Numerical Approximation of the Average Run Length on a Modified EWMA Control Chart for an ARX(1,1) Process with Exponential White Noise

Abstract

The purpose of this study is to evaluate the average run length (ARL) by using a numerical integral equation (NIE) method based on the Gauss-Legendre quadrature rule on a modified exponentially weighted moving average (EWMA) control chart for a first-order autoregressive process with an explanatory variable (ARX(1,1)) with exponential white noise. In addition, the performance of the modified EWMA control chart for this process was compared with the standard EWMA control chart based on the relative mean index (RMI), in which the modified EWMA control chart was found to be better than the standard EWMA control chart for all smoothing parameter values.