在工業製程中，越來越多控制器應用到產品製程上，為了確保產品品質，希望控制器能保持在一定的性能水準，因此控制器性能的評估與監控受到學者們的重視，一般而言，使用輸出誤差的變異數來當作控制系統監控的統計量，然而只看當前控制器輸出誤差的變異數是否發生改變是不夠的，這只能看出控制系統是否發生改變，提供的信息並不完整，無法提取完整的信息，另外還需要透過統計量與最好或滿足工程需要的控制器性能之統計量進行比較，判斷控制器是否有改進的空間，而這個控制系統的性能指標通常是一個相對的數值，在Harris(1989)發表奠基性文章也就是最小變異數控制基準(minimum variance control benchmark MVC)以後，此領域開始蓬勃發展，多篇的研究文獻顯示在這領域取得了重大的成果。
在多變數系統中，共變異數矩陣(Covariance Matrix)數值之間的關係提供了許多可以分析的資訊，因此監控共變異數矩陣的改變，是十分重要的事情，Harris首先把MVC從單變數引入到多變數系統，透過共變異數矩陣的數值來提取製程信息，此外還有一些學者發展其他監控共變異數矩陣的方法。然而上述的方法並沒有將整個共變異數矩陣的信息考慮進去，為了提取共變異數矩陣整體的信息，本文採用對共變異數矩陣的相等性進行假設檢定，透過比較兩樣本之共變異數矩陣差異的方式，不只把考慮變數本身的變化，同時也把變數間變化的程度也考慮進去，抓取矩陣整體的信息。並且導入滑動窗口理論，透過不同的窗口大小，達到線上監控控制性能的目的。
本文透過即時性的數據採集方式與三種數據假設檢定準則，配合不同的製程
與不同的目的，希冀達到一個全面性的控制器性能之評估與監控，並依據所得的統計量結果，用來建立與管制圖類似之圖表，讓一般使用者與工程師都能夠輕鬆使用。

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