Journal of the Korean Data and Information Science Society

The Korean Data and Information Science Society (한국데이터정보과학회)
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Multivariate control charts for monitoring correlation coefficients in dispersion matrix

  • Chang, Duk-Joon (Department of Statistics, Changwon National University) ;
  • Heo, Sun-Yeong (Department of Statistics, Changwon National University)
  • Received : 2012.08.23
  • Accepted : 2012.09.25
  • Published : 2012.09.30
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Abstract

Multivariate control charts for effectively monitoring every component in the dispersion matrix of multivariate normal process are considered. Through the numerical results, we noticed that the multivariate control charts based on sample statistic $V_i$ by Hotelling or $W_i$ by Alt do not work effectively when the correlation coefficient components in dispersion matrix are increased. We propose a combined procedure monitoring every component of dispersion matrix, which operates simultaneously both control charts, a chart controlling variance components and a chart controlling correlation coefficients. Our numerical results show that the proposed combined procedure is efficient for detecting changes in both variances and correlation coefficients of dispersion matrix.

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References

  1. Alt, F. B. (1984). Multivariate control charts. In Encyclopedia of Statistical Sciences, edited by S. Kotz and M. L. Johnson, Wiley, New York.
  2. Chang, D. J. and Heo, S. (2012). Switching properties of CUSUM charts for controlling mean vector. Journal of the Korean Data & Information Science Society, 23, 859-866. https://doi.org/10.7465/jkdi.2012.23.4.859
  3. Chang, D. J., Kwon, Y. M. and Hong, Y. W. (2003). Markovian EWMA control chart for several correlated quality characteristics. Journal of the Korean Data & Information Science Society, 14, 1045-1053.
  4. Cho, G. Y. (2010). Multivariate Shewhart control charts with variable sampling intervals. Journal of the Korean Data & Information Science Society, 21, 999-1008.
  5. Hotelling, H. (1947). Multivariate quality control, techniques of statistical analysis, McGraw-Hill, New York, 111-114.
  6. Hotelling, H. (1951). A generalized t test and measure of multivariate dispersion, Proceedings of Second Berkely Symposium on Mathematical Statistics and Probability, University of California Press, 23-42.
  7. 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.
  8. Lawley, D. N. (1938). A generalization of Fisher's z test. Biometrika, 30, 180-187. https://doi.org/10.1093/biomet/30.1-2.180
  9. Lowry, C. A., Woodall, W. H., Champ, C. W. and Rigdon, S. E. (1992). A multivariate exponentially weighted moving average control charts. Technometrics, 34, 46-53. https://doi.org/10.2307/1269551