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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)
  • Received : 2012.05.14
  • Accepted : 2012.06.05
  • Published : 2012.07.31

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.

References

  1. Alt, F. B. (1984). Multivariate control charts. In Encyclopedia of Statistical Sciences, edited by S. Kotz and N. L. Johnson, John Wiley, New York.
  2. 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.
  3. Cho, G. Y. (2010). Multivariate Shewhart control charts with variable sampling intervals. Journal of the Korean Data & Information Science Society, 21, 999-1008.
  4. Crowder, S. V (1987). A simple method for studying run length distributions of exponentially weighted moving average control charts. Technometircs, 29, 401-407.
  5. Crowder, S. V (1989). Design of exponentially weighted moving average schemes. Journal of Quality Tech- nology, 21, 155-162.
  6. Ghare, P. H. and Torgerson, P. E. (1968). The multicharacteristic control chart. Journal of Industrial Engineering, 19, 269-272.
  7. Hotelling, H. (1947). Multivariate quality control, techniques of statistical analysis, McGraw-Hill, New York, 111-184.
  8. Hunter, J. S. (1968). The exponentially weighted moving average. Journal of Quality Technology, 18, 203- 210.
  9. 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.
  10. Jackson, J. S. (1959). Quality control methods for several related variables. Technometrics, 1, 359-377. https://doi.org/10.1080/00401706.1959.10489868
  11. 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.
  12. Lowry, C. A. and Montgomery, D. C. (1995). A review of multivariate control charts. IIE Transactions, 27, 800-810. https://doi.org/10.1080/07408179508936797
  13. 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. https://doi.org/10.2307/1269551
  14. Lucas, J. M. and Saccucci, M. S. (1990). Exponentially weighted moving average control schemes: Properties and enhancements. Technometrics, 32, 1-12. https://doi.org/10.1080/00401706.1990.10484583
  15. MacGregor, J. F. and Jarris, T. J. (1993). The exponentially weighted moving variance. Journal of Quality Technology, 25, 106-118.
  16. Reynolds, M. R., Jr. and Kim, G. (2005). Multivariate monitoring of the mean vector using sequential sampling. Journal of Quality Technology, 37, 149-162.
  17. Roberts, S. W. (1959). Control chart tests based on geometric moving averages. Technometrics, 1, 239-250. https://doi.org/10.1080/00401706.1959.10489860
  18. Robinson, P. B. and Ho, T. Y. (1978). Average run length of geometric moving average charts by numerical methods. Technometrics, 20, 85-93. https://doi.org/10.1080/00401706.1978.10489620
  19. Prabhu, S. S. and Runger, G. C. (1997). Designing a multivariate EWMA control chart. Journal of Quality Technology, 29, 8-15.
  20. 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.
  21. Sweet, A. L. (1986). Control chart using coupled exponentially weighted moving averages. IIE Transactions 18, 26-33. https://doi.org/10.1080/07408178608975326
  22. Wierda, S. J. (1994). multivariate statistical process control - recent results and directions for future research. Statistica Neerlandica, 48, 147-168. https://doi.org/10.1111/j.1467-9574.1994.tb01439.x

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