統計製程管制（SPC）已廣泛用於監測各種工業流程，管制圖是統計製程管制的一個重要的工具，隨著製程技術的發展，許多用於監測不同品質特徵值的管制圖也趨於成熟。傳統單變量管制圖多數是假設參數已知且服從特定分配，出於計算上的便利性，最常假設的分配為常態，這並不符合實際製程的情況，且製程初始階段，無法收集足夠的樣本資料，來驗證假設是否正確，若分配假設錯誤，也將計算出錯誤的管制界線，導致管制圖在監測製程時，發生虛警率過高的現象發生，影響管制圖的績效表現。有別於參數管制圖存在此缺陷，無母數管制圖可以避免分配假設錯誤的情況發生，提高管制圖在監測來自不同分配資料的檢定力。本研究使用Kullback-Leibler Distance(之後簡稱K-L Distance)，資訊理論的概念來建構無母數管制圖，目的是監測穩定狀態收集的一組資料與新收集的另一組資料，兩組資料中位數的分佈是否相同。採用由後往前考慮每期所加入樣本的方式，有效利用近期的樣本資訊，來判斷變異，首先由後往前依序加入三期或以上樣本資料，與穩定狀態收集資料進行排序，獲得Mann-Whitney U統計量，並為了使Mann-Whitney統計量分配一致，進一步將統計量標準化，計算K-L Distance的每筆資料，每考慮一期樣本便重新計算標準化統計量，便帶入檢定統計量公式，並與管制界線進行比較，超出則代表製程脫離管制，發出警告。本研究為了檢視所建構管制圖的表現，將與EWMA及CUSUM類型的無母數管制圖，在不同分配下及不同穩定樣本大小下，透過觀察不同位移設定下之平均連串長度的方式，進行管制圖績效之比較。結果顯示本研究提出的管制圖，當穩定樣本較少時，在右偏分佈廣泛位移及對稱分佈位移較小的情況，相較NP-EWMA及NP-CUSUM兩類型無母數管制圖，具有較佳的績效表現，代表當製程提供資訊量較少的情況，本研究提出之管制圖能在樣本來自右偏分佈時，在廣泛位移下具有良好的監測能力，而在樣本來自對稱分佈的條件下，當製程發生小位移時表現較好。

This study uses Kullback-Leibler Distance (K-L Distance) to construct nonparametric control charts, K-L Distance is mainly used to measure the information discrepancy between two probability distributions (one is distribution of in-control samples and the other is distribution of empirical samples). When the value of K-L Distance is too large, we believe there are some variations caused by the attribution cause in the process. We name this control chart nonparametric information-theoretical control chart (NPITC control chart).The purpose of this study is to monitor whether the median of two groups of data are the same to ensure that the process is in control. Because our study uses nonparametric statistic method to construct the control chart, it is different from the parametric statistic method, which has assumption of distribution for the process. This chart is established by Mann-Whitney statistic, which is one of nonparametric statistic. To calculate this statistic, we firstly sort two different groups of samples by ascending order, and then calculate how many samples that are collected in the steady state sorted after each newly collected sample. Secondly standardize the Mann-Whitney statistic and take it to calculate K-L Distance, lastly compare it with the control limit, if it is lager than the control limit, it means that the process is out of control. To evaluate the ability of detect variations caused by the attribution cause, we compare it to EWMA and CUSUM nonparametric control chart by the average of the length of samples to signal when process is under different shift size. After Comparing with the EWMA and CUSUM nonparametric control chart, the results show that when there are fewer samples collected from the steady states, the NP-ITC control chart will be better, and when the samples are come from the right-skewed distribution, it shows the NP-ITC also has a good monitoring capability under wide shift size.

中文文獻：
楊瑋欣，應用幾何分佈於監控伯努力過程之資訊理論管制圖，國立成功大學工業與資訊管理研究所碩士論文，民國一百零五年六月。
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