The GWMA charts are generally more sensitive than the EWMA charts in detecting small shifts (see the results in Sheu and Lin, Lu and Sheu and Yang).In addition, Graham et al. showed that in many cases the EWMA-SR chart outperforms the EWMA-SN chart and the Shewhart-SR chart with non-normal distributions. Given the available results, it is of interest to compare the proposed GWMA-SR chart with the GWMA-X chart, the GWMA-SN chart and the EWMA-SR chart.