對一個多變量製程來說，共變異數矩陣的監控是個重要的議題，而傳統的 Shewhart 管制圖在監控多變量製程的共變異數矩陣時，需要樣本觀測值個數大於品質特性個數的條件。本文將介紹一種新的管制圖來監控多變量製程的共變異數矩陣，並且證明這種管制圖在樣本觀測值個數小於品質特性個數的某些情形下也能進行監控。我們同時會使用統計模擬的方法對新的管制圖與傳統的管制圖做一個比較，最後再提出一種保證管制圖來改善所提出的新管制圖。

1. Alt, F. (1985). “Multivariate Quality Control.”Encycloped of Statistical Science, 6, 110-122.
2. Gandy, A. and Kvaløy, J. T. (2013). “Guaranteed Conditional Performance of Control Charts via Bootstrap Methods.” Scandinavian Journal of Statistics, 40, 647-668.
3. Hawking, D. M. and Maboudou-Tchao, E. M. (2008). “Multivariate Exponentially Weighted Moving Covariance Matrix.” Technometrics, 50, 155-166.
4. Kano, M., Hasebe, S. and Hashimoto, I. (2002). “Statistical Process Monitoring Based on Dissimilarity of Process Data.” AIChE Journal, 48, 1231-1240.
5. Li, Z., Zou, C. and Wang, Z. (2013). “A Multivariate Sign Chart for Monitoring Process Shape Parameters.” Journal of Quality Technology, 45, 149-165.
6. Montgomery, D. C. (2013). Statistical Quality Control: A Model Introduction, 7th ed, John Wiley & Sons, New York.
7. Page, E. S. (1954). “Continuous Inspection Schemes.” Bionetrics, 41, 100-115.
8. Quesenberry, C. P. (2001). “The Multivariate Short-Run Snapshot Q Chart.” Quality Engineering, 13, 679-683.
9. Robert, S. W. (1959). “Control Chart Test Based on Geometric Moving Averages.” Technometrics, 42, 97-102.
10. Villasenor-Alva, J. A. and Gonzalez-Estrada, E. (2009). “A Generalization of Shapiro-Wilk's Test for Multivariate Normality.” Communications in Statistics-Theory and Method, 38, 1870-1883.