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系統識別號 U0026-2506201516392400
論文名稱(中文) 應用資訊理論於監控伯努力過程之管制圖
論文名稱(英文) An Information-theoretical Control Chart for Monitoring Bernoulli Processes
校院名稱 成功大學
系所名稱(中) 資訊管理研究所
系所名稱(英) Institute of Information Management
學年度 103
學期 2
出版年 104
研究生(中文) 劉英守
研究生(英文) Ying-Shou Liu
學號 R76021037
學位類別 碩士
語文別 中文
論文頁數 52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 修華特管制圖  累積和管制圖  指數加權移動平均管制圖  伯努力過程  一般化概似比管制圖  資訊理論  Kullback-Leibler distance、Bernoulli GLR 
英文關鍵字 Kullback-Leibler distance  CUSUM  EWMA  GLR control chart 
學科別分類
中文摘要 統計製程管制圖是應用在品質管理活動中最常用的工具之一,用來偵測製程中重要的品質特性是否有變異發生。最常用的3種管制圖分別為:修華特管制圖、累積和管制圖(CUSUM)與指數加權移動平均管制圖(EWMA)。修華特管制圖廣泛地應用在即時監控製程平均數與變異數,其缺點在於品質特性的偏移量較小時無法快速地偵測出來。CUSUM與EWMA皆加入過去樣本資訊來改善偵測偏移量較小時的績效且在偵測特定位移時績效較佳,可透過設定最佳偏移量參數來偵測特定位移值。
若想同時偵測多個不同位移有兩種方法,其中一個方法為結合多個管製圖,當每個管制圖皆要設定參數時會導致須設定多個參數,會讓使用管制圖變得更複雜。另一個則使用一般化概似比管制圖 (GLR管制圖),優點為不需設定欲偵測位移量參數且在整體而言監測能力都不錯。Kullback 和 Leibler 學者從資訊理論所延伸出來的Kullback-Leibler distance,為GLR管制圖的延伸,其概念為衡量兩個函數之間的距離,當距離大於管制界線則判定為製程落在管制界線外。
本研究使用KL distance來建立管制圖基於伯努力過程下,在三個不合格率(0.1,0.01,0.001)案例下討論在不同情況下之績效,當不合格率0.1時偵測20%位移量以內績效會比Bernoulli GLR管制圖來的好。當不合格率0.01時偵測三倍位移量以內績效會比Bernoulli GLR管制圖來的好。當不合格率0.001時偵測十倍位移量以內績效會比Bernoulli GLR管制圖來的好。由此可知,隨著不合格率下降所能偵測較好績效的位移量比例也增加,因此本研究KL distance管制圖在小位移績效表現均會優於Bernoulli GLR管制圖。
英文摘要 This study considers the problem of monitoring the proportion of nonconforming of a Bernoulli process based on the Kullback-Leibler distance of information theory. The traditional control chart for fraction nonconforming is p chart, but there are several disadvantages of it. Therefore, many other methods for monitoring the fraction have been proposed. In this research, we propose an Information-Theoretical Based Bernoulli Processes Control Chart (ITB control chart) for detecting the fraction nonconforming shift. We use a statistic which is a derivation of Kullback-Leibler distance to construct the control chart. The performance of control charts is measured by average number of observations to signal (ANOSS). We consider three different fraction nonconforming as 0.1, 0.01, and 0.001 when the process is in control. Using the control limits acquired above, we derive the out of control SSANOS for various shift sizes. Comparisons of the ITB to the Bernoulli cumulative sum (Bernoulli CUSUM) and Bernoulli generalized likelihood ratio (Bernoulli GLR) control chart show that the performance of the ITB is better than its competitors when the shift size is small. The ITB control chart is effective in detecting small shift sizes, but less effective in detecting larger shift sizes. It is shown that the shift of small size performance of ITB control chart is good. In addition, one advantage of ITB control chart is that it does not require users to specify control chart parameters while Bernoulli CUSUM and Bernoulli EWMA control chart have to in order to detecting a specific process shift faster.
論文目次 第一章緒論1
1.1研究背景1
1.2研究動機3
1.3研究目的4
1.4研究架構與流程 4
第二章文獻探討6
2.1 p 管制圖6
2.2 時間加權管制圖(Time-Weighted Control Chart)7
2.2.1 以不同分配為基礎之累積和管制圖(CUSUM)7
2.2.2 以不同分配為基礎之指數加權移動平均管制圖(EWMA)9
2.3 Change Point Model10
2.4伯努力一般化概似比率管制圖(Bernoulli GLR Chart),探討11
2.5管制圖績效衡量指標13
2.6Kullback-Leibler Distance15
2.7Information-Theoretical Based Process管制圖16
2.8 小結16
第三章研究方法與步驟18
3.1 研究假設與參數設定18
3.2 研究問題描述19
3.3 管制圖之建構20
3.3.1 的計算21
3.3.2 計算KL distance22
3.3.3 計算管制界線23
3.4 以KL distance角度看資料聚合24
3.5 小結 24
第四章結果分析25
4.1管制圖參數設定25
4.2管制圖比較與結果分析29
4.3案例討論39
第五章結論與未來研究方向42
5.1研究結論42
5.2未來研究方向43
參考文獻44
附錄I47
附錄II49
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