隨著產品日漸複雜，在生產過程中需要為產品考量多個品質特徵之間的相關性才能確保品質的穩定性。傳統單變量管制圖因將製程中多個品質特徵皆當成相互獨立，有時會導致誤判而未發覺出其實製程已產生變異進而產生缺陷品。因此本研究建立一個同時監控均向量與共變異數矩陣位移之多變量管制圖，且資料樣本服從多元常態分配。透過此管制圖來監控所考慮的估計統計量是否落在規定的管制界線內。即便已經有諸多如Hotelling〖 T〗^2、MCUSUM(Multivariate Cumulative Sum)、MEWMA(Multivariate Exponentially Weighted Moving Average)等多變量管制圖用來監控製程，但這些管制圖中前者無法快速檢測出小位移變化的發生，後面兩者則需要事前設定設計參數，若參數估計錯誤可能導致管制圖監控變異的績效不如預期。因此本研究建立一個不需要事前進行參數設定的多變量管制圖，並在相關係數為0、0.5與0.7的情況下，針對平均向量與共變異數矩陣位移皆偏移的案例去做討論。而根據第四章的結果分析，本研究之KLI多變量管制圖在相關係數ρ=0.0與ρ=0.7時之績效表現優於MVMAX以及NCS管制圖，而在相關系數為ρ=0.5時則略輸。但因KLI管制圖與所比較之管制圖有諸多優勢，例如無需制定設計參數來降低使用門檻、不需為多個品質特徵計算多個統計量、在廣泛位移下具有不錯的製程變異監控效果。因此當考量到品質特徵間的相關性且製程樣本在服從多元常態分布下，建議可使用本研究之KLI多變量管制圖作為監控擁有多個品質特徵製程的選擇。

This study utilizes Kullback-Leibler Information (KLI) theory to establish a multivariate control chart that considers the correlation between multiple quality characteristics. And is mainly used for Phase II process monitoring. This control chart does not require any design parameters and can widely monitor varying degrees of shifts in the mean vector and covariance matrix within the process. The performance of the KLI multivariate control chart is compared with the MVMAX control chart and the NCS (Non-central Chi-Square) control chart. According to the result analysis, both the NCS and MVMAX control charts require finding suitable design parameters to achieve the best performance. In contrast, the KLI multivariate control chart outperforms the compared control charts in most scenarios and doesn’t require any design parameters. Therefore, the KLI multivariate control chart is suitable for detecting variations in the mean vector and covariance matrix among multiple quality characteristics in a process.

中文文獻：
廖可歆(民105)。應用資訊理論於建構多變量管制圖。國立成功大學工業與資訊管理研究所碩士論文。
黃昱霖(民112)。Kullback-Leibler資訊管制圖警訊後之診斷。國立成功大學工業與資訊管理研究所碩士論文。
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