Multivariate coefficient of variation control charts in phase I of SPC

Abstract

Multivariate control charts are mostly available for monitoring the process mean vector or the covariance matrix. Recently, work has been done on monitoring the multivariate coefficient of variation (CV) in phase II of the statistical process control (SPC). However, no study has investigated the performance of the multivariate CV charts in phase I. The phase I procedures are more important and involve the estimation of the charts’ limits from a historical or reference dataset that represents the in-control state of the process. In real life, contaminations are mostly present in the historical samples; hence, the phase I procedures are mostly adopted to get rid of these contaminated samples. In this study, we investigate the performance of a variety of multivariate CV charts in phase I considering both diffuse symmetric and localized CV disturbance scenarios, using probability to signal as a performance measure. A real-life application, concerning carbon fiber tubing, is also provided to show the implementation of the proposed charts in phase I. The findings of this study will be useful for practitioners in their selection of an efficient phase I control chart for monitoring multivariate CV.