Monitoring multivariate coefficient of variation for high-dimensional processes

Multivariate coefficient of variation (MCV) charts are effective tools for monitoring process relative variability. They are developed on the assumption that the process subgroup size available for monitoring the MCV parameter is larger than the number of process characteristics. In such a case, the unbiased estimates of the in-control mean vector and covariance matrix are used to calculate the chart monitoring statistic. Here, we study the performance of MCV control charts when only a small subgroup size is available for estimating the in-control mean vector and covariance matrix. We examine the use of a shrinkage estimate of the covariance matrix and propose two one-sided upward and downward least absolute shrinkage and selection operator (LASSO)-based MCV charts for detecting upward and downward shifts in the process MCV parameter, respectively. Our simulation study shows that the LASSO-based MCV charts outperform the classical two one-sided MCV charts when small subgroup sizes are available for monitoring. The improved performance of the proposed LASSO-based MCV charts in monitoring shifts in the MCV parameter is demonstrated via an illustrative case study of carbon fiber tube application, where changes are detected earlier than the classical two one-sided MCV charts.