Journal of Integrative Natural Science (통합자연과학논문집)

The Basic Science Institute Chosun University (조선대학교 기초과학연구원)
권호 표지
DOI QR코드

DOI QR Code

Comparison of EWMA and CUSUM Charts with Variable Sampling Intervals for Monitoring Variance-Covariance Matrix

  • Received : 2020.10.02
  • Accepted : 2020.11.28
  • Published : 2020.12.31
Download PDF
⟨ Previous Next ⟩

Abstract

To monitor all elements simultaneously of variance-covariance matrix Σ of several correlated quality characteristics under multivariate normal process Np($\underline{\mu}$, Σ), multivariate exponentially weighted moving average (EWMA) chart and cumulative sum (CUSUM) chart are considered and compared. Numerical performances of the considered variable sampling interval (VSI) charts are evaluated using average run length (ARL), average time to signal (ATS), average number of switches (ANSW) to signal, and the probability of switch Pr(switch) between two sampling interval d1 and d2 where d1 < d2. For small or moderate changes of Σ, the performances of multivariate EWMA chart is approximately equivalent to that of multivariate CUSUM chart.

Keywords

References

  1. H. Hotelling, "Multivariate quality control", Techniques of Statistical Analysis, McGraw-Hill, New York, pp. 111-184, 1947.
  2. F. B. Alt, "Multivariate quality control" in The Encyclopedia of Statistical Sciences, eds. S. Kotz and Johnson, New York : John Wiley, 1984.
  3. J. E. Jackson, "Multivariate quality control", Communications in Statistics-Theory and Methods, Vol. 14, pp. 2657-2688, 1985. https://doi.org/10.1080/03610928508829069
  4. J. S. Jackson, "Quality control methods for several related variables", Technometrics, Vol. 1, pp. 359-377, 1959. https://doi.org/10.1080/00401706.1959.10489868
  5. P. H. Ghare and P. E. Torgersen, "The multicharacteristic control chart", Journal of Industrial Engineering, Vol. 19, pp. 269-272, 1968.
  6. S. W. Roberts, "Control chart tests based on geometric moving averages", Technometrics, Vol. 1, pp 239-250, 1959. https://doi.org/10.1080/00401706.1959.10489860
  7. S. V. Crowder and M. D. Hamilton, "An EWMA for monitoring a process standard deviation", Journal of Quality Technology, Vol. 24, pp 12-21, 1992. https://doi.org/10.1080/00224065.1992.11979369
  8. W. H. Woodall and M. M. Ncube, "Multivariate CUSUM quality control procedure", Technometrics, Vol. 27, pp 285-292, 1985. https://doi.org/10.1080/00401706.1985.10488053
  9. V. C. C. Vargas, L. F. D. Lopes, and A. M. Sauza, "Comparative study of the performances of the CuSum and EWMA control charts", Computer & Industrial Engineering, Vol. 46, pp. 707-724, 2004. https://doi.org/10.1016/j.cie.2004.05.025
  10. D. J. Chang, "Comparison of two sampling intervals and three sampling intervals VSI charts for monitoring both means and variances", Journal of the Korean Data & Information Science Society, Vol. 26, pp 997-1006, 2015. https://doi.org/10.7465/jkdi.2015.26.4.997
  11. J. H. Ryu and H. Wan, "Optimal design of a CUSUM chart for a mean shift of unknown size", Journal of Quality Technology, Vol. 42(3), pp. 311-326, 2010. https://doi.org/10.1080/00224065.2010.11917826