Journal of the Korean Data and Information Science Society

The Korean Data and Information Science Society (한국데이터정보과학회)
권호 표지
DOI QR코드

DOI QR Code

Multivariate CUSUM control charts for monitoring the covariance matrix

  • Choi, Hwa Young (Department of Statistics, Kyungpook National University) ;
  • Cho, Gyo-Young (Department of Statistics, Kyungpook National University)
  • Received : 2016.01.18
  • Accepted : 2016.03.21
  • Published : 2016.03.31
Download PDF
⟨ Previous Next ⟩

Abstract

This paper is a study on the multivariate CUSUM control charts using three different control statistics for monitoring covariance matrix. We get control limits and ARLs of the proposed multivariate CUSUM control charts using three different control statistics by using computer simulations. The performances of these proposed multivariate CUSUM control charts have been investigated by comparing ARLs. The purpose of control charts is to detect assignable causes of variation so that these causes can be found and eliminated from process, variability will be reduced and the process will be improved. We show that the charts based on three different control statistics are very effective in detecting shifts, especially shifts in covariances when the variables are highly correlated. When variables are highly correlated, our overall recommendation is to use the multivariate CUSUM control charts using trace for detecting changes in covariance matrix.

Keywords

References

  1. Chang, D. J. and Heo, S. Y. (2011). Control charts for monitoring correlation coecients in variance-covariance matrix. Journal of the Korean Data & Information Science Society, 22, 1-5.
  2. Hotelling, H. (1947). Multivariate quality control, techniques of statistical analysis, McGraw-Hill, New York.
  3. Hotelling, H. (1951). A generalized T test and measure of multivariate dispersion, Proceedings of the second Berkeley symposium on mathematical statistics and probability, University of California Press, Berkeley.
  4. Hui, Y. V. (1980). Topics in statistical process control. Ph.D. dissertation, Virginia Polytechnic Institute and State University, Blacksburg, Virginia.
  5. Jeong, J. I. and Cho, G. Y. (2012a). Multivariate control charts for monitoring the variance-covariance matrix. Journal of the Korean Data & Information Science Society, 23, 807-814. https://doi.org/10.7465/jkdi.2012.23.4.807
  6. Jeong, J. I. and Cho, G. Y. (2012b). Multivariate Shewhart control charts for monitoring the vatiance-covariance matrix. Journal of the Korean Data & Information Science Society, 23, 617-626. https://doi.org/10.7465/jkdi.2012.23.3.617
  7. 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
  8. Nagarsenker, B. N. and Pillai, K. C. S. (1973). The distribution of the sphericity test criterion. Journal of Multivariate Analysis, 3, 226-235. https://doi.org/10.1016/0047-259X(73)90025-0
  9. Page, E. S. (1954). Continuous inspection schemes. Biometrika, 41, 100-114. https://doi.org/10.1093/biomet/41.1-2.100
  10. Reynolds, M. R., Jr. and Cho, G. Y. (2006). Multivariate control charts for monitoring the mean vector and covariance matrix. Journal of Quality Technology, 38, 230-253. https://doi.org/10.1080/00224065.2006.11918612
  11. Reynolds, M. R., Jr. and Cho. G. Y. (2011). Multivariate control charts for monitoring the mean vector and covariance matrix with variable sampling intervals. Sequential Analysis, 30, 1-40. https://doi.org/10.1080/07474946.2010.520627

Cited by

  1. 비모수적 Shewhart-Lepage 관리도의 최적 설계 vol.28, pp.2, 2016, https://doi.org/10.7465/jkdi.2017.28.2.339
  2. Multivariate control charts based on regression-adjusted variables for covariance matrix vol.28, pp.4, 2016, https://doi.org/10.7465/jkdi.2017.28.4.937