Statistical Design for Monitoring Process Mean on Modified EWMA Control Chart based on Autocorrelated Data

Abstract

This research endeavor is focused on establishing explicit formulas for the computation of the average run length (ARL) within the context of a moving average process characterized by exogenous variables, denoted as MAX(q,r), and subjected to exponential white noise. Additionally, we aim to conduct a comparative analysis of their performance against the exponentially weighted moving average (EWMA) and the modified exponentially weighted moving average (modified EWMA) methodologies. The evaluation of their performance will be based on metrics such as the absolute percentage relative error (APRE) and the relative mean index (RMI). Furthermore, we undertake a rigorous assessment of the accuracy of these explicit formulas in relation to ARL by considering CPU time, utilizing the numerical integral equation (NIE) method derived through the application of the Gauss-Legendre quadrature rule. This comparative evaluation is carried out for both control chart methodologies. To ascertain the efficacy of our explicit formulas approach, we apply it to two distinct datasets. The first dataset pertains to the closing price of natural gas, with the crude oil WTI price serving as the exogenous variable. The second dataset encompasses the closing stock price of KTB Public Company Limited, with daily foreign exchange rates for USD/JPY and EUR/USD as the exogenous variables. The results of applying the ARL based on the explicit formulas to these two datasets demonstrate that, under these conditions, the modified EWMA control chart outperforms the EWMA control chart.