近來已有愈來愈多的無母數管制圖(Nonparametric control chart)被提出，其目的不外乎是為了避免直接假設製程的原始分配。然而，在缺乏原始分配的資訊之下，要完整地評估其設計的管制圖之表現是似乎頗有難度。於是，有些學者便考慮以參考樣本(Reference sample)來建立經驗分配函數(Empirical distribution function)，藉以彌補不足。
在這篇論文中，我們研究了由Rafajlowicz， Pawlak 以及 Steland (2004) 這三位學者所提出的V-Box管制圖，並加入參考樣本的觀念。V-Box管制圖的設計概念是以考量當製程產生偏移時，利用是否有足夠多的觀察點落進V-Box裡來進行偵測；其中V-Box是一個固定大小並隨時間點而移動的矩形。
我們推導出了平均連串長度(ARLs)的一般式，並利用此公式所算出的平均連串長度與累積和管制圖(CUSUM)以及指數加權移動平均管制圖(EWMA)做比較。在可以計算平均連串長度的同時，我們考慮尋找最佳化的V-Box管制圖，並發現其在偵測異常點的效率頗為良好。此外，我們亦可發現V-Box管制圖在偵測平均數已產生小偏移的同時，對形如均勻分配(Uniform distribution)這類的原始製程分配，有極為亮眼的表現。

More and more nonparametric control charts are proposed recently, with a common thought of not assuming the underlying distribution of the process. However, without the information about the distribution, it would be difficult to evaluate and analyze the performance of these control charts. Some authors suggest to use a reference sample to avoid this problem, by using its empirical distribution function.
In this thesis, we investigate a nonparametric control chart, namely V-Box control chart proposed by Rafajlowicz, Pawlak and Steland (2004), with a reference sample. This V-Box chart has a intuitive design on whether there are enough points inside a control V-Box over a moving window of time. We derive the general form of average run lengths (ARLs) and compare the V-Box chart with the CUSUM and EWMA control charts. With the ARLs available, we also discuss how to design an optimal V-Box chart. V-Box chart has an efficient performance in detecting outliers (out-of-control points). Furthermore, under a distribution with heavy tails and a short range, e.g. Uniform(0,1), the V-Box chart significantly outperforms the CUSUM and EWMA charts

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