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http://dx.doi.org/10.7465/jkdi.2012.23.4.807

Multivariate EWMA control charts for monitoring the variance-covariance matrix  

Jeong, Jeong-Im (Department of Statistics, Kyungpook National University)
Cho, Gyo-Young (Department of Statistics, Kyungpook National University)
Publication Information
Journal of the Korean Data and Information Science Society / v.23, no.4, 2012 , pp. 807-814 More about this Journal
Abstract
We know that the exponentially weighted moving average (EWMA) control charts are sensitive to detecting relatively small shifts. Multivariate EWMA control charts are considered for monitoring of variance-covariance matrix when the distribution of process variables is multivariate normal. The performances of the proposed EWMA control charts are evaluated in term of average run length (ARL). The performance is investigated in three types of shifts in the variance-covariance matrix, that is, the variances, covariances, and variances and covariances are changed respectively. Numerical results show that all multivariate EWMA control charts considered in this paper are effective in detecting several kinds of shifts in the variance-covariance matrix.
Keywords
Average run length; multivariate exponentially weighted moving average control chart; variance-covariance matrix;
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Times Cited By KSCI : 3  (Citation Analysis)
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1 Roberts, S. W. (1959). Control chart tests based on geometric moving averages. Technometrics, 1, 239-250.   DOI
2 Robinson, P. B. and Ho, T. Y. (1978). Average run length of geometric moving average charts by numerical methods. Technometrics, 20, 85-93.   DOI   ScienceOn
3 Prabhu, S. S. and Runger, G. C. (1997). Designing a multivariate EWMA control chart. Journal of Quality Technology, 29, 8-15.
4 Saccucci, M. S. and Lucas, J. M. (1990). Average run lengths for exponentially weighted moving average control schemes using the Markov chain approach. Jounal of Quality Technology, 22, 154-162.
5 Sweet, A. L. (1986). Control chart using coupled exponentially weighted moving averages. IIE Transactions 18, 26-33.   DOI
6 Wierda, S. J. (1994). multivariate statistical process control - recent results and directions for future research. Statistica Neerlandica, 48, 147-168.   DOI   ScienceOn
7 Crowder, S. V (1989). Design of exponentially weighted moving average schemes. Journal of Quality Tech- nology, 21, 155-162.
8 Ghare, P. H. and Torgerson, P. E. (1968). The multicharacteristic control chart. Journal of Industrial Engineering, 19, 269-272.
9 Hotelling, H. (1947). Multivariate quality control, techniques of statistical analysis, McGraw-Hill, New York, 111-184.
10 Hunter, J. S. (1968). The exponentially weighted moving average. Journal of Quality Technology, 18, 203- 210.
11 Im, C. D. and Cho, G. Y. (2009). Multiparameter CUSUM charts with variable sampling intervals. Journal of the Korean Data & Information Science Society, 20, 593-599.   과학기술학회마을
12 Jackson, J. S. (1959). Quality control methods for several related variables. Technometrics, 1, 359-377.   DOI
13 Lim, C and Cho, G. Y. (2008). A new EWMA control chart for monitoring the covariance matrix of bivariate processes. Journal of the Korean Data & Information Science Society, 19, 677-683.
14 Lowry, C. A. and Montgomery, D. C. (1995). A review of multivariate control charts. IIE Transactions, 27, 800-810.   DOI   ScienceOn
15 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.   DOI   ScienceOn
16 Lucas, J. M. and Saccucci, M. S. (1990). Exponentially weighted moving average control schemes: Properties and enhancements. Technometrics, 32, 1-12.   DOI   ScienceOn
17 MacGregor, J. F. and Jarris, T. J. (1993). The exponentially weighted moving variance. Journal of Quality Technology, 25, 106-118.
18 Reynolds, M. R., Jr. and Kim, G. (2005). Multivariate monitoring of the mean vector using sequential sampling. Journal of Quality Technology, 37, 149-162.
19 Alt, F. B. (1984). Multivariate control charts. In Encyclopedia of Statistical Sciences, edited by S. Kotz and N. L. Johnson, John Wiley, New York.
20 Chang, D. J. and Shin, J. K. (2009). Variable sampling interval control charts for variance-covariance matrix. Journal of the Korean Data & Information Science Society, 21, 999-1008.   과학기술학회마을
21 Cho, G. Y. (2010). Multivariate Shewhart control charts with variable sampling intervals. Journal of the Korean Data & Information Science Society, 21, 999-1008.   과학기술학회마을
22 Crowder, S. V (1987). A simple method for studying run length distributions of exponentially weighted moving average control charts. Technometircs, 29, 401-407.