統計製程管制（Statistical Process Control，簡稱SPC）是監控製程品質特性的重要方法。透過管制圖（Control Charts）的監控，吾人能夠迅速地偵測出非機遇原因何時發生或是製程何時改變，再及時予以修正即可防止不良品之產生，並減少不必要的品質損失。相對於傳統之管制圖，前置管制圖著重於製程量產前製程能力的評估及量產後對製程的及時監控。
現代化的產品及其生產過程日趨複雜，一個產品或製程的品質往往取決於兩個或兩個以上彼此相關的品質特性，因此本研究乃針對品質特性服從多變量常態分配時，比較多變量前置管制圖與Hotelling 管制圖在監控製程上之表現利用平均串長度（ARL）進行評估。除了分別探討當製程處於穩定狀態下及製程發生變動時，管制方法偵測到製程異常所需之樣本數外，本研究尚利用常態轉換法，對品質特性呈非常態多變量分配下之資料作進一步之分析。
最後，我們亦提出一套修正原多變量前置管制圖之設定及監控準則的方式，可供業界參考使用。

Statistical process control (SPC) is an important tool to detect the process change and prevent the defects from occurring by identifying and eliminating assignable causes of variation. In contrast to the traditional control charts, pre-control charts focus on evaluating the process capability during the set-up stage and detecting the process change during the mass production stage.
The quality of output of a production process is often measured by the joint level of several correlated characteristics. The main purpose of this research is to compare the performance of detecting process change using multivariate pre-control charts versus Hotelling control charts when quality characteristics follow multivariate normal distributions. This can be achieved by two statistical measures known as the out of control ARL (Average Run Length) = , where is the type-II error probability (the probability of not being able to detect the change when the process mean has been shifted) as well as the in control ARL= , where is the type-I error probability (the probability of claiming the process is out-of-control when the process is actually in control). In addition, this research will utilize normal transformation to deal with the non-normal multivariate data.
Finally, this research proposes some new set-up and monitoring criteria for multivariate pre-control charts which may provide a useful reference for the industries.

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