【文章內(nèi)容簡(jiǎn)介】 rocess Control, SPC 2023/2/7 37 Dr. Weihua Zhou Zhejiang University 統(tǒng)計(jì)過程控制 Statistical Process Control (SPC) ? 目的 Purpose – 質(zhì)量的一致性 Quality of conformance ? 使用統(tǒng)計(jì)方法防止不良品的出現(xiàn) Using statistical approaches to prevent the bad products to occur – 測(cè)定一個(gè)操作流程是“在控制中”還是“超出控制范圍” to determine whether an operation process is “in control” or has gone “outofcontrol” – 確認(rèn)流程中導(dǎo)致變差的原因 to identify the causes of variation in a process – 改進(jìn)流程 to improve the process 2023/2/7 Dr. Weihua Zhou Zhejiang University 38 兩種類型的變動(dòng) Two Types of Variation ? 正常變動(dòng)（隨機(jī)誤差） Normal variation (Random errors) – 在輸出過程中由無數(shù)小因素造成的自然變化 Natural variations in the output of process, created by countless minor factors – 隨機(jī)產(chǎn)生 Common or random cause – 貫穿整個(gè)過程 Inherent in the process – 無法追查到單一因素 Not traceable to a single factor ? 異常變動(dòng)（系統(tǒng)誤差） Abnormal variation (Systematic errors) – 引起變化的原因是可知的 variation whose causes can be identified – 由特殊的原因引起（如工具磨損，材料缺陷，人為錯(cuò)誤等） created by special or assignable causes (., worn tool, defective material, human error 2023/2/7 39 Dr. Weihua Zhou Zhejiang University “受控”還是“失控” “ In Control” or “Out of Control”? ? 假如沒有異常變動(dòng)出現(xiàn)，則過程處于受控狀態(tài)，若有異常變動(dòng)出現(xiàn)，則處于失控狀態(tài)。 A process is IN CONTROL if it is operating without special cause variation. If special cause variation is present, the process is OUT OF CONTROL. ? 一個(gè)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。 – (2) 改進(jìn)過程 improve the process。 – (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(gè)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(cè)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(gè)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(shí)間區(qū)間里，收集正在進(jìn)行的過程中的樣本，測(cè)量質(zhì)量特性。 At fixed time intervals, collect samples from the ongoing process and measure the quality characteristics ? 判斷過程處于“受控”還是“失控” Characterizes the state of the process as incontrol or outofcontrol ? 如果過程處于失控，則終止該過程，解決可確定的引起原因，然后重新開始該過程。 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(gè)正態(tài)分布。 Sampling distribution is a normal distribution even if the process distribution isn’t normal ? 這兩個(gè)分布的均值相等，但是樣本分布的方差較小。 The mean of the two are equal。 however, the variance of the sampling distribution is smaller Sampling distribution Process distribution Mean 2023/2/7 46 Dr. Weihua Zhou Zhejiang University 控制圖 Control Charts 970 980 990 1000 1010 1020 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 UCL LCL 采樣數(shù)目 Mean 不受控制 Out of control 正常的變動(dòng) Normal variation due to chance 由不可忽視的原因?qū)е碌漠惓? Abnormal variation due to assignable sources 由不可忽視的原因?qū)е碌漠惓? Abnormal variation due to assignable sources 2023/2/7 47 Dr. Weihua Zhou Zhejiang University 控制圖的類型 Types of Control Charts ? 計(jì)量值控制圖 Variable charts – 基于測(cè)量的數(shù)據(jù) based on data that are measured – Mean Chart (XChart) （均值控制圖） – and Range Chart (RChart)（極差控制圖） ? 計(jì)數(shù)值控制圖 Attribute charts – 基于計(jì)算所得的數(shù)據(jù) based on data that are counted – 不合格品率控制圖和缺陷數(shù)控制圖 pChart and cChart 2023/2/7 Dr. Weihua Zhou Zhejiang University 48 一個(gè)棘手的問題：花生醬的延展性 A Sticky Problem: Spreadability of Peanut Butter 花生醬的延展性是一個(gè)重要的質(zhì)量特性值。這個(gè)特性值依賴于成分的混合程度，以及焙燒時(shí)間和溫度。延展性是這樣測(cè)定的，將一根像針一樣的探測(cè)器投進(jìn)一罐花生醬中，十秒鐘后，測(cè)量它掉進(jìn)的深度。標(biāo)準(zhǔn)深度在 。Spreadability of peanut butter is an important quality characteristic. This characteristic depends on the mix of ingredients, as well as roasting time and temperature. Spreadability is determined by dropping a needlelike probe into a jar of peanut butter and measuring its depth after ten seconds. The specifications are inches to inches. Is the process capable of meeting design specifications? 2023/2/7 49 Dr. Weihua Zhou Zhejiang University 花生醬延展性的過程控制 Process Control for Peanut Butter Spreadability 過程能力是否滿足設(shè)計(jì)規(guī)范 specifications ( to )取決于延展性的分布。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