Monitoring the Coefficient of Variation Using a Synthetic Exponentially Weighted Moving Average Chart

Coefficient of variation (gamma) charts are widely adopted in many industries to monitor processes without a consistent mean (mu) and which has a standard deviation (sigma) that is dependent on mu. The exponentially weighted moving average (EWMA) and synthetic (Syn) gamma charts show different strengths, where the EWMA gamma chart is sensitive toward small and moderate shifts, while the synthetic gamma chart shows better sensitivities toward large shifts. Hence, the Syn-EWMA gamma chart is proposed, where it combines the features of both charts. This paper contributes to the literature by (i) developing the proposed chart's operations; (ii) deriving the formulae of the average run length (ARL), standard deviation of the run length (SDRL), and expected average run length (EARL); and (iii) formulating algorithms that optimize its performance. The proposed chart is shown to outperform the Shewhart, EWMA, and synthetic gamma charts across all shifts. Lastly, the implementation on a sintering process is shown.