率 加侖 /分鐘 39 品質(zhì)統(tǒng)計(jì)圖表 直方圖 (Histograms) 140 145 150 155 16040 品質(zhì)統(tǒng)計(jì)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(diǎn) 41 品質(zhì)統(tǒng)計(jì)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(diǎn)中找重點(diǎn) ! 42 Pareto圖分析 Pareto 圖 根據(jù) frequency 欄的內(nèi)容判斷各個缺陷影響的大小，並按從大到小的次序排列。 該圖右側(cè) Y 軸表示占總?cè)毕莸陌俜直?，左側(cè) Y 軸表示缺陷數(shù) 。在圖的下方列出所有的值 百分比 缺陷的 Pareto圖 缺陷 計(jì)數(shù) 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(zhì)統(tǒng)計(jì)圖表 柏拉圖 (Pareto Diagrams) 43 層別 Pareto圖 : 解釋分組資料 上圖使用了一個 By Variable（ 從屬變數(shù)），所有的圖都在一頁上。 當(dāng)選擇每頁一張圖時(shí) ， 所有的圖的計(jì)數(shù) (左軸 )刻度相同 。 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 )。然而，晚班和周末班出現(xiàn)的缺陷樣式是不同的。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. 45 品質(zhì)統(tǒng)計(jì)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 e46 品質(zhì)統(tǒng)計(jì)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(qiáng)正相關(guān) No Correlation無關(guān) Weak Negative Correlation 弱負(fù)相關(guān) Weak Positive Correlation 弱正相關(guān) Strong Negative Correlation 強(qiáng)負(fù)相關(guān) 47 品質(zhì)統(tǒng)計(jì)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(guān) Outliers 特異 NonLinear Relationship 非線性相關(guān) 48 品質(zhì)統(tǒng)計(jì)圖表 散佈圖 (Scatterplots) Correlation and Causation We must always take care not to conf