Journal of the Korean Data and Information Science Society

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

DOI QR Code

A statistical quality control for the dispersion matrix

  • Jo, Jinnam (Department of Statistics and Information Science, Dongduk Women's University)
  • Received : 2015.06.30
  • Accepted : 2015.07.20
  • Published : 2015.07.31
Download PDF
⟨ Previous Next ⟩

Abstract

A control chart is very useful in monitoring various production process. There are many situations in which the simultaneous control of two or more related quality variables is necessary. When the joint distribution of the process variables is multivariate normal, multivariate Shewhart control charts using the function of the maximum likelihood estimator for monitoring the dispersion matrix are considered for the simultaneous monitoring of the dispersion matrix. The performances of the multivariate Shewhart control charts based on the proposed control statistic are evaluated in term of average run length (ARL). The performance is investigated in three cases, where the variances, covariances, and variances and covariances are changed respectively. The numerical results show that the performances of the proposed multivariate Shewhart control charts are not better than the control charts using the trace of the covariance matrix in the Jeong and Cho (2012) in terms of the ARLs.

Keywords

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. Anderson, T. W. (1958). An introduction to multivariate statistical analysis, Wiley, New York.
  3. Aparisi, F., Jabaioyes, J. and Carrion, A. (2009). Statistical properties of the $\left|S\right|$ multivariate control chart. Communications in Statistics-theory and methods, 28, 2671-2686.
  4. 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.
  5. Ghare, P. H. and Torgerson, P. E. (1968). The multicharacteristic control chart. Journal of Industrial Engineering, 19, 269-272.
  6. Hotelling, H. (1947). Multivariate quality control, techniques of statistical analysis, McGraw-Hill, New York, 111-184.
  7. Hui, Y. V. (1980). Topics in statistical process control, Ph. D. Thesis, Virginia Politechnic Institute and State University, Blacksberg, Virginia.
  8. 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.
  9. Jackson, J. S. (1959). Quality control methods for several related variables. Technometrics, 1, 359-377. https://doi.org/10.1080/00401706.1959.10489868
  10. Jeong, J. I. and Cho, G. Y. (2012). Multivariate Shewhart control charts for monitoring the variance-covariance matrix. Journal of the Korean Data & Information Science Society, 23, 617-628. https://doi.org/10.7465/jkdi.2012.23.3.617
  11. 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
  12. Na, O., Ko, B. and Lee, S. (2010). Cusum of squares test for discretely observed sample from multidimen-sional diffusion processes. Journal of the Korean Data & Information Science Society, 21, 555-560.
  13. Wierda, S. J. (1994). Multivariate statistical process control - recent results and directions for future re-search. Statistica Neerlandica, 48, 147-168. https://doi.org/10.1111/j.1467-9574.1994.tb01439.x