Wai Chung YeongSok Li LimChong Zhi LinMichael B. C. KhooSajal SahaEugene Demidenko2024-10-182024-10-182022-07-0510.1371/journal.pone.0270151https://dspace-cris.utar.edu.my/handle/123456789/3465Control charts for the coefficient of variations (<i>γ</i>) are receiving increasing attention as it is able to monitor the stability in the ratio of the standard deviation (<i>σ</i>) over the mean (<i>μ</i>), unlike conventional charts that monitor the <i>μ</i> and/or <i>σ</i> separately. A side-sensitive synthetic (SS) chart for monitoring <i>γ</i>was recently developed for univariate processes. The chart outperforms the non-side-sensitive synthetic (NSS )<i>γ</i> chart. However, the SS chart monitoring <i>γ</i> for multivariate processes cannot be found. Thus, a SS chart for multivariate processes is proposed in this paper. A SS chart for multivariate processes is important as multiple quality characteristic that are correlated with each other are frequently encountered in practical scenarios. Based on numerical examples, the side-sensitivity feature that is included in the multivariate synthetic <i>γ</i> chart significantly improves the sensitivity of the chart based on the run length performance, particularly in detecting small shifts (<i>τ</i>), and for small sample size (<i>n</i>), as well as a large number of variables (<i>p</i>) and in-control <i>γ</i> (<i>γ</i>0). The multivariate SS chart also significantly outperforms the Shewhart <i>γ</i>chart, and marginally outperforms the Multivariate Exponentially Weighted Moving Average (MEWMA) <i>γ</i>chart when shift sizes are moderate and large. To show its implementation, the proposed multivariate SS chart is adopted to monitor investment risks.journal-article