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Including three existing charts, a new approach employing a modified one-step M-estimator (MOM) with Cumulative Sum (CUSUM) control structure were evaluated and compared for their Phase II performances based on the average run length (ARL) under various skewed distributions. The primary focus was on the robustness of the CUSUM charts in two separate cases: (i) when the process parameters are known and (ii) when the process mean is unknown and estimated from an in-control Phase I sample. The simulation and real data analysis showed the proposed technique is comparable or sometimes better than the existing charts. [ABSTRACT FROM AUTHOR]