Design of the Multivariate Side-Sensitive Synthetic Coefficient of Variation Chart Based on the Median Run Length

Abstract

The multivariate side-sensitive synthetic chart shows good detection capabilities for shifts in the coefficient of variation (γ); however, its design and evaluation is dependent on the average run length (ARL), which fairly represents its performance only for symmetrically distributed run lengths, and a skewed run length will result in an actual performance that frequently differs from its ARL, resulting in a loss of trust for the chart. Through numerical analysis, this paper has shown that the in-control run length and out-of-control run length of small shift sizes (τ) has a right-skewed distribution, showing that the chart could not be evaluated based on only its ARL. Following this finding, a design building upon the median run length (MRL) is proposed. This design resulted in a smaller out-of-control MRL (MRL1) than the design based on its ARL. Hence, the design shows faster detection and presents a more accurate representation of the chart’s performance. A design based on the expected MRL (EMRL) was also proposed for practitioners who are unable to estimate the exact value for τ. The proposed designs are also implemented in a real-life application monitoring investment risk.