The traditional exponentially weighted moving average (EWMA) chart is one of the most popular control
charts used in practice today. The in-control robustness is the key to the proper design and implementation of
any control chart, lack of which can render its out-of-control shift detection capability almost meaningless.
To this end, Borror et al.  studied the performance of the traditional EWMA chart for the mean for
i.i.d. data. We use a more extensive simulation study to further investigate the in-control robustness (to
non-normality) of the three different EWMA designs studied by Borror et al. . Our study includes a
much wider collection of non-normal distributions including light- and heavy-tailed and symmetric and
asymmetric bi-modal as well as the contaminated normal, which is particularly useful to study the effects
of outliers. Also, we consider two separate cases: (i) when the process mean and standard deviation are
both known and (ii) when they are both unknown and estimated from an in-control Phase I sample. In
addition, unlike in the study done by Borror et al. , the average run-length (ARL) is not used as the
sole performance measure in our study, we consider the standard deviation of the run-length (SDRL), the
median run-length (MDRL), and the first and the third quartiles as well as the first and the 99th percentiles
of the in-control run-length distribution for a better overall assessment of the traditional EWMA chart’s
in-control performance. Our findings sound a cautionary note to the (over) use of the EWMA chart in
practice, at least with some types of non-normal data. A summary and recommendations are provided.