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系統識別號 U0026-1706201423513500
論文名稱(中文) 應用資訊理論於管制圖之建構
論文名稱(英文) An information-theoretical based process control chart
校院名稱 成功大學
系所名稱(中) 工業與資訊管理學系
系所名稱(英) Department of Industrial and Information Management
學年度 102
學期 2
出版年 103
研究生(中文) 李庭媁
研究生(英文) Ting-Wei Li
學號 R36024087
學位類別 碩士
語文別 中文
論文頁數 58頁
口試委員 指導教授-張裕清
口試委員-王泰裕
口試委員-蔡青志
中文關鍵字 Kullback-Leibler distance  管制圖  累積和管制圖  指數加權移動平均管制圖  一般概似比管制圖 
英文關鍵字 Kullback-Leibler distance  control chart  cumulative sum control chart  exponentially weighted moving average control chart  generalized likelihood ratio control chart 
學科別分類
中文摘要 品質管理的概念廣泛應用在各種行業,相關的理論與應用在近幾十年來逐漸發展成熟,透過這些品管方法能夠有效地為公司帶來效益,其中SPC (Statistical Process Control)是一套強而有力的方法用來提升製程的穩定度,透過蒐集製程中的資料,使用統計分析來找出製程中的變異,並採取正確因應措施的一套方法。SPC的主要工具之一就是管制圖,傳統的修華特管制圖(Shewhart control chart)適合用在Phase I,目的是移除較大的變異因素將製程帶入穩定,並獲得Phase I參數估計。常見用於Phase II的管制圖有累積和管制圖(cumulative sum control chart, CUSUM control chart)、指數加權移動平均管制圖(exponentially weighted moving average control chart, EWMA control chart),CUSUM、EWMA在小位移時有很好的監測效果,但缺點是有參數選擇的問題。近來年新發展出的一般概似比管制圖(generalized likelihood ratio control chart, GLR control chart)也適用於Phase II的製程監測,GLR的優點在於不需選擇參數、管制界限可查表而得,但其缺點是當位移較小時監測能力差。因此本研究欲建構一個不需選擇參數、用於製程Phase II的管制圖,主要針對連續資料進行製程平均數(process mean)的位移監測,稱為Information-Theoretical Based Process Control Chart。
管制圖之間的監測能力比較將採用平均連串長度(average run length, ARL),根據模擬結果分析發現,Information-Theoretical Based Process Control Chart在小位移時的監測能力和CUSUM、EWMA control chart相當,大位移時則略差於GLR control chart,但差異僅一兩個樣本,整體而言Information-Theoretical Based Process Control Chart是一個在大範圍位移能有不錯表現且相對容易使用的管制圖。
英文摘要 The objective of this study is to construct a new type of control chart based on Kullback-Leibler distance of information theory. We name this control chart Information-Theoretical Based Process Control Chart. This study considers detecting the mean shift of a normally distributed process given that process variance is consistent. We use a statistic which is a derivation of Kullback-Leibler distance to construct the Information-Theoretical Based Process Control Chart. The control limits of the chart are obtained by simulation with 100,000 runs when in-control average run length is 500. Using the control limits acquired above, we get the out of control average run length for various shift sizes. The performance of control charts are measured by average run length in this study. The results of Information-Theoretical Based Process Control Chart are compared with cumulative sum (CUSUM), exponentially weighted moving average (EWMA), and generalized likelihood ratio (GLR) control chart. The Information-Theoretical Based Process Control Chart is effective in detecting shift of small sizes, but less effective in detecting shift of large sizes. The results are close to the CUSUM and EWMA control charts. It is shown that the overall performance of Information-Theoretical Based Process Control Chart is good. An advantage of Information-Theoretical Based Process Control Chart is that it does not require users to specify control chart parameters while CUSUM and EWMA control chart have to in order to detecting a specific mean shift faster.
論文目次 第一章 緒論 1
第一節 研究背景 1
第二節 研究動機 2
第三節 研究目的 3
第四節 模型假設 4
第五節 研究流程 4
第二章 文獻探討 6
第一節 修華特管制圖(Shewhart Control Chart) 6
2.1.1 Shewhart Control Chart基本模型 8
2.1.2 Shewhart Control Chart分類 8
第二節 Change-Point Model 9
第三節 Time-Weighted Control Chart 11
2.3.1 累積和管制圖(CUSUM Control Chart) 11
2.3.2 The Fast Initial Response or The Headstart Feature 12
2.3.3 指數加權移動平均管制圖(EWMA Control Chart) 13
第四節 GLR control chart 14
2.4.2 μ0、σ0^2為已知,探討process mean、variance的GLR Control Chart 16
2.4.3 Window size 17
第五節 平均連串長度(Average Run Length,ARL) 17
第六節 Kullback-Leibler Information 18
第三章 研究方法與步驟 20
第一節 研究流程建構 20
第二節 研究假設與參數定義 22
第三節 管制圖建構 23
3.2.1 τ^*的計算 23
3.2.2 計算K-L distance 24
3.2.3 設定管制界限 26
第四章 結果分析與案例討論 28
第一節 管制圖參數設定 28
第二節 管制圖比較與結果分析 31
第二節 案例討論 35
第五章 結論與未來研究方向 47
第一節 本研究結論 47
第二節 未來研究方向 48
參考文獻 49
附錄I 52
附錄II 53
附錄III 54
附錄IV 56
附錄V 57
附錄VI 58
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