A comparison of EWMA control charts for dispersion based on estimated parameters

The exponentially weighted moving average (EWMA) chart for dispersion is designed to detect structural changes in the process dispersion quickly. The various existing designs of the EWMA chart for dispersion differ in the choice of the dispersion measure used. The most popular choice in the literature is the logarithm of the variance. Other possibilities are the sample variance and the sample standard deviation. In practical applications, parameter estimates are needed to set up the chart before monitoring can start. Once process parameters are estimated, the performance is conditional on the estimates obtained. It is well known that using so-called Phase I estimates affect the performance of control charts. We compare three EWMA dispersion charts based on Phase I estimates. We compare the conditional performance under normally distributed data as well as non-normally distributed data, in order to compare the robustness of the various charts. We show that the chart based on the sample variance is least influenced by estimation error under normally distributed data. We also show that the chart based on the logarithm of the variance shows the most constant performance under deviations from the normality assumption. As we are never sure in practice if the normality assumption is exactly satisfied, we argue that the chart which is most robust to the normality assumption - the chart based on the logarithm of the variance - should be used in practice.