在大多數的統計製程管制應用中，當品質特徵彼此有相關性時，需用多變量管制圖進行品質特徵監控，然而變數之間可能存在更複雜的關係，像是以輸入與輸出形式所呈現，此時以反應變數與一個或多個以上解釋變數的函數來表達該關係是更好的選擇，此函數關係則稱為剖面(profile)，而關於描述輸入與輸出間的函數關係，文獻上大多是以線性迴歸模型所描述，又稱線性剖面。關於線性剖面監控管制圖的相關研究，主要探討統計製程監控第一階段中製程係數如何估計，以及製程監控於第二階段時，盡可能快速地監測出製程係數發生位移之情形，本論文為探討統計製程監控於第二階段之穩定狀態中，監測線性迴歸之截距與斜率及其對應變異數位移之情況，而建構管制圖之方法為應用資訊理論中的Kullback-Leibler distance來監控線性函數關係是否發生改變。本論文提出一不須事先設定管制圖統計量中之設計參數並採用一較貼近現實情況計算樣本統計量之管制圖，由最新一期樣本並往前考慮之方式，該流程之優點為能更有效地運用最新一期之樣本資訊，最後本論文以平均連串長度作為管制圖之績效指標，透過蒙地卡羅模擬方法，估計平均連串長度值並與其它管制圖進行績效比較。研究結果表示，本研究所提出之管制圖在監測線性迴歸之斜率發生小位移時，優於欲比較之其它類型管制圖，當位移量逐漸增加時，亦能與其它管制圖有相近的績效表現；當監測變異數時，本研究所提出之管制圖皆優於其它管制圖，尤其當位移量較小時，偵測速度比其它管制圖來的靈敏，最後，本研究也提供一查表方式來求得管制界限，使得現場操作人員更容易使用。

In many statistical process control applications, we use control chart to monitor process where performance is measured by one or multiple quality characteristics. However, some processes can be characterized better by a linear function (called linear profile). The objective of this thesis is to monitor a linear functional relationship between a response variable and two explanatory variables. Namely, we focus on monitoring the regression coefficients and the variance of error term. We design a control chart to measure difference between process in control and out of control by Kullback-Leibler distance (called ITPM chart). The performances of ITPM chart, generalized likelihood ratio (GLR) chart, and exponential weight moving average (EWMA-type) chart are compared by average run length (ARL). The simulation results show that the performance of ITPM chart is much better than other charts in detecting a range of small shift sizes when we consider detecting the regression coefficients. The overall performance of ITPM chart is much better than other charts in detecting a wide range of shift sizes when we consider detecting the variance of error term. The ITPM chart also has the advantage that users only need to design control limit. Finally, we provide an equation to obtain control limit given an in-control ARL. It will be more simple and effective to obtain the control limit for practitioners.

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