【正文】 統(tǒng)計圖表 散佈圖 (Scatterplots) Until now, all the graphical tools we39。 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。 右側的百分比只反映該圖占總體的百分比 。 下圖使用同樣的命令，沒有從屬變數(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 ) 。 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 。泵流量點落入指定區(qū)間的次數(shù)決定區(qū)間條的高度。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”。 按照節(jié)拍對泵的實際流量進行了 100次獨立測量 。 X 。 8 07 06 05 04 03 02 0100.9 9 9. 9 9. 9 5. 8 0. 5 0. 2 0. 0 5.0 1. 0 0 1負偏斜分佈負偏斜平均： 70標準偏差： 10資料個數(shù)： 500Anderson Darling 常態(tài)測試A 平方： P 值 :概率負偏斜分佈負偏斜平均：標準偏差：資料個數(shù)：常態(tài)測試平方：值概率29 資料收集時的重點 How the data are collected affects the statistical appropriateness and analysis of a data set(資料如何收集可影響統(tǒng)計的適切性 ). Conclusions from properly collected data can be applied more generally to the process and output. Inappropriately collected data CANNOT be used to draw valid conclusions about a process. Some aspects of proper data collection that must be accounted for are: The manufacturing environment(製程環(huán)境 )from which the data are collected. When products are manufactured in batches or lots, the data must be collected from several batches or lots. Randomization(隨機 ). When the data collection is not randomized, statistical analysis may lead to faulty conclusions. 30 Continuous Manufacturing (連續(xù) )occurs when an operation is performed on one unit of product at a time. An assembly line is typical of a continuous manufacturing environment, where each unit of product is worked on individually and a continuous stream of finished products roll off the line. The automotive industry is one example of Continuous Manufacturing. Other examples of continuously manufactured product are: ? television sets, ? fast food hamburgers, ? puters. Lot/Batch Manufacturing (批次 ) occurs occurs when operations are performed on products in batches, groups, or lots. The final product es off the line in lots, instead of a stream of individual parts. Product within the same lot are processed together, and receive the same treatment while inprocess. Lot/Batch Manufacturing is typical of the semiconductor industry and many of its suppliers. Other examples of lot/batch manufactured product include: ? chemicals, ? semiconductor packages, ? cookies. 生產(chǎn)製造環(huán)境 31 In Continuous Manufacturing the most important variation is between parts In Lot/Batch Manufacturing, the variation can occur between the parts in a lot and between the lots: ? Product within the same lot is manufactured together. ? Product from different lots are manufactured separately. Because of this, each lot has a different distribution. This is important because Continuous Manufacturing is a basic assumption for many of the standard statistical methods found in most textbooks or QC handbooks. These methods are not appropriate for Lot/Batch Manufacturing. Different statistical methods need to be used to take into account the several sources of variation in Lot/Batch Manufacturing. 要注意 : 連續(xù)和批量生產(chǎn)所用的統(tǒng)計方法有些不同 32 With Lot/Batch Manufacturing, each lot has a different mean. Due to random processing fluctuations, these lots will vary even though the process may be stable. This results in several “l(fā)evels” of distributions, each level with its own variance and mean: ? A distribution of units of product within the same lot. ? A distribution of the means of different lots. ? The total distribution of all units of product across all lots. Lot X 1 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 33 2 2 2 2 2 2 2 X 1 2 X 2 2 1 2 1 2 1 , , 。 有 數(shù)學 技術可 將 其 轉變成常態(tài)分佈 來作分析 。 即使在資料不完全符合常態(tài)分配時 ， 分析結果也很接近 。1 統(tǒng)計運用及品管實務工具 資料數(shù)據(jù) 基礎統(tǒng)計運用概念 生產(chǎn)製造環(huán)境 實用品質統(tǒng)計工具 製程能力分析 與 SPC統(tǒng)計 製程 控制 2 資料及數(shù)據(jù) 3 你想瞭解什麼 ? 資訊源 : 分組 離散型 名義型 順序型 間距型 “ 資料本身並不能提供資訊 —— 必頇對資料加以處理以後才能得到資訊 , 而處理資料的工具就是統(tǒng)計學 ” . 衡量 連續(xù)型 比率型 ● 文字的 (A to Z) ● 圖示的 ● 口頭的 ● 數(shù)位的 (09) 數(shù)據(jù) 4 FAIL PASS 計時器 NOGO GO 數(shù)量 單價 說明 總價 1 $ $ 3 $ $ 10 $ $ 2 $ $ 裝貨單 離散型資料和連續(xù)型資料 電氣電路 溫度 溫度計 連續(xù)型 離散型 卡尺 錯誤 5 ? 離散型資料 (通常 ) ? 分組 / 分類 ? 是 /否 , 合格 / 不合格 ? 不能計算 ? 離散型資料 ? 分級 ? 很少用 ? 很難加以計算 ? 連續(xù)型資料 ? 最常見的尺規(guī) ? 計算時要很小心 ? 連續(xù)型資料 ? 比例關係 ? 可應用演算法的多數(shù)公式 ? 分類 ? 標簽 ? 第一、第二、第三 ? 相對高度 ? 字母順序 ? 1234 ? 溫度計 ? 刻度盤 ? 速度 = 距離 /時間 ? 直尺 衡量工具 分類 說明 例子 衡量工具 分類 名義型 :不相關類 , 只代表符合條件或不符合條件個體數(shù) . 順序型 :順序類 ,但沒有各類間隔的資訊 . 間距型 :順序類 ,兩類之間間隔相等 ,但沒有絕對零點 . 比例型 :順序類 ,兩 類之間間隔相等 , 同時存在絕對零點 . . 離 散 型 連 續(xù) 型 6 $ $ 連續(xù)資料的優(yōu)勢 連續(xù)的 信息量少 信息量多 7 基礎統(tǒng)計運用概念 8 變異 (Variation) 當我們從一過程中收集數(shù)據(jù) ,會發(fā)現(xiàn)數(shù)據(jù)不會永遠相同 ,因為變異 (Variation)在過程中隨時存在 製造流程 Step 1 Step 2 Step 3 Process Output Output of Process Step Equipment Materials Environment People Methods Information 9 變異 (Process) =變異 (Step 1) +變異 (Step 2) +變異 (Step 3) + . . . 變異 ( Process Step) = 變異 (Methods) +變異 (Materials) +變異 (Environment) +變異 (Peo