Comparisons of steady-state optimal EWMA and DEWMA charts

The double EWMA (DEWMA) has been proposed as a more efficient control charting procedure for monitoring the mean of a process. Comparisons of the DEWMA and the EWMA charts, which often indicate the superiority of the DEWMA, are often flawed because the same smoothing constant is used in both charts. We take the approach of first selecting a shift that we would like to detect, and then compare the optimal DEWMA chart and the optimal EWMA chart for that particular shift. We consider the DEWMA chart whose smoothing constants are restricted to be the same and the general DEWMA. We find that there are situations where the optimal DEWMA outperforms, in the sense of a shorter out-of-control average run length (ARL) for a fixed in-control ARL, but the improvement is slight. The optimal EWMA chart usually performs much better than the optimal DEWMA chart when the actual shift differs from the shift used to optimize the chart. The poor performance of the DEWMA chart away from the shift for which it was optimized, the nonmonotonicity of the DEWMA weights, and the additional computations required of the DEWMA chart indicate that the EWMA is a better overall choice than the DEWMA chart.