A side-sensitive synthetic chart for the multivariate coefficient of variation.

Control charts for the coefficient of variations (γ) are receiving increasing attention as it is able to monitor the stability in the ratio of the standard deviation (σ) over the mean (μ), unlike conventional charts that monitor the μ and/or σ separately. A side-sensitive synthetic (SS) chart for monitoring γ was recently developed for univariate processes. The chart outperforms the non-side-sensitive synthetic (NSS) γ chart. However, the SS chart monitoring γ 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 γ chart significantly improves the sensitivity of the chart based on the run length performance, particularly in detecting small shifts (τ), and for small sample size (n), as well as a large number of variables (p) and in-control γ (γ0). The multivariate SS chart also significantly outperforms the Shewhart γ chart, and marginally outperforms the Multivariate Exponentially Weighted Moving Average (MEWMA) γ chart when shift sizes are moderate and large. To show its implementation, the proposed multivariate SS chart is adopted to monitor investment risks.