大多數情況下，產品或製程的品質可以用反應變數與一個或多個解釋變數之間的函數關係來衡量，這種關係被稱為輪廓（profile）。利用管制圖來觀察該函數關係是否隨時間變化的過程，稱為輪廓監控（profile monitoring）。傳統上透過管制圖進行監控時並未考慮量測誤差（measurement error）存在的情況，然而現實生活中儘管量測過程嚴密仍不可避免存在量測誤差，已有學者指出量測誤差之存在會對管制圖的監控表現造成影響，因此我們不應該隨意將其忽略。本研究係假設簡單線性輪廓，並考慮解釋變數存在量測誤差的情況，使用廣義動差法（generalized method of moments）進行參數估計，該方法之優點是不需要假設資料分配，並以此基礎建構多變量指數加權移動平均（multivariate exponential weighted moving average; MEWMA）管制圖進行製程監控。為了評估管制圖的偵測表現，我們藉由統計模擬分析，結果發現本研究之方法在大樣本的情況下對於偵測製程發生偏移時有良好的偵測能力。最後，本研究藉由一實例資料說明如何使用本研究提出之管制圖進行監控，供實務工作者作為參考。

In most cases, the quality of a product or process can be measured by the functional relationship between a response variable and one or more explanatory variables, known as a profile. The process of using control charts to observe whether this functional relationship changes over time is called profile monitoring. Traditionally, control charts have not considered the presence of measurement error, although in practice, measurement errors are inevitable despite rigorous measurement procedures. Previous researchers have noted that the presence of measurement error can affect the performance of control charts. Therefore, we should not ignore them lightly. This study assumes a simple linear profile and considers the presence of measurement errors in the explanatory variables. We use the generalized method of moments (GMM) for parameter estimation, which has the advantage of not requiring assumptions about data distribution. Based on this, we construct a multivariate exponential weighted moving average (MEWMA) control chart for process monitoring. To evaluate the detection performance of the control chart, we conducted statistical simulation analysis. The results indicate that the proposed method has good detection capability for identifying process shifts in large sample scenarios. Finally, we demonstrate the application of the proposed control chart with a real dataset, providing a reference for practitioners.

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