統計製程管制方法廣泛地應用在工業製程中，在當代的工業製程中產品的品質可能同時由多項品質特徵所影響，為了維持產品的品質普遍都得同時監控多項品質特徵，因此多變量統計製程管制方法 (multivariate statistical process control, 簡稱MSPC) 在工業製程領域中扮演重要的角色。
本文將提出一種新的管制圖，此管制圖建立的目的是為了監控多變量製程的共變異數矩陣。我們將利用不相似度指標量化兩個共變異數矩陣之間的不相似程度，再藉由無母數重複抽樣方法建立管制圖的管制界限，並且推廣成指數加權移動平均 (exponentially weighted moving average, 簡稱EWMA) 型態的管制圖。

Statistical process control (SPC) has been widely used to monitor various industrial processes. In modern industrial manufacturing, the quality of a product is usually related to several quality characteristics simultaneously. Therefore, multivariate statistical process control plays an important role in monitoring the industrial manufacturing processes.
In the article, we propose a new multivariate statistical process control chart for monitoring the covariance matrix of several quality characteristics, which is based on integrating the dissimilarity index between two covariance matrices and the exponentially weighted moving average (EWMA) control scheme.

[1] Bersimis, S., Psarakis, S. and Panaretos, J. (2007). “Multivariate Statistical Process Control Charts: An Overview”. Quality and Reliability Engineering International 23, 517-543.
[2] Crosier, R. B. (1988). “Multivariate Generalizations of Cumulative Sum Quality Control Schemes”. Technometrics 30, 291–303.
[3] Gandy, A. and Kvaløy, J. T. (2013). “Guaranteed Conditional Performance of Control Charts via Bootstrap Methods”. Scandinavian Journal of Statistics 40, 647-668.
[4] Hawking, D. M. and Maboudou-Tchao, E. M. (2008). “Multivariate Exponentially Weighted Moving Covariance Matrix”. Technometrics 50, 155-166.
[5] Healy, J. D. (1987). “A Note on Multivariate CUSUM Procedures”. Technometrics 29, 409–412.
[6] Hotelling, H. (1947). “Multivariate Quality Control. Eisenhart, C., Hastay, M. W., and Wallis, W. A. eds.”. Techniques of Statistical Analysis. McGraw-Hill, New York.
[7] Kano, M., Hasebe, S. and Hashimoto, I. (2002). “Statistical Process Monitoring Based on Dissimilarity of Process Data”. AIChE Journal 48, 1231-1240.
[8] Lowry, C. A., Woodall, W. H., Champ, C. W. and Rigdon, S. E. (1992). “A Multivariate Exponentially Weighted Moving Average Control Chart”. Technometrics 34, 46-53.
[9] Lucas, J. M. and Saccucci, M. S. (1990). "Exponentially weighted moving average control schemes: Properties and enhancements". Technometrics 32, 1-29.
[10] Montgomery, D. C., Woodall, W. H. (1999). “Research Issues and Ideas in Statistical Process Control”. Journal of Quality Technology 31, 376-387.
[11] Page, E. S. (1954). “Continuous Inspection Schemes”. Bionetrics 41, 100-115.
[12] Pignatiello, J. J. and Runger, G. C. (1990). “Comparison of Multivariate CUSUM Charts”. Journal of Quality Technology 22, 173–186.
[13] Robert, S. W. (1959). “Control Chart Test Based on Geometric Moving Averages”. Technometrics 42, 97-102.
[14] Shewhart, W. A. (1924). “Some applications of statistical methods to the analysis of physical and engineering data”. Bell System Technical Journal 3, 43-87.
[15] Stoumbos, Z. G., Reynolds Jr, M. R., Ryan, T. P., & Woodall, W. H. (2000). “The state of statistical process control as we proceed into the 21st century”. Journal of the American Statistical Association 95, 992-998.
[16] Yeh, A. B., Huwang, L. and Wu, C.-W. (2005). “A Multivariate EWMA Control Chart for Monitoring Process Variability with Individual Observations”. IIE Transactions 37, 1023-1035.
[17] Yeh, A. B., Huwang, L. and Wu, Y.-F. (2004). “A Likelihood-Ratio-Based EWMA Control Chart for Monitoring Variability of Multivariate Normal Processes”. IIE Transactions 36, 865-879.
[18] Yeh, A. B., Lin, D., Zhou, H. and Venkataramani, C. (2003). “A Multivariate Exponentially Weighted Moving Average Control Chart for Monitoring Process Variability”. Journal of Applied Statistics 30, 507-536.
[19] Zamba, K. D. and Hawkins, D. M. (2006). “A Multivariate Change-Point Model for Statistical Process Control”. Technometrics 48, 539-549.

[20] 鄭宇翔 (2014). “使用不相似度準則監控多變量製程的共變異數矩陣”. 國立清華大學統計學研究所碩士論文, 新竹市, 台灣