Design of the synthetic multivariate coefficient of variation chart based on the median run length

Objectives: The aim of this study is to use median run length (MRL) as an alternative criterion to evaluate the performance of the synthetic multivariate coefficient of variation (Syn MCV) chart, where the MRL is the 50th percentile of the run length distribution. 

Methods/Statistical analysis: A Markov chain approach is used to compute the MRL and the probabilities of the run length distribution of the Syn MCV chart. The design procedure of the Syn MCV chart based on the MRL is presented to obtain the optimal design parameters by minimizing the out-of-control MRL at a specified shift. 

Findings: The plots of the probability of the run length distribution show that the skewness of the run length distribution for the Syn MCV chart decreases with the increase in the magnitude of shift. This indicates that when evaluating the performance of the Syn MCV chart, the MRL is a more meaningful criterion compared to the average run length (ARL). The comparison results reveal that the Syn MCV chart is superior against the standard MCV (Std MCV) chart in terms of the MRL. 

Application/Improvements: The synthetic scheme can be employed to improve the performance of the Std MCV chart based on the MRL. In addition, the numerical results show that the MRL is a better performance measure for the Syn MCV chart compared to the ARL.