ARL Evaluation of a DEWMA Control Chart for Autocorrelated Data: A Case Study on Prices of Major Industrial Commodities

Abstract

The double exponentially weighted moving average (DEWMA) control chart, an extension of the EWMA control chart, is a useful statistical process control tool for detecting small shift sizes in the mean of processes with either independent or autocorrelated observations. In this study, we derived explicit formulas to compute the average run length (ARL) for a moving average of order q (MA(q)) process with exponential white noise running on a DEWMA control chart and verified their accuracy by comparison with the numerical integral equation (NIE) method. The results for both were in good agreement with the actual ARL. To investigate the efficiency of the proposed procedure on the DEWMA control chart, a performance comparison between it and the standard and modified EWMA control charts was also conducted to determine which provided the smallest out-of-control ARL value for several scenarios involving MA(q) processes. It was found that the DEWMA control chart provided the lowest out-of-control ARL for all cases of varying the exponential smoothing parameter and shift size values. To illustrate the efficacy of the proposed methodology, the presented approach was applied to datasets of the prices of several major industrial commodities in Thailand. The findings show that the DEWMA procedure performed well in almost all of the scenarios tested. Doi: 10.28991/ESJ-2023-07-05-020 Full Text: PDF