【文章內(nèi)容簡(jiǎn)介】 ld 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) ) x40 : : . . . : . . :: : :::.:: :: . :: . : .. .:.:.:::::::::::::::.::.::::..: : . +++++加侖 /分鐘 點(diǎn)圖分佈 設(shè)想有一個(gè)泵流量爲(wèi) 50加侖 /分鐘的計(jì)量泵 。 按照節(jié)拍對(duì)泵的實(shí)際流量進(jìn)行了 100次獨(dú)立測(cè)量 。 畫出各個(gè)點(diǎn)，每點(diǎn)代表一個(gè)給定值的輸出 “ 事件 ” 。當(dāng)點(diǎn)聚集起來(lái)時(shí)，泵的實(shí)際性能狀況可以看作泵流量的 “ 分佈 ” 。 41 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”。泵流量點(diǎn)落入指定區(qū)間的次數(shù)決定區(qū)間條的高度。 頻率 加侖 /分鐘 42 品質(zhì)統(tǒng)計(jì)圖表 直方圖 (Histograms) 140 145 150 155 16043 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) 44 練習(xí) 45 品質(zhì)統(tǒng)計(jì)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. 46 品質(zhì)統(tǒng)計(jì)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 47 品質(zhì)統(tǒng)計(jì)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% Conf i denc e Interv al f or Mean “ S hor tes t Hal f” Dens es t region of data , ( c ontai ns 50% of data ) . 48 品質(zhì)統(tǒng)計(jì)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. 49 品質(zhì)統(tǒng)計(jì)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: 50 練習(xí) 51 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) ! 52 Pareto圖分析 Pareto 圖 根據(jù) frequency 欄的內(nèi)容判斷各個(gè)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(biāo)有 “ 其他 ” ， 並以默認(rèn)方式包括所有缺陷的分類計(jì)算 ， 這幾類缺陷非常少 ， 它們占總?cè)毕莸? 5% 以下 。 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) 。 紅線 (在螢?zāi)簧峡梢钥吹?) 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(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) 53 Pareto圖分析 : 創(chuàng)建一個(gè)加權(quán)的 Pareto圖 通過(guò)指定金額 /缺陷或用其他的加權(quán)方法，可以給次數(shù)加權(quán)。 列在 C1中的缺陷發(fā)生次數(shù)的價(jià)格列在 C3 (value) 中 ， 價(jià)格乘以次數(shù)等於這類缺陷的費(fèi)用 (c4) 。 繪製費(fèi)用（ cost） 曲線圖，而不是繪製次數(shù)（ count） 圖， 這樣可以更好地說(shuō)明每個(gè)缺陷對(duì)業(yè)務(wù)的影響。 缺陷的 Pareto圖 缺陷 計(jì)數(shù) 百分比