在多數情況下，製程或產品的品質可藉由反應變數與一個或多個解釋變數的函數關係來衡量，此關係稱之為輪廓(profile)。輪廓監控(profile monitoring)則是用以確認或檢驗此函數關係是否隨時間改變，其想法是為輪廓資料建立參數模型，並對每個時間點的輪廓資料參數進行估計，進而監控參數是否隨時間產生變異。過去用以輪廓監控的參數模型中經常假設輪廓內觀察值彼此獨立，然而在某些應用中獨立的假設並不成立，即輪廓內觀察值可能具有一系列的相關。本研究使用逆高斯過程(inverse Gaussian process)模型描述輪廓內相關(within-profile correlation)，並為模型參數建立多變量指數加權移動平均管制圖(multivariate exponential weighted moving average; MEWMA)與兩個單變量管制圖於階段II(phase II)進行製程監控，藉由監控模型參數來判斷製程是否呈管制內狀況。為了評估管制圖的表現，我們以統計模擬方式對相關的輪廓管制圖進行比較，模擬比較結果發現我們所提出之MEWMA管制圖的偵測能力較過去方法更佳。此外，並將此方法應用於實際例子供使用者做為參考。

In many circumstances, the quality of a process or product is best characterized by the functional relationship between a response variable and one or more explanatory variables that is typically referred to as the profile. Profile monitoring is used to understand and check the stability of the association over time. The idea is often to model the profile via some parametric method and then monitor estimated parameters over time to determine if there have been changes in the profiles. The existing methods are usually based on the assumption that the observations within each profile are independent of each other. However, in some applications, it is not always true. Successive measurements within profiles often exhibit serial correlation. In this study, we use the inverse Gaussian process model to describe the within-profile correlation. A multivariate exponentially weighted moving average (MEWMA) control chart and two univariate control charts are proposed to monitor process on phase II when within-profile data are correlated. The performance of the proposed methods will be evaluated by simulation studies. The comparison result of our proposed MEWMA control chart with other control charts favors the former. Furthermore, the proposed method is applied to a real data set.

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