Alternative Design of One-Sided Shewhart Control Charts for the Multivariate Coefficient of Variation

The control charting technique is an approach to quality control and was implemented in various industries. There are many control charts, where the coefficient of variation control chart was one of the common charts and greatly used in Statistical Process Control. Since most processes are multivariate, the multivariate coefficient of variation charts has received great attention in the past few years. However, the existing multivariate coefficient of variation control charts was evaluated in terms of the average run length criterion, which may misinterpret the actual performance of the charts. This paper designs an alternative for the Shewhart multivariate coefficient of variation chart by considering the median run length and expected median run-length criteria to circumvent this problem. The research on the multivariate coefficient of variation chart is very limited in the existing literature by considering the median run length criterion. This proposed chart in this paper can minimize this research gap. The formulas and algorithms of the proposed chart are presented. The outputs of the proposed charts are shown by examining the different upward and downward process shifts. Additionally, the sample sizes, the process shifts, and the variation of the run-length distribution are investigated for their effects on the proposed chart. The findings reveal that the run-length distribution's variation is inversely proportional to the shift size. Furthermore, it shows that the variation decreases if the shift size increases.