A variable sampling interval run sum chart for monitoring multivariate coefficient of variation

The coefficient of variation (CV) is employed to develop control charts to measure the relative dispersion of the data. The multivariate coefficient of variation (MCV) chart is used to monitor the CV in Phase-II in a multivariate framework. In this paper, the upward and downward variable sampling interval run sum multivariate coefficient of variation (VSI RS MCV) charts are developed to detect MCV shifts. The developed VSI RS MCV charts are evaluated and compared with their existing MCV and RS MCV counterparts using the average time to signal (ATS), standard deviation of the time to signal (SDTS) and expected average time to signal (EATS) criteria. Optimization programs incorporating the Markov chain methodology are developed in MATLAB to compute the optimal parameters and scores of the developed VSI RS MCV charts that minimize the charts' out-of-control ATS or EATS value. The findings show that the developed VSI RS MCV charts outperform both the existing RS MCV and MCV charts, for all shift sizes, in terms of the out-of-control ATS, SDTS and EATS criteria. An example is provided to elucidate the implementation of the proposed VSI RS MCV charts.