統計製程管制是一些使製程穩定和經由降低變異改善製程能力的有力工具集合，其中管制圖被廣泛的應用在製程的監控上，在過去單變量管制圖已被廣泛地應用於製程管制中，且具有相當良好的監控績效。然而，隨著製程複雜度的增加，製程品質往往受到多個品質特性所影響，且品質特性之間通常存在著相關性。此時，如果繼續沿用單變量管制圖，將容易出現嚴重的誤判。若要同時監控數個彼此間具有相關性之品質特性，則必須使用多變量管制圖(multivariate control chart)。常見的多變量管制圖有：Hotellings T^2管制圖、MCUSUM管制圖及MEWMA管制圖。本研究利用Kullback-Leibler Distance以及最大概似法的概念，使用兩種方式計算K-L Distance，建構不需要事先設定參數，在多變量過程中同時監測平均向量與共變異數矩陣位移的管制圖，稱為Multivariate Information Theoretical Based Process Control Chart，簡稱MIPC管制圖；在品質參數間無相關性或具有相關性的情況下與MCUSUM、MEWMA、Hotellings T^2、混合型管制圖進行管制績效比較，根據分析結果可知MIPC管制圖相較於其他類型的管制圖，在平均向量位移的偵測上，在廣泛位移都有不錯的監測效果，而在共變異數矩陣的監控上，則是在發生小位移時有很好的表現，且品質參數間的相關性越大MIPC管制圖會有越好的監測效果。整體而言，MIPC管制圖有兩種計算資訊落差的方式，其中使用由後往前增加考慮樣本期數的方式要比使用最大概似法估計的方式監控效果好，但是使用最大概似法的這個方式可以預估出發生位移的樣本期數，進而估計出位移後的平均向量的估計量。整體來說MIPC管制圖是個易於使用且具有良好監測效果的管制圖。

This paper develop a statistical process control (SPC) chart based on Kullback Leibler distance of information theory to monitor the mean vector, covariance matrix ,or both shift of the multivariate normal process. We name this control chart Multivariate Information Theoretical Based Process Control Chart (MIPC).We construct two approaches to calculate the information gap between the probability distributions. This two approaches are named MIPC-L and MIPC-I, respectively. The control limits of the control chart are obtained by 100,000 runs when in-control average time to signal is 800. The performance of MIPC Control Chart is depended on the direction of the shift in mean vector or covariance matrix, so performance is investigated for specific shift direction and also averages overall direction. The best overall performance is achieves using a MIPC-I.

中文文獻:
李庭媁，應用資訊理論於管制圖之建構，國立成功大學工業與資訊管理研究所碩士論文，民國一百零三年六月
翁奕軒，應用資訊理論於建構同時監控製程平均數及製程變異數之管制圖，國立成功大學工業與資訊管理研究所碩士論文，民國一百零四年六月
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