Average Run Length Approximation on a Double Exponentially Weighted Moving Average Control Chart through the Numerical Integral Equation Approach

Abstract

In this paper, we suggest utilizing the midpoint rule, trapezoidal rule, Simpson’s rule, and Gaussian rule in conjunction with the Numerical Integral Equation (NIE) method to estimate the Average Run Length (ARL). These techniques are applied to the Double Exponentially Weighted Moving Average (DEWMA) control chart in situations where the observations follow continuous distributions, like the Weibull and exponential distributions. Furthermore, we contrast the Exponentially Weighted Moving Average (EWMA) control chart’s performance with that of the DEWMA control chart. Out-of-control Average Run Length (ARL₁) and CPU Times are the performance metrics. All of the methods perform similarly, according to the results. It is clear from the results that the DEWMA control chart performs better than the EWMA control chart. Additionally, a wide range of real-world datasets can be used to illustrate the efficacy of the suggested method by applying the NIE method to approximate the ARL.