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Switching properties of multivariate Shewhart control charts

  • Kim, Bo-Jung (Department of Statistics, Kyungpook National University) ;
  • Cho, Gyo-Young (Department of Statistics, Kyungpook National University)
  • Received : 2017.06.08
  • Accepted : 2017.07.05
  • Published : 2017.07.31

Abstract

We investigate the properties of multivariate Shewart control charts with VSI procedure for monitoring simultaneous monitoring mean vector and covariance matrix in term of ANSW (average number of switches), probability of switch and ASI (average sampling interval), ATS (average time to signal). From examining the ANSW values, we know that it does not switch frequently. The VSI control charts are superior to the corresponding FSI control charts in terms of ATS. And, it can be also seen that the VSI procedures have substantially fewer switches for small or moderate shifts of the mean vector and variances.

Keywords

References

  1. Alt, F. A. (1984). Multivariate quality control, in Encyclopedia of Statistical Sciences, edited by. S. Kotz and N. L. Johnson, Wiley, New York.
  2. Amin, R. W. and Lestinger, W. C. (1991) Improved switching rules in control procedures using variable sampling interval. Communications in Statistics-Simulation and Computation, 20, 205-203. https://doi.org/10.1080/03610919108812949
  3. Arnold, J. C. (1970). A Markovian sampling policy applied to quality monitoring of streams. Biometrics, 26, 739-747. https://doi.org/10.2307/2528720
  4. Bersimis, S., Psarakis, S. and Panaretos, J. (2007). Multivariate statistical process control charts: An Overview, Quality and Reliability Engineering International, 23, 517-543. https://doi.org/10.1002/qre.829
  5. Chang, D. J. and Cho, G. Y. (2005). CUSUM charts for monitoring mean vector with variable sampling intervals. Journal of the Korean Data Analysis Society, 7, 1133-1143.
  6. Chang, D. J. and Heo, S. Y. (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
  7. Chengalur-Smith, I. N., Arnold, J. C. and Reynolds, M. R., Jr. (1989). Variable sampling intervals for multiparameter Shewhart charts. Communications in Statistics - Theory and Methods, 18, 1769-1792. https://doi.org/10.1080/03610928908830000
  8. Gwon, H. J. and Cho, G. Y. (2015). Switching properties of bivariate Shewhart control charts for monitoring the covariance matrix. Journal of the Korean Data & Information Science Society, 26, 1593-1600. https://doi.org/10.7465/jkdi.2015.26.6.1593
  9. Hotelling, H. (1947). Multivariate quality control-illustrated by the air testing of sample bombsights, in techniques of statistical analysis, C. Eisenhart, M. W. Hastay, and W. A. Wallis, McGraw-Hill, New-York.
  10. Jeong, J. I. and Cho, G. Y. (2012a). 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
  11. Jeong, J. I. and Cho, G. Y. (2012b). Multivariate EWMA 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
  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. Montgomery, D. C. (2009). Introduction to statistical quality control, 6th edition, Wiley, New York.
  14. Reynolds, M. R., Jr. and Arnold, J. C. (1989). Optimal one-sided Shewhart control charts with variable sampling intervals between samples. Sequential Analysis, 8, 51-77. https://doi.org/10.1080/07474948908836167
  15. 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
  16. 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
  17. Reynolds, M. R., Jr. and Stoumbos, Z. G. (2001). Monitoring the process mean and variance using individual observations and variable sampling intervals. Journal of Quality Technology, 33, 181-205. https://doi.org/10.1080/00224065.2001.11980066
  18. Smeach, S. C. and Jernigan, R. W. (1977). Further aspect of a Markovian sampling policy for water quality monitoring. Biometrics, 33, 41-46. https://doi.org/10.2307/2529301
  19. Stoumbos, Z. G. and Reynolds, M. R., Jr. (2005). Economic statistical design of adaptive control schemes for monitoring the mean and variance: An application to analyzers. Nonlinear Analysis-Real-World Applications, 6, 817-844. https://doi.org/10.1016/j.nonrwa.2005.05.002
  20. 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
  21. Zhang, S. and Wu, Z. (2006). Monitoring the process mean and variance using a weighted loss function CUSUM scheme with variable sampling intervals. IIE Transactions, 38, 377-387. https://doi.org/10.1080/07408170500232578