Exact Average Run Length Evaluation on a Two-Sided Extended EWMA Control Chart for the Moving Average Process

The Extended Exponentially Weighted Moving Average (Extended EWMA) control chart is a type of control chart that is effective in promptly identifying minor deviations. The evaluation of control charts can be conducted using the average run length (ARL). Finding the explicit formulas for the ARL on a two-sided Extended EWMA control chart for the moving average process (MA(q)) has not been reported previously and the purpose of this research. The processes considered the MA(2) and MA(3) processes, all with exponential white noise. The accuracy of the analytical solution was assessed using the Extended EWMA control chart compared to the numerical integral equation (NIE) approach. The results show that there is minimal difference between the ARL by the explicit formula and the NIE. In addition, the performance of the Extended EWMA control chart is better than the EWMA control chart for all shift sizes, both the MA(2) and MA(3) processes. Finally, the analytical solution for the ARL is utilized using actual data on the monthly fuel price in Thailand, to showcase the effectiveness of the suggested approach.