【文章內(nèi)容簡介】 2 3 4 5 * * * * * * * * * * Distribution of Individual Lot Distribution of Lot Means Overall Distribution of Combined Lots Variation Within Each Lot Variation Between Lots Total Variation 統(tǒng)計 37 Jason Lee 2023/07/04 The different variances of a Lot/Batch Manufacturing process form a hierarchy 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 ssss ???生產(chǎn)線 統(tǒng)計 38 Jason Lee 2023/07/04 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(shù)可相加 , 標準差則不能相加 輸入變數(shù)變異數(shù)相加計算輸出中的總變異數(shù) 所以 那麼 引起的變異數(shù)輸入變數(shù) 引起的變異數(shù)輸入變數(shù) 過程輸出的變異數(shù) 如果 s s s s s s s s 統(tǒng)計 39 Jason Lee 2023/07/04 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: 統(tǒng)計 40 Jason Lee 2023/07/04 實用品質(zhì)統(tǒng)計工具 直方圖 (Histograms) 柏拉圖 (Pareto Diagrams) 散佈圖 (Scatterplots) 趨勢圖 (Trend Charts) 統(tǒng)計 41 Jason Lee 2023/07/04 品質(zhì)統(tǒng)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(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 ) x統(tǒng)計 42 Jason Lee 2023/07/04 : : . . . : . . :: : :::.:: :: . :: . : .. .:.:.:::::::::::::::.::.::::..: : . +++++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(jié)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 ” 。 統(tǒng)計 43 Jason Lee 2023/07/04 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)在設想將其分組後歸入“區(qū)間”。泵流量點落入指定區(qū)間的次數(shù)決定區(qū)間條的高度。 頻率 加侖 /分鐘 統(tǒng)計 44 Jason Lee 2023/07/04 品質(zhì)統(tǒng)計圖表 直方圖 (Histograms) 140 145 150 155 160統(tǒng)計 45 Jason Lee 2023/07/04 品質(zhì)統(tǒng)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 統(tǒng)計 46 Jason Lee 2023/07/04 品質(zhì)統(tǒng)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 ! 統(tǒng)計 47 Jason Lee 2023/07/04 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。 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?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(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)計圖表 柏拉圖 (Pareto Diagrams) 統(tǒng)計 48 Jason Lee 2023/07/04 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。 下圖使用同樣的命令，沒有從屬變數(shù)。 當選擇每頁一張圖時 ， 所有的圖的計數(shù) (左軸 )刻度相同 。 右側(cè)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(xiàn)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