The Group Runs (GR) and Side Sensitive Group Runs (SSGR) control charts are the improvement of the synthetic chart without and with side sensitivity. Both the SSGR and GR charts are effective for detecting small to moderate process mean shifts. The performances of the SSGR and GR charts, in terms of the average time to signal (ATS), are compared in this paper. In this comparative study, the Monte Carlo simulation approach by means of the Statistical Analysis System (SAS) software is used to compute the ATS values for the GR and SSGR charts. The results revealed that the SSGR chart's performance is better than that of the GR chart for all levels of mean shifts.