Optimal Designs of EWMA Charts for Monitoring the Coefficient of Variation Based on Median Run Length and Expected Median Run Length

The shape of run-length distribution changes with process shifts. This leads to complexity in interpreting the average run length performance. In this article, we show that the percentiles of the run-length distribution, especially the median run length (MRL), are more intuitive. The 5th and 95th percentiles of the run-length distribution are also provided in order to investigate the variation and spread of the run length. We develop two new optimal-design procedures for the exponentially weighted moving average (EWMA) charts, for monitoring the coefficient-of-variation (CV) squared (EWMA-gamma(2)). These include minimization of the out-of-control MRL and the out-of-control expected MRL for deterministic and unknown shift sizes, respectively. Both the zero and steady states are discussed in this article. The optimal EWMA-gamma(2) chart is illustrated with real industrial data obtained from a metal sintering process. A comparative study reveals the superiority of the EWMA-gamma(2) charts for certain ranges of shifts in the CV.