Abstract: Classical Shewhart kind control charts are based on normality assumption and ignore the skewness of the plotted statistic in the construction of control charts. Generally the skewness is large enough to be overlooked and in such situation the traditional chart is improper to give satisfactory performance. In this paper, we present a comparative study and present best control chart based on skewness and kurtosis for random queue length for M/M/1 queueing model evaluated on the basis of performance measure false alarm rate.