一般情況下，製程的表現可以根據產品的品質特性來衡量，現今許多的品質特性與製程變數間具有函數關係，此函數關係稱為輪廓（profile），並可以藉由觀察輪廓是否發生變化來監控製程狀態。線性模型（linear model）為較常用來配適輪廓資料的模型，此模型大多假設資料來自常態分配（normal distribution），但實際輪廓資料並非皆服從常態分配，在上述情況下，使用常態假設的線性輪廓管制圖可能會有監控效率不佳的問題。對於不符合常態假設的線性輪廓，有學者提出不需分配假設的無母數線性輪廓管制圖來監控輪廓是否發生變化，不論輪廓資料的分配為何，此學者提出之無母數管制圖的表現皆非常穩健。但在輪廓資料分配已知的情況下，使用針對特定分配而建立的有母數管制圖在偵測製程是否已經脫離管制狀況的效率較高，因此本研究假設輪廓資料為較為廣義的偏斜常態分配（skew normal distribution），利用線性模型配適輪廓資料，並根據線性模型中迴歸係數與標準差的計分檢定（score test）統計量提出多變量指數加權移動平均（multivariate exponential weighted moving average; MEWMA）管制圖，藉由監控線性模型參數來判斷製程是否呈管制狀況。同時也藉由統計模擬評估本研究所提出之管制圖表現，並舉數值實例說明如何使用本研究提出之管制圖來對輪廓資料進行監控，最後，利用R語言編寫成一套監控程式讓實務工作者使用，以增加本研究之實用性。

Generally, in some applications, the quality of process or product is characterized and summarized by a functional relationship between a response variable and one or more explanatory variables. The functional relationship is called the profile. We can monitor the quality of process by checking the stability of the profile over time. Linear profile monitoring is most used in practice because it is much easier and can deal with many distinct situations. However, the existing linear profile monitoring approaches usually assumed that the error term is normal distribution which may not always be true. Because the skew distribution represents a broad distribution class and is more flexible than the normal distribution. We propose a multivariate exponential weighted moving average (MEWMA) control chart under linear when the distribution of error term is assumed to be skew normal distribution. The performance of our proposed method is evaluated by simulation studies. Moreover, the proposed method is applied to a real data set, and the R code for monitoring profile is made available to users.

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