傳統管制圖主要監控平均數和變異數之單變量品質特徵，隨著科技的進步，在管制圖之應用不僅僅只是單變量之品質特徵，而衍生出多變量品質特徵。變數之間以輸入與輸出的關係表達為函數關係，在管制圖中，解釋反應變數與一個以上的解釋變數稱之為剖面監控(profile)，本研究將探討製程監控中發生漂移(drift)情況進行研究分析，漂移變異例如:現場作業人員的疲憊操作、設備刀具的磨損。研究假設情境為製程函數係數在第一階段中被精確估計出來且為已知，在此階段中較大之變異因素均已排除，隨後進入製程監控第二階段穩定狀態中，在此僅考慮製程第二階段的即時監控問題，在製程第二階段中，線性函數係數發生線性漂移情形，將建構以資論理論Kullback - Leibler distance，簡稱K-L distance之概念的管制圖，稱為ITPM-D管制圖(Information-Theoretical Profile Monitoring-Drift)，其管制圖統計量計算方式為由最新一期樣本資訊往前累積，稱為backward sequential testing，其概念為當製程發生變異時，變異後的樣本資料比尚未發生變異的樣本資料有更多的製程變異證據，資訊蘊含量為最大，將ITPM-D管制圖與其他管制圖進行績效指標比較，最後利用AIC赤池信息量準則判定製程變異的種類。
本研究進行蒙地卡羅模擬方式模擬ITPM-D管制圖，並記錄在不同漂移率下的ARL_1值，與T^2管制圖、EWMA-R管制圖、EWMA-3管制圖、MEWMA管制圖、CUSUM-3管制圖、LRT管制圖進行績效指標比較，透過分析結果可以發現線性迴歸模型Α_0與Α_1在小漂移率下具有良好的監測能力，線性迴歸模型變異數發生線性漂移時，其效能皆優於其他比較之管制圖；使用AIC赤池信息準則判別造成製程變異的種類做佐證，可以發現當漂移量越大時，判定製程漂移種類準確率越來越準確。

The relationship between input and output is expressed as a functional relationship between variables. In the control chart, the interpretation reaction variable and more than one interpretation variable are called profile monitoring. In this study, we will discuss the occurrence of drift in process monitoring. Drift variations such as fatigue operations of field workers and wear of equipment tools. A control chart based on the concept of capital theory Kullback-Leibler distance will be constructed, called ITPM-D control chart (Information-Theoretical Profile Monitoring-Drift), its control chart statistics calculation method is accumulated from the latest sample information forward, called backward sequential testing, the concept is that when the process occurs variation, the sample data after variation has not yet The sample data of the mutation has more evidence of process variation, and the information content is the largest. Compare the performance indicators of the ITPM-D control chart with other control charts, and finally use the Akaike information criterion (AIC) to determine the type of process variation.
Monte Carlo simulation method was used to simulate the ITPM-D control chart, and the ARL_1 value at different drift rates was recorded, compared with the T^2 control chart, EWMA-R control chart, EWMA-3 control chart, MEWMA control chart, comparing the performance indicators of the CUSUM-3 control chart and the LRT control chart, through the analysis results, it can be found that the linear regression models A_0 and A_1 have good monitoring capabilities at small drift rates. When the linear regression model has linear drift, its performance is excellent compared with other control charts; using the Akaike Information Criteria (AIC)to determine the type of process variation as evidence, we can find that when the drift amount is larger, the accuracy rate of the process drift type is more and more accurate.

中文文獻:
陳長明，以Kullback-Leibler資訊建構剖面監控管制圖，國立成功大學工業與資訊管理研究所碩士論文，民國一百零八年六月。
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