ABSTRACT The generally weighted moving average (GWMA) control chart has been proposed as a generalization and alternative to the exponentially weighted moving average (EWMA) chart. Proponents of the GWMA claim that it is more efficient in detecting shifts in the process mean than the EWMA. Most research on the GWMA chart compares its out‐of‐control properties against an EWMA chart that is not appropriate for the given situation. Detractors of the GWMA chart point out that (1) the GWMA is usually compared against an EWMA chart that is not ideal for the given situation, (2) the GWMA has no recursive formula so all previous data values must be stored and used to compute the next GWMA chart, and (3) the GWMA can have weights that do not decrease as the age of the data increases. We compare this optimal GWMA chart against the EWMA chart that is optimal for the same shift. For a given shift, a GWMA chart can be constructed that has a shorter cyclic steady‐state average run length than the optimal EWMA chart. The optimal GWMA chart will usually have poor out‐of‐control performance for shifts other than those for which the GWMA was designed to be optimal. The GWMA chart is the preferred chart only in very specific circumstances.