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, composite trapezoidal rule, composite Simpson’s rule, composite Boole’s rule and Gauss-Legendre rule for approximating the average run length on extended exponentially weighted moving average (extended EWMA) control chart for autoregressive process with explanatory variables when white noise follows an exponential distribution. Furthermore, the comparison on performance of classical EWMA and extended EWMA control chart had been conducted. The results show that extended EWMA control chart can detect changes quicklier than EWMA control chart for all conditions.