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。

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.

李庭媁.(2014)。應用資訊理論於管制圖之建構。國立成功大學工業與資訊管理學系碩士論文，台南市。
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