【正文】 我們採用措施修正控制圖表中非隨機(jī)型式，這是成功使用 SPC的關(guān)鍵 。 統(tǒng)計(jì) 67 Jason Lee 2023/07/04 什麼是 統(tǒng)計(jì) 製程 控制 （ SPC） 所有過程都有固有變動（由於一般原因）和非固有變動（由於特殊原因）， 我們使用 SPC來監(jiān)測並改善過程 。 :製程中只有共同原因的變異 此種現(xiàn)象是穩(wěn)定的 ” 不良 ” 。 右側(cè)的百分比只反映該圖占總體的百分比 。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。 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(fù)偏斜分佈負(fù)偏斜平均： 70標(biāo)準(zhǔn)偏差： 10資料個(gè)數(shù)： 500Anderson Darling 常態(tài)測試A 平方： P 值 :概率負(fù)偏斜分佈負(fù)偏斜平均：標(biāo)準(zhǔn)偏差：資料個(gè)數(shù)：常態(tài)測試平方：值概率統(tǒng)計(jì) 33 Jason Lee 2023/07/04 資料收集時(shí)的重點(diǎn) 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(jì)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(jī) ). When the data collection is not randomized, statistical analysis may lead to faulty conclusions. 統(tǒng)計(jì) 34 Jason Lee 2023/07/04 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 統(tǒng)計(jì) 35 Jason Lee 2023/07/04 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(jì)方法有些不同 統(tǒng)計(jì) 36 Jason Lee 2023/07/04 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 統(tǒng)計(jì) 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(jì) 38 Jason Lee 2023/07/04 2 2 2 2 2 2 2 X 1 2 X 2 2 1 2 1 2 1 , , 。 樣本通常爲(wèi)所關(guān)心母體的子集 “ 母體參數(shù) ” “ 樣本統(tǒng)計(jì)量 ” m = 母體均值 s = 樣本標(biāo)準(zhǔn)偏差 母體 s = 母體標(biāo)準(zhǔn)偏差 ~ 統(tǒng)計(jì) 21 Jason Lee 2023/07/04 抽樣方法 抽樣方法 上面介紹了幾種從母體中抽樣的方式 隨機(jī)性 從母體中抽取的樣本設(shè)計(jì)應(yīng)使母體中每一個(gè)都有同等機(jī)會抽中 . 代表性 作為同一母體中其他樣本的實(shí)例 . 系統(tǒng)隨機(jī)抽樣 分組抽樣 每一小時(shí)在該點(diǎn) 抽 3個(gè)樣本 隨機(jī)抽樣 每個(gè)均有被選上的相等機(jī)會 層別式抽樣 母體被“層別”成幾個(gè)組 ,在每個(gè)組內(nèi)隨機(jī)選擇 . 行進(jìn)中的過程 每隔 n個(gè)柚樣 統(tǒng)計(jì) 22 Jason Lee 2023/07/04 一般準(zhǔn)則 計(jì)數(shù)數(shù)據(jù) :50100 計(jì)量數(shù)據(jù) :每個(gè)分組最少是 30 統(tǒng)計(jì) 23 Jason Lee 2023/07/04 ? 均值 : 一 組 值的算 術(shù) 平均 均值 : 反映所有值的影響 受極值影響嚴(yán)重 ? 中位數(shù) : 反應(yīng) 50% 的序一組數(shù)排序後居中的數(shù) 在計(jì)算中不必包含所有值 相對於極值具有 “可靠性 ” ? 眾數(shù)值 : 在一組資料中最常發(fā)生的值 nnn nxx??? 1Median (Mean平均 ) (Median中數(shù) ) 眾數(shù) Center(中心 ) 50% 50% 統(tǒng)計(jì) 24 Jason Lee 2023/07/04 1n)X(Xn1i2i?????s1n)X(Xn1i2i2?????全距 : 在一組資料中，最高值和最低值 間的數(shù)值距離 變異 (s2): 每個(gè)資料點(diǎn)與均值的平均平方偏差 標(biāo)準(zhǔn)偏差 (s): 變異數(shù)的平方根 . 量化變動最常用的量 全距＝最大值－最小值 Spread(散佈 ) 6s 統(tǒng)計(jì) 25 Jason Lee 2023/07/04 The s Rule states how m and s can be used to describe the entire distribution: ? 示例中的名義尺規(guī)包括魚骨圖上的 “ 原因 ” , 是 /否 , 合格 /不合格 , 等等。 比例尺規(guī) 通常用來表示等距類別的數(shù)位資訊，但在測量範(fàn)圍內(nèi)有絕對零點(diǎn)。 特別不正常的分佈若假設(shè)為常態(tài)而去分析則有可能得到誤導(dǎo)結(jié)果 。 畫出各個(gè)點(diǎn)，每點(diǎn)代表一個(gè)給定值的輸出 “ 事件 ” 。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