Approximation of average run length on extended EWMA control chart for autoregressive process with explanatory variables using numerical integral equation method

Abstract The objective of this research is to study numerical integral equation method (NIE) using five quadrature rules namely, composite midpoint rule, trapezoidal Simpson’s Boole’s rule and Gauss-Legendre for approximating the average run length on extended exponentially weighted moving (extended EWMA) control chart autoregressive process with explanatory variables when white noise follows an exponential distribution. Furthermore, comparison performance classical EWMA had been conducted. results show that can detect changes quicklier than all conditions.