本研究旨在建立監控多項分配管制圖，可應用於連續或非連續生產，抽樣方式為全部檢驗。使用多項分配管制圖的應用有許多種，其中一種應用為研究工廠中，生產中缺陷分析的報廢品比例是否改變，通常會有多種比例，透過分析報廢品比例的變化，能讓我們找出報廢品發生的不同類型可歸屬原因，並加以改進。本研究建構出多項分配Kullback-Leibler資訊管制圖，相較於其他管制圖，使用不同的誤報率之下可以容易得到管制界線，因此不需要設計管制圖參數，也不會因為估計錯誤而使績效變低，適用於偵測偏移範圍較廣的狀況。針對極端比例以及平均比例等兩種情況，分別比較雙邊伯努力累計和管制圖以及多項分配廣義概似比管制圖與多項分配KLI管制圖，使用穩定狀態達到警報平均觀測次數來評估對於不同比例變動之偵測能力，發現雙邊伯努力累計和管制圖在小範圍以及比例接近特定調整參數時有較佳的表現，多項分配廣義概似比管制圖在平均比例以及廣泛偏移情況下有較好的表現。多項式KLI管制圖除了俱有多項分配廣義概似比管制圖，對於廣泛偏移偵測有較佳表現，卻不需要設計管制圖參數，相較之下更有使用彈性。最後在案例應用的部分，本研究示範了KLI管制圖如何監控100筆數據與MGLR管制圖進行比較，並給出一般情況下MGLR管制界線之轉換通式。

This study aims to establish multinomial control charts applicable to both continuous and non-continuous production, employing full inspection sampling methods. There are many applications of multinomial control charts, one of which is to study various attributes in a factory to analyze changes in the proportion of defective products during manufacturing, identifying different types of assignable causes for scrapped items and improving them accordingly. This research develops multinomial Kullback-Leibler information control charts, which, compared to other charts, easily determine control limits under various false alarm rates without needing designed control chart parameters. This avoids performance degradation due to estimation errors, making it suitable for detecting a wide range of process deviations. The study further compares the two-sided Bernoulli cumulative sum control charts with multinomial generalized likelihood ratio control charts and multinomial KLI control charts under extreme and average proportions scenarios. It evaluates their detection capabilities for different proportion changes using the average number of observations to signal in a stable state. Findings indicate that two-sided Bernoulli cumulative sum control charts perform better within small ranges and when proportions are close to specific adjustment parameters, while multinomial generalized likelihood ratio control charts show superior performance in average proportions and extensive shift scenarios. The multinomial KLI control charts, aside from offering robust detection of extensive shifts similar to multinomial generalized likelihood ratio charts, do not require designed control chart parameters, thus providing greater flexibility in usage. In the final section on practical applications, this study demonstrates how KLI control charts are used to monitor 100 data points in comparison with MGLR control charts, and provides a general formula for converting MGLR control limits under typical circumstances.

中文文獻:
呂倢瑩(民111)。用於監控批次生產之不合格率Kullback-Leibler資訊管制圖。國立成功大學工業與資訊管理研究所碩士論文。
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