【正文】 N CONTROL if it is operating without special cause variation. If special cause variation is present, the process is OUT OF CONTROL. ? 一個受控過程則是統(tǒng)計(jì)的穩(wěn)定狀態(tài) A process that is in control is said to be in a state of statistical stability. ? 管理者應(yīng)該 A manager should – (1) 使得過程受控 get the process in control。 – (3) 回到步驟 1go back to step 1. 2023/2/7 40 Dr. Weihua Zhou Zhejiang University 控制上限 Upper Control Limit 失控 Out of Control 受控 In Control 改善 Improved 范圍 Time 控制下限 Lower Control Limit 由控制到改進(jìn) Form control to improve 2023/2/7 Dr. Weihua Zhou Zhejiang University 41 誰是一個有潛質(zhì)的好射手？ Who is the Potentially Better Shooter? A B 2023/2/7 42 Dr. Weihua Zhou Zhejiang University 反饋控制原則 The Feedback Control Principle 干擾：一般或特殊原因 Disturbances: Common or special causes 性能測量 Measure 執(zhí)行 Actions 過程 Process Performance 決策 Decision 信息 Information 過程控制：有沒有特殊原因？ Process control: Are there any special causes? 2023/2/7 Dr. Weihua Zhou Zhejiang University 43 控制圖 Statistical Process Control ? 使用控制圖（一個圖形化的統(tǒng)計(jì)學(xué)方法） Uses process control charts (a graphical as well as statistical approach) ? 在固定時間區(qū)間里，收集正在進(jìn)行的過程中的樣本，測量質(zhì)量特性。 If the process is outofcontrol, terminate the process, resolve the assignable causes, and then start the process again 2023/2/7 44 Dr. Weihua Zhou Zhejiang University 正態(tài)分布 Normal Distribution Mean ??? ??? ??? ??? % % ? ? 標(biāo)準(zhǔn)差 Standard deviation 2023/2/7 45 Dr. Weihua Zhou Zhejiang University 樣本分布和過程分布 Sampling distribution and process distribution ? 樣本均值和樣本分布范圍的抽樣統(tǒng)計(jì) The distribution of a sample statistic such as sample mean or sample range ? 即使過程分布不是正常狀態(tài)，樣本分布也是一個正態(tài)分布。 The mean of the two are equal。這個特性值依賴于成分的混合程度，以及焙燒時間和溫度。標(biāo)準(zhǔn)深度在 。我們可以收集樣本數(shù)據(jù)來監(jiān)控延展性的均值和標(biāo)準(zhǔn)差，保證他們是穩(wěn)定的，并且過程不受 特殊原因 影響 Process capability in meeting the design specifications ( to inches) depends on the distribution of spreadability. We can collect sample data to monitor the mean and the standard deviation of spreadability to ensure that they are stable and the process is not subject to special cause variation. 延展性分布 Distribution of spreadability ? ?? ? m ean 1 . 25缺陷 defective 缺陷 defective 2023/2/7 Dr. Weihua Zhou Zhejiang University 50 花生醬問題的樣本數(shù)據(jù) Sample Data for the Peanut Butter Problem Sa m p le A B C D X R 1 0 .94 0 .87 1 .15 1 .01 0 .99 0 .2 8 2 1 .10 1 .05 0 .78 1 .07 1 .00 0 .32 3 1 .23 1 .65 0 .67 1 .21 1 .19 0 .98 4 0 .91 0 .82 1 .20 1 .37 1 .07 0 .55 5 0 .81 0 .76 1 .36 0 .71 0 .91 0 .6 5 6 1 .07 1 .18 1 .24 0 .96 1 .11 0 .28 7 1 .26 1 .09 1 .49 1 .12 1 .24 0. 40 8 1 .11 1 .51 1 .14 0 .90 1 .17 0 .61 9 1 .05 0 .95 0 .90 1 .08 0 .99 0 .1 8 10 1 .60 0 .84 1 .41 1 .30 1 .29 0 .7 6 11 1 .54 0 .96 1 .33 0 .99 1 .21 0 .58 12 1 .33 1 .22 1 .33 1 .46 1 .33 0 .24 13 1 .24 1 .09 1 .31 1 .12 1 .19 0 .22 Sa m p le A B C D X R 14 0 .79 1 .27 1 .07 1 .27 1 .10 0 .48 15 0 .92 1 .47 0 .87 1 .35 1 .15 0. 60 16 0 .78 1 .61 1 .23 1 .00 1 .16 0 .83 17 1 .29 1 .07 1 .60 1 .15 1 .28 0 .53 18 1 .36 0 .98 1 .33 1 .51 1 .29 0 .53 19 1 .20 1 .27 1 .58 1 .18 1 .31 0 .40 20 1 .47 1 .09 1 .59 1 .27 1 .36 0 .50 21 0 .67 1 .35 1 .46 0 .95 1 .11 0 .79 22 1 .05 1 .54 0 .96 1 .53 1 .27 0 .58 23 1 .02 1 .48 1 .31 1 .23 1 .26 0 .46 24 1 .24 1 .25 0 .94 1 .47 1 .22 0 .53 25 1 .12 1 .23 1 .07 1 .12 1 .14 0 .1 6 樣本均值 用來控制延展性的 均值。 Sample range is used to control the standard deviation of spreadability 2023/2/7 51 Dr. Weihua Zhou Zhejiang University 均值控制圖 Mean ( X ) Chart ? 功能 Function – 控制過程輸出的主要趨勢 monitor the central tendency of a process output ? 控制界限 Control limits 2023/2/7 52 Dr. Weihua Zhou Zhejiang University 22U CL x A RL CL x A R????xxU CL x zL CL x z??????0 . 70 . 80 . 911 . 11 . 21 . 31 . 41 . 51 . 60 5 10 15 20 25LCL = UCL = C o n t r o l L i m i ts = A v e r a g e o f X + 3 S t a n d a r d D ev i a ti o n o f X 假設(shè)：延展性的均值不變。 花生醬問題的極差控制圖 另一個例子 采樣 Sample 1 2 3 4 5 1 2 3 4 極差 Range 均值 Average 5.1)(52????????????????? RNxxxi?2023/2/7 57 Dr. Weihua Zhou Zhejiang University 計(jì)算控制界限 ? 利用標(biāo)準(zhǔn)偏差計(jì)算控制界限 ? 利用樣本極差計(jì)算控制界限 nzxLCLnzxUCL//??????)4/()4/(????????RAxLCLRAxUCL22??????????????2023/2/7 58 Dr. Weihua Zhou Zhejiang University 均值控制圖 Mean Control Chart 1 2 .0 81 2 .1 11 2 .1 42023/2/7 59 Dr. Weihua Zhou Zhejiang University 極差控制圖 Range Control Chart RDLCLRDUCLRR34?????????00 .0 40 .0 82023/2/7 60 Dr. Weihua Zhou Zhejiang University 均值控制圖和極差控制圖對比 Mean Control Chart vs Range Control Chart LCL UCL LCLR UCLR LCL UCL LCLR UCLR 2023/2/7 61 Dr. Weihua Zhou Zhejiang University 計(jì)數(shù)值控制圖 Control Chart for Attributes ? p控制圖：用于監(jiān)控過程中的次品比例 pChart Control chart used to monitor the proportion of defectives in a process ? C控制圖：用于控制每計(jì)量單位的缺陷數(shù) cChart Control chart used to monitor the number of defects per unit 由計(jì)數(shù)得到 Attributes generate data that are counted. 2023/2/7 62 Dr. Weihua Zhou Zhejiang University 不合格品率控制圖的應(yīng)用 Use of pCharts ? 當(dāng)觀測結(jié)果可以分成兩類時。 When the data consists of multiple samples of several observations each 2023/2/7 63 Dr. Weihua Zhou Zhejiang University pchart 不合格 不合格 1 14 11 8 2 10 12 12 3 12 13 9 4 13 14 10 5 9 15 11 6 11 16 10 7 10 17 8 8 12 18 12 9 13 19 10 10 10 20 16 Total 220 20組樣本 ， 每組 100個芯片