We demonstrate that the recently introduced triple generally weighted moving average (GWMA) chart and its counterpart, the double GWMA chart, incorporate sub‐optimal weighting patterns that may assign more weight to certain historical data points at the expense of more recent ones. Moreover, these control charts, when compared to the exponentially weighted moving average (EWMA) chart, exhibit a substantial computational burden. Our findings underscore that a well‐designed EWMA chart offers superior overall performance in comparison to these control charts.