Multiparameter CUSUM charts with variable sampling intervals

  • Im, Chang-Do (Department of Statistics, Kyungpook National University) ;
  • Cho, Gyo-Young (Department of Statistics, Kyungpook National University)
  • 발행 : 2009.05.31

초록

We consider the problem of using control charts to monitor more than one parameter with emphasis on simultaneously monitoring the mean and variance. The fixed sampling interval (FSI) control charts are modified to use variable sampling interval (VSI) control charts depending on what is being observed from the data. In general, approaches of monitoring the mean and variance simultaneously is to use separate charts for each parameter and a combined chart. In this paper, we use three basic strategies which are separate Shewhart charts for each parameter, a combined Shewhart chart and a combined CUSUM chart. We showed that a combined VSI CUSUM chart is comparatively more efficient than any other chart if the shifts in both mean and variance are small.

참고문헌

  1. Chengalure-Smith, I. N., Arnold, J. C. and Reynolds, M. R., Jr. (1989). Variable sampling intervals for multiparameter Shewhart charts. Communication in Statistics-Theory and Methods, 18, 1769-1792. https://doi.org/10.1080/03610928908830000
  2. Cui, R. and Reynolds, M. R., Jr. (1988). X -charts with runs rules and variable sampling intervals. Communication in Statistics-Theory and Methods, 17, 1073-1093.
  3. Page, E. S. (1954). Continuous inspection schemes. Biometrika, 41, 100-114. https://doi.org/10.1093/biomet/41.1-2.100
  4. Reynolds, M. R., Jr., Amin, R. W. and Arnold, J. C. (1990). Cusum charts with variable sampling intervals. Technometrics, 32, 371-384. https://doi.org/10.2307/1270114
  5. Reynolds, M. R., Jr., Amin, R. W., Arnold, J. C. and Nachlas, J. A. (1988). X-charts with variable sampling intervals. Technometrics, 30, 181-192. https://doi.org/10.2307/1270164
  6. Reynolds, M. R., Jr. (1988). Markovian variable sampling interval control charts, Technical Report 88-22, Virginia Polytechnic Institute and State University, Dept. of Statistics.
  7. Woodall, W. H. (1984). On the Markov chain approach to the two-sided CUSUM procedure. Technometrics, 26, 41-46. https://doi.org/10.2307/1268414