Journal of the Korean Data and Information Science Society

The Korean Data and Information Science Society (한국데이터정보과학회)
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Comparison of accumulate-combine and combine-accumulate methods in multivariate CUSUM charts for mean vector

  • Chang, Duk-Joon (Department of Statistics, Changwon National University) ;
  • Heo, Sunyeong (Department of Statistics, Changwon National University)
  • Received : 2013.06.09
  • Accepted : 2013.07.06
  • Published : 2013.07.31
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Abstract

We compared two basic methods, combine-accumulate method and accumulate-combine method, using the past quality information in multivariate quality control procedure for monitoring mean vector of multivariate normal process. When small or moderate shifts have occurred, accumulate-combine method yields smaller average run length (ARL) and average time to signal (ATS) than combine-accumulate method. On the other hand, we have found from our numerical results that combine-accumulate method has better performances in terms of switching behavior than accumulate-combine method. In industry, a quality engineer could select one of the two method under the comprehensive consideration about the required time to signal, switching behavior, and other physical factors in the production process.

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References

  1. Amin, R. W. and Letsinger, W. C. (1991). Improved switching rules in control procedures using variable sampling intervals. Communications in Statistics-Simulation and Computation, 20, 205-230. https://doi.org/10.1080/03610919108812949
  2. Bai, D. S. and Lee, K. T. (2002). Variable sampling interval $\overline{X}$ control charts with an improved switching rule. International Journal of Production Economics, 76, 189-199. https://doi.org/10.1016/S0925-5273(01)00161-X
  3. Barnard, G. A. (1959). Control charts and stochastic process. Journal of Royal Statistical Society B, 2, 239-257.
  4. Brook, D. and Evans, D. A. (1972). An approach to the probability distribution of CUSUM run length. Biometrika,59, 539-549. https://doi.org/10.1093/biomet/59.3.539
  5. Champ, C. W. and Woodall, W. H. (1987). Exact results for Shewhart control charts with supplementary runs rules. Technometrics, 29, 393-399. https://doi.org/10.1080/00401706.1987.10488266
  6. Chang, D. J. and Heo, S. (2010). Properties of variable sampling interval control charts. Journal of the Korean Data & Information Science Society, 21, 819-829.
  7. Chang, D. J., Kwon, Y. M. and Hong, Y. W. (2003). Markovian EWMA control chart for several correlated quality characteristics. Journal of the Korean Data & Information Science Society, 14, 1045-1053.
  8. Cho, G. Y. (2010). Multivariate Shewhart control charts with variable sampling intervals. Journal of the Korean Data & Information Science Society, 21, 999-1008.
  9. Crosier, R. B. (1988). Multivariate generalizations of cumulative sum quality-control schemes, Technometrics, 30, 291-303. https://doi.org/10.1080/00401706.1988.10488402
  10. Cui, R. Q. and Reynolds, M. R., Jr. (1988). $\overline{X}$ charts with runs rules and variable sampling intervals. Communications in Statistics-Simulation and Computation, 17, 1073-1093. https://doi.org/10.1080/03610918808812713
  11. 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.
  12. Johnson, R. A. and Wichern, D. W. (1988). Applied multivariate statistical analysis, 2nd ed. Prentice Hall. Englewood Cliffs, NY.
  13. Moore, P. G. (1958). Some properties of runs in quality control procedures. Biometrika, 45, 89-95. https://doi.org/10.1093/biomet/45.1-2.89
  14. Page, E. S. (1954). Continuous inspection schemes. Biometrika, 41, 100-114. https://doi.org/10.1093/biomet/41.1-2.100
  15. Page, E. S. (1955). Control charts with warning lines. Biometrika, 42, 243-260. https://doi.org/10.1093/biomet/42.1-2.243
  16. Page, E. S. (1962). A modified control chart with warning lines. Biometrika, 49, 171-176. https://doi.org/10.1093/biomet/49.1-2.171
  17. Pignatiello, J. J., Jr. and Runger, G. C. (1990). Comparisons of multivariate CUSUM charts, Journal of Quality Technology, 22, 173-186. https://doi.org/10.1080/00224065.1990.11979237
  18. Reynolds, M. R., Jr., Amin, R. W. and Arnold, J. C. (1990). CUSUM chart with variable sampling intervals. Technometrics, 32, 371-396. https://doi.org/10.1080/00401706.1990.10484721
  19. Woodall, W. H. and Ncube, M. M. (1985). Multivariate CUSUM quality control procedure. Technometrics, 27, 285-292. https://doi.org/10.1080/00401706.1985.10488053