An Approximation of Average Run Length on Extended EWMA Control Chart for the Moving Average Process

Abstract. The objective of this research is to develop the Numerical Integral Equation (NIE) methods for approximating the Average Run Length (ARL) on Extended Exponentially Weighted Moving Average control chart (Extended EWMA) for the first order moving average process under exponential white noise. Also, this research compares the performance of Extended EWMA and EWMA of NIE method using the Gaussian rule, Midpoint rule, Simpson's rule and Trapezoidal rule. The results from this research shown that the performance of Extended EWMA control chart is superior to EWMA control chart for all shift size of change. Additionally, the approximation of NIE methods to obtain the ARL by Midpoint rule takes intervals time (CPU) less than other methods.