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 Shewhart 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 : 2012.04.29
  • Accepted : 2012.05.22
  • Published : 2012.05.31
Download PDF
⟨ Previous Next ⟩

Abstract

Multivariate Shewhart control charts are considered for the simultaneous monitoring the variance-covariance matrix when the joint distribution of process variables is multivariate normal. The performances of the multivariate Shewhart control charts based on control statistic proposed by Hotelling (1947) are evaluated in term of average run length (ARL) for 2 or 4 correlated variables, 2 or 4 samples at each sampling point. The performance is investigated in three cases, that is, the variances, covariances, and variances and covariances are changed respectively.

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. 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. Ghare, P. H. and Torgerson, P. E. (1968). The multicharacteristic control chart. Journal of Industrial Engineering, 19, 269-272.
  5. Hotelling, H. (1947). Multivariate quality control, techniques of statistical analysis, McGraw-Hill, New York, 111-184.
  6. Hui, Y. V. (1980). Topics in statistical process control, Ph.D. Dissertation, Virginia Politechnic Institute and State University, Blacksberg, Virginia.
  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. Jackson, J. S. (1959). Quality control methods for several related variables.Technometrics, 1, 359-377. https://doi.org/10.1080/00401706.1959.10489868
  9. 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.
  10. Mason, R. L. and Young, J. C. (2002). Multivariate statistical process control with industrial applications, ASASIM, Philadelphia, PA.
  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. 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
  13. Na, O., Ko, B. and Lee, S. (2010). Cusum of squares test for discretely observed sample from multidimen- sional di usion processes. Journal of the Korean Data & Information Science Society, 21, 555-560.
  14. Prabhu, S. S. and Runger, G. C. (1997). Designing a multivariate EWMA control chart. Journal of Quality Technology, 29, 8-15.
  15. Reynolds, M. R., Jr. and Stoumbos, Z. G. (2004a). Control charts and the ecient allocation of sampling resources. Technometrics, 46, 200-214. https://doi.org/10.1198/004017004000000257
  16. Reynolds, M. R., Jr. and Stoumbos, Z. G. (2004b). Should observations be grouped for e ective process monitoring? Journal of Quality Technology, 36, 343-366.
  17. Reynolds, M. R., Jr. and Kim, G. (2005). Multivariate monitoring of the mean vector using sequential sampling. Journal of Quality Technology, 37, 149-162.
  18. 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.
  19. Tang, P. F. and Barnett, N. S. (1996a). Dispersion control for multivariate processes. Australian Journal of Statistics, 38, 235-251. https://doi.org/10.1111/j.1467-842X.1996.tb00680.x
  20. Tang, P. F. and Barnett, N. S. (1996b). Dispersion control for multivariate processes - Some comparisons. Australian Journal of Statistics, 38, 253-2731. https://doi.org/10.1111/j.1467-842X.1996.tb00681.x
  21. 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

Cited by

  1. Switching properties of bivariate Shewhart control charts for monitoring the covariance matrix vol.26, pp.6, 2015, https://doi.org/10.7465/jkdi.2015.26.6.1593
  2. Comparison of two sampling intervals and three sampling intervals VSI charts for monitoring both means and variances vol.26, pp.4, 2015, https://doi.org/10.7465/jkdi.2015.26.4.997
  3. A statistical quality control for the dispersion matrix vol.26, pp.4, 2015, https://doi.org/10.7465/jkdi.2015.26.4.1027
  4. Multivariate CUSUM control charts for monitoring the covariance matrix vol.27, pp.2, 2016, https://doi.org/10.7465/jkdi.2016.27.2.539
  5. Switching performances of multivarite VSI chart for simultaneous monitoring correlation coefficients of related quality variables vol.28, pp.2, 2012, https://doi.org/10.7465/jkdi.2017.28.2.451
  6. Switching properties of multivariate Shewhart control charts vol.28, pp.4, 2012, https://doi.org/10.7465/jkdi.2017.28.4.911
  7. Multivariate control charts based on regression-adjusted variables for covariance matrix vol.28, pp.4, 2012, https://doi.org/10.7465/jkdi.2017.28.4.937