根據Steiner (1999) 提出指數加權移動平均 (EWMA) 管制圖之管制界限應伴隨時間變動，相較於傳統以漸近管制界限建構的 X-bar EWMA 管制圖，具備類似於快速起始反應之功能。然而，無母數EWMA 管制圖相關文獻中，大多採用漸近管制界限，甚少提及變動管制界限對於製程初期偵測能力之影響，因此本研究依據Wilcoxon 符號排序統計量為基礎，建構無母數EWMA 管制圖，並定義變動管制界限之形式，進而探討在製程初期的監控效果。假設製程為常態、均勻或雙指數分配下，使用非齊一性馬可夫鏈及蒙地卡羅模擬，求得製程穩定或失控狀態下的平均連串長度。模擬結果顯示，當加權常數越小，若採用變動管制界限能有效提升對於製程初期異常之偵測能力，且在厚尾分配下(例如：雙指數分配) 效果更為明顯。 / According to Steiner (1999), the control limits of exponentially weighted moving average (EWMA) control charts should vary with time, so that the charts would have properties similar to the fast initial response (FIR) feature, when compared with asymptotic X-bar EWMA charts. However, previous analyses of nonparametric EWMA control charts consider only asymptotic control limits and are not sensitive to the shifts in a process at early stages. In this thesis, a nonparametric control chart with time-varying control limits is constructed based on EWMA control chart built upon the Wilcoxon signed-rank statistics. When the underlying distribution is normal, uniform, or double exponential, the average run lengths in both in-control and out-of-control conditions are approximated using non-homogenous Markov chain and based on Monte Carlo simulations. Simulation results show that EWMA charts with varying control limits are more efficient to detect early process shifts when weighting constants are small, and the underlying distributions are heavy-tailed distribution (such as double exponential distribution).

隨著品質管制技術的開發，越來越多產業將品質管制的理念應用在產業資料中，而品質管制的方法非常多樣，其中統計製程管制(SPC)為品質管制中重要的技術，其主要是以統計理論背景做支持對產品製程進行監控，本文也將針對SPC中理論背景較完整的管制圖方法做進一步的研究，然而品管在實務應用上，母體資料通常為非特定分配或者未知分配，諸多文獻中已證實，若使用特定假設分配的有母數管制圖用於製程狀態為非假設分布時，會導致管制狀態下的平均連串長度不穩健的情形，若使用無母數管制圖做監控，其管制狀態平均連串長度具有穩健性，因此無母數管制圖實用性能高出許多，近年來對無母數管制圖的研究越來越進步，然而現存的無母數管制圖大多是針對產品製程中平均數、變異數的變動，或者是使用符號函數(sign function)、排序(rank)等方式對觀測值和目標值的差距做監控，又或者觀察資料的分佈狀況監控其分配或目標值是否有偏移的情形等，較少有針對觀測值前後之間變動的差距來偵測資料出現偏移的狀況，因此本文提出一個新的無母數管制圖，想利用模糊相關權重統計量的性質來呈現觀測值之間變動的情形，以此統計量為基礎，建構無母數模糊相關權重指數加權平均(FRWEWMA)管制圖，對製程資料中的平均數(位置參數)和標準差(尺度參數)進行監控，並透過平均連串長度來比較FRWEWMA 管制圖和其他管制圖偵測效能的差異與優勢為何。

自舒華特發明以管制圖監測製程以來，管制圖在工程的應用日趨重要。在特殊工程中，一個高效的管制圖方法尤為重要。基於此項事實，在文獻中各式各樣的管制圖層出不窮且技術日益完善。但傳統管制圖往往受制于常態分佈，因此在無母數管制圖研究方向仍有大量工作值得探討。於是本文在母體分佈未知情況下，推廣Yang (2015)的無母數平均值管制圖方法建立變動樣本指数加权移动平均管制圖，VSS EWMA-np control chart。新的管制圖將變動樣本大小（VSS）和指數加權移動平均（EWMA）方法結合建立一種新的管制圖方法，並用這種新型管制圖監測未知分佈母體的平均值是否發生變動。而為了監測平均數是否發生變化，也為了減少抽樣損失，本文評估管制圖監測效力的指標為管制圖偵測出異常訊息所需抽樣的樣本數期望值（EN）、平均連串長度（ARL）和平均觀測值總數（ANOS）。從本文的比較結果看出新的變動樣本指數加權移動平均管制圖擁有更好的失控偵測力。 / Since Shewhart invention control chart monitor the process, control charts are increasingly important in engineering applications. In special projects, an efficient control chart is especially important. Based on this fact, the various kinds of control charts in the literature are not poor and the technology is improving. However, traditional control charts are often subject to normal distribution, so there is still a lot of work to be discussed in the direction of the study of non-parametric control charts. So in this paper under unknown distribution in the matrix, Yang (2015) established on the basis of the theory of a non-parametric method of control chart - Exponentially Weighted Moving Average Control Chart with Variable Sampling Sizes (VSS EWMA - np control chart). New control chart will change the sample size (VSS) and exponential weighted moving average (EWMA) method to establish a new control chart, and use new control chart for monitoring the mean of unknown distribution matrix is changed. And whether to monitor the average changes in order to reduce the loss of sampling, this paper mainly evaluate control chart for monitoring the effectiveness of the statistics for the expected value of the sample size (EN), the average run length (ARL) and the average number of observations to signal (ANOS). From the comparison shown in this paper, the new control chart has better detection.