Run sum chart for monitoring multivariate coefficient of variation

- The downward and upward run sum (RS) charts for monitoring the multivariate coefficient of variation (CV) are proposed.
- The downward and upward RS charts monitor decreasing and increasing shifts in the multivariate CV, respectively.
- Markov chain procedures to evaluate the proposed chart, in terms of ARL, SDRL and EARL, are presented.
- Results show that the proposed chart outperforms the existing multivariate chart for monitoring the CV.
- An illustrative example is provided to explain the application of the proposed chart.

Coefficient of variation (CV) is an important quality characteristic to take into account when the process mean and standard deviation are not constants. A setback of the existing chart for monitoring the multivariate CV is that the chart is slow in detecting a multivariate CV shift in the Phase-II process. To overcome this problem, this paper proposes a run sum chart for monitoring the multivariate CV in the Phase-II process. The average run length (ARL), standard deviation of the run length (SDRL) and expected average run length (EARL), under the zero state and steady state cases, are used to compare the performance of the proposed chart with the existing multivariate CV chart. The proposed chart's optimal parameters are computed using the Mathematica programs, based on the Markov chain model. Two one-sided run sum charts for monitoring the multivariate CV are considered, where they can be used simultaneously to detect increasing and decreasing multivariate CV shifts. The effects of different in-control CV values, number of regions, shift and sample sizes, and number of variables being monitored are studied. The implementation of the proposed chart is illustrated with an example using the data dealing with steel sleeve inside diameters.