Evaluating the Performance of Modified EWMA Control Schemes for Serially Correlated Observations

Abstract

In this study, we propose the explicit formula of the average run length (ARL) for the autoregressive process with a quadratic trend on the modified exponentially weighted moving average (modified EWMA) control chart. The accuracy of the ARL from the explicit formula was compared with the ARL from the numerical integral equation (NIE) method derived by using the quadrature rule. The metrics of comparison were percentage accuracy and computational time. After that, the performance of the modified EWMA control chart is investigated in terms of the average run length, standard deviation of run length (SDRL), and median run length (MRL). In addition, the performance comparison on modified EWMA and the exponentially weighted moving average (EWMA) control charts was presented by using the relative mean index (RMI), the average extra quadratic loss (AEQL), and the performance comparison index (PCI) as the criteria. Furthermore, to determine the ability of the explicit formulas approach, the crude oil WTI price was applied, and it was shown that the modified EWMA control chart performed more significantly than the EWMA control chart under this condition.