An approximation of average run length using numerical integration methods on EWMA control chart for MAX(q,r) process

Abstract

This research aims to measure a method for estimating the average run length (ARL) of an exponentially weighted moving average control chart using numerical integration when the data is a moving average model with exogenous variables. We compare the average run lengths achieved using three distinct methodologies. The midpoint, trapezoid, and Gaussian rules are all used. Additionally, we compare the CPU time used by the ARL assessment. The simulations show that the ARL values obtained from using the midpoint and Gaussian rules are similar. The result obtained from using the trapezoid approach, on the other hand, is less different at roughly 1%. Additionally, the midpoint and trapezoid approaches were the fastest when CPU time was considered, requiring between 4-6 seconds. On the other hand, Gaussian's rule requires around 37-43 seconds.