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系統識別號 U0026-3006201914485100
論文名稱(中文) 以Kullback-Leibler資訊建構剖面監控管制圖
論文名稱(英文) A Kullback-Leibler information control chart for profile monitoring
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 107
學期 2
出版年 108
研究生(中文) 陳長明
研究生(英文) Chang-Ming Chen
學號 R36061039
學位類別 碩士
語文別 中文
論文頁數 47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
口試委員-胡政宏
中文關鍵字 線性剖面監控管制圖  資訊理論  Kullback-Leibler distance 
英文關鍵字 linear profile  average run length  Kullback-Leibler distance  generalized likelihood ratio control chart  EWMA chart 
學科別分類
中文摘要 在大多數的統計製程管制應用中,當品質特徵彼此有相關性時,需用多變量管制圖進行品質特徵監控,然而變數之間可能存在更複雜的關係,像是以輸入與輸出形式所呈現,此時以反應變數與一個或多個以上解釋變數的函數來表達該關係是更好的選擇,此函數關係則稱為剖面(profile),而關於描述輸入與輸出間的函數關係,文獻上大多是以線性迴歸模型所描述,又稱線性剖面。關於線性剖面監控管制圖的相關研究,主要探討統計製程監控第一階段中製程係數如何估計,以及製程監控於第二階段時,盡可能快速地監測出製程係數發生位移之情形,本論文為探討統計製程監控於第二階段之穩定狀態中,監測線性迴歸之截距與斜率及其對應變異數位移之情況,而建構管制圖之方法為應用資訊理論中的Kullback-Leibler distance來監控線性函數關係是否發生改變。本論文提出一不須事先設定管制圖統計量中之設計參數並採用一較貼近現實情況計算樣本統計量之管制圖,由最新一期樣本並往前考慮之方式,該流程之優點為能更有效地運用最新一期之樣本資訊,最後本論文以平均連串長度作為管制圖之績效指標,透過蒙地卡羅模擬方法,估計平均連串長度值並與其它管制圖進行績效比較。研究結果表示,本研究所提出之管制圖在監測線性迴歸之斜率發生小位移時,優於欲比較之其它類型管制圖,當位移量逐漸增加時,亦能與其它管制圖有相近的績效表現;當監測變異數時,本研究所提出之管制圖皆優於其它管制圖,尤其當位移量較小時,偵測速度比其它管制圖來的靈敏,最後,本研究也提供一查表方式來求得管制界限,使得現場操作人員更容易使用。
英文摘要 In many statistical process control applications, we use control chart to monitor process where performance is measured by one or multiple quality characteristics. However, some processes can be characterized better by a linear function (called linear profile). The objective of this thesis is to monitor a linear functional relationship between a response variable and two explanatory variables. Namely, we focus on monitoring the regression coefficients and the variance of error term. We design a control chart to measure difference between process in control and out of control by Kullback-Leibler distance (called ITPM chart). The performances of ITPM chart, generalized likelihood ratio (GLR) chart, and exponential weight moving average (EWMA-type) chart are compared by average run length (ARL). The simulation results show that the performance of ITPM chart is much better than other charts in detecting a range of small shift sizes when we consider detecting the regression coefficients. The overall performance of ITPM chart is much better than other charts in detecting a wide range of shift sizes when we consider detecting the variance of error term. The ITPM chart also has the advantage that users only need to design control limit. Finally, we provide an equation to obtain control limit given an in-control ARL. It will be more simple and effective to obtain the control limit for practitioners.
論文目次 摘要………………………………………………………………………………………………………….........II
誌謝………………………………………………………………………………………………………………..X
目錄………………………………………………………………………………………………………………XI
表目錄………………………………………………………………………………………………...………XIII
圖目錄…………………………………………………………………………………………………………XIV
第一章 緒論 1
1.1 研究背景 1
1.2 研究動機 2
1.3 相關研究與應用 3
1.4 研究目的 4
1.5 研究假設 4
第二章 文獻回顧 5
2.1.1 線性剖面監控管制圖 5
2.1.2 EWMA3管制圖 6
2.1.3 累積和管制圖 7
2.1.4 概似比指數加權移動平均管制圖 8
2.1.5 多變量指數加權移動平均管制圖 9
2.1.6 廣義概似比管制圖 10
2.1.7 非線性剖面監控管制圖 12
2.1.8 管制圖之績效指標 14
2.1.9 資訊理論 15
第三章 管制圖建構與步驟 17
3.1 問題描述與研究假設 17
3.2 ITPM管制圖建構 20
3.2.1 K-L distance估計量之計算 20
3.2.2 製程係數估計量之計算 21
3.2.3 管制界限之設定 22
3.3 以蒙地卡羅模擬求管制界限與管制圖之績效指標 23
3.4 小結 29
第四章 結果分析與案例討論 30
4.1 管制圖參數之設定 30
4.1.1 管制圖之績效指標 30
4.1.2 模擬情境與管制界限之設定 31
4.2 管制圖之績效比較與分析 32
4.3 ITPM管制圖之管制界限設定 38
4.4 管制圖呈現之範例說明 39
第五章 結論 42
參考文獻 43
附錄I ………………………………………………………………………………………..47

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