傳統迴歸分析是假設觀測值的不確定性來自於隨機現象，本文則應用模糊隨機變數概念於迴歸模式的架構，考慮將隨機現象和模糊認知並列研究。針對樣本模糊數(x_i, Y_i)，我們進行模糊迴歸參數估計，並稱此為模糊迴歸模式分析。模糊迴歸參數估計大都採用線性規劃，求出適當區間，將觀測模糊數Y_i的分佈範圍全部覆蓋。但是此結果並不能充分反映觀測樣本Y_i的特性。本研究提出一套模糊迴歸參數的估計方法，其結果對觀測樣本的解釋將更為合理，且具有模糊不偏的特性。在分析過程中，我們亦提出一些模糊統計量如模糊期望值、模糊變異數、模糊中位數的定義，以增加對這些參數的模糊理解。最後在本文中也針對台灣景氣指標與經濟成長率作實務分析，說明模糊迴歸模式的適用性。 / Conventional study on the regression analysis is based on the conception that the uncertainty of observed data comes from the random property. However, in this paper we consider both of the random property and the fuzzy perception to construct the regression model by using of fuzzy random variables. For the fuzzy sample (x_i,Y_i), we will process the parameters estimation of the fuzzy regression, and we call this process as fuzzy regression analysis. The parameters estimation for a fuzzy regression model is generally derived by the linear programming scheme. But it's result usually doesn't sufficiently reflect the characteristics of the observed samples. Hence in this paper we propose an alternative technique for parameters estimation in constructing the fuzzy regression model. The result will describe the observed data better than the conventional method did, moreover it will have the fuzzy unbiased properties. For the purpose of fuzzy perception on the fuzzy random variables, we also give definitions for certain important fuzzy statistics such as fuzzy expected value, fuzzy variance and fuzzy median. Finally, we give an example about the Taiwan Business Cycle and the Taiwan Economic Growth Rate for illustration.

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.