【正文】 cookies. Manufacturing Environment製造環(huán)境 33 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 34 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 35 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: 222L o t2T o t a l 線班 ssss ???生產(chǎn)線 36 2 2 2 2 2 2 2 X 1 2 X 2 2 1 2 1 2 1 , , 。 27 A Normal probability plot is a cumulative distribution plot where the vertical scale is changed in such a way that data from a Normal distribution will form a straight line: Histogram Cumulative Distribution Normal Probability Plot 常態(tài)概率圖 Normal Distribution常態(tài)分佈 28 第一個屬性 : 只要知道下面兩項就可以完全描述常態(tài)分配 : 均值 標準差 常態(tài)分配 的好處 簡化 第一個分佈 第二個分佈 第三個分佈 這三個分佈有什麼不同 ? 29 常態(tài)曲線和其概率 4 3 2 1 0 1 2 3 4 40% 30% 20% 10% 0% % 第二個屬性 : 曲線下方的面積可以用於估計某“事件”發(fā)生的累積概率 95% 68% 樣本值的概率 距離均值的標準偏差數(shù) 得到兩值之間的值的累積概率 30 1 8 0 1 3 0 8 0 3 0 1 2 0 1 1 0 1 0 0 9 0 8 0 Stat Basic Statistics Display Descriptive Statistics Graphs Graphical Summary A2 描述性統(tǒng)計 圖形分析總結 變數(shù)：神秘 中值的 95%信賴區(qū)間 181。 特別不正常的分佈若假設為常態(tài)而去分析則有可能得到誤導結果 。 Roughly 99100% of the data are within ?3s of m. 6075% 9098% 99100% m m s m 2 s m + s m + 2 s m + 3 s m 3 s Spread(散佈 ) 24 The shape of a distribution can be described by skewness 歪斜 (denoted by ?1) and by kurtosis凹擊平坦 (denoted by ?2). ?1 0 ?1 = 0 ?1 0 ?2 0 ?2 = 0 ?2 0 歪斜 凹擊平坦 Shape (形狀 ) 25 N)(Xn1i2i2????msNX= 1i??Nimnx=xn1=ii?N) (X= N1=i2i? ? ms ? ?1 21?????nxxniis母體均值 樣本均值 母體標準偏差 樣本標準偏差 常用 計算公式 ~ 母體 變異 樣本 變異 1n)X(Xn1i2i2?????s~ 26 The most important and useful distribution shape is called the Normal distribution, which is symmetric(對稱 ), unimodal(單峰 ), and free of outliers (沒有特異點 ): Normal Distribution常態(tài)分佈 “ 常態(tài) ” 分佈是具有某些一致屬性的資料的分佈 這些屬性對理解基礎過程 （ 資料從該過程中收集 ） 的特徵非常有用 . 大多數(shù)自然現(xiàn)象和人爲過程都符合常態(tài)分配 ， 可以用常態(tài)分配表示 , 故大部份統(tǒng)計都假設是常態(tài)分佈 。 Roughly 6075% of the data are within ?1s of m. 間距尺規(guī)舉例 : (沒有絕對零點 ) 比例尺規(guī)舉例 : (有絕對零點 ) 3. 相對速度 1. 直尺 2. 恒定速度下位置 相對於時間的值 爲變數(shù)的函數(shù)值 表座 11 基礎 品質(zhì) 統(tǒng)計學 12 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 13 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 (People) +變異 (Equipment) +變異 (Information) 變異 (Variation) 我們觀察到的變異 ,是在過程中各種擾動累積起來的 . 14 變異 (Variation) 參數(shù) X X X X X X X X X 量測值 分佈 多數(shù)在此 少數(shù)在此 Center均值 Spread散佈 雖然變異是隨機的 ,但他們的隨機性通常有模式存在 ,這種模式可用統(tǒng)計上的分佈 (Distribution)來形容 .如此變異加以統(tǒng)計分析 ,便可有某種程度的預測性存在並易於被理解或控制 . 15 變異 (Variation) 中心 Center: 數(shù)據(jù)最集中在何處 ? 散佈 Spread:數(shù)據(jù)變異程度及分散狀況如何 ? 形狀 Shape:分佈是否對稱 ?扁平 ?凹擊 ? 是否有異常區(qū) 描述 分佈 (Distribution) Shape形狀 Center中心 Spread散佈 16 變異 (Variation) 變異可以是穩(wěn)定 (Stable)或 不 穩(wěn)定 (Unstable)的 . 穩(wěn)定變異 :變化的分佈較具預測性及一致性 ,對時間而言具可預測性 不穩(wěn)定變異 :對時間而言不具可預測性 PROCESS 1 Stable Variation穩(wěn)定 Part T h i c k n e s s PROCESS 2 Unstable Variation不 穩(wěn)定 Part Distribution Distribution T h i c k n e s s 17 變異 (Variation) 在製造過程中 ,有變異都是不好 .問題是我們能容忍到何種範圍 .我們能容忍的變異是具有以下兩項特徵 : Time P a r a m e t e r STABLE (., consistent and predictable over time). CAPABLE (., small variation pared to the product specifications.) Product Specifications Parameter Distribution 穩(wěn)定 散佈小 18 控制 變異 (Variation) 1. Characterize 2. Improve 3. Control 瞭解過程 : 使制程更好 : 保持穩(wěn)定並維持高制程能力 ?過程由時間來看是否穩(wěn) ? ?制程能力是否能滿足目標規(guī)格 ? ? 確認並除去不穩(wěn)定原因 ? 確認並降低變異程度使?jié)M足規(guī)格 ? 持續(xù)監(jiān)視及控制過程的變異源 特徵化 改善 控制 19 因為用抽樣統(tǒng)計 ,其結果只是估計 , 和真實可能有差異 .