Comparisons of some exponentially weighted moving average control charts for monitoring the process mean and variance

An exponentially weighted moving average (EWMA) control chart for monitoring the process mean mu may be slow to detect large shifts in mu when the EWMA tuning parameter lambda is small. An additional problem, sometimes called the inertia problem, is that the EWMA statistic may be in a disadvantageous position on the wrong side of the target when a shift in g occurs, which may significantly delay detection of a shift in mu. Options for improving the performance of the EWMA chart include using the EWMA chart in combination with a Shewhart chart or in combination with an EWMA chart based on squared deviations from target. The EWMA chart based on squared deviations from target is designed to detect increases in the process standard deviation sigma, but it is also very effective for detecting large shifts in mu. Capizzi and Masarotto recently proposed the option of an adaptive EWMA control chart in which lambda is a function of the data. With the adaptive feature, the EWMA chart behaves like a standard EWMA chart when the current observation is close to the previous EWMA statistic, and like a Shewhart chart otherwise. Here we extend the use of the adaptive feature to EWMA charts based on squared deviations from target, and also consider an alternate way of defining the adaptive feature. We discuss performance measures that we believe are appropriate for assessing the effects of inertia, and compare the performance of various charts and combinations of charts. Standard practice is to simultaneously monitor both mu and sigma, so we consider control chart performance when the objective is to detect small or large changes in mu or increases in sigma. We find that combinations of EWMA control charts that include a chart based on squared deviations from target give good overall performance whether or not these charts have the adaptive feature.