WSEAS Transactions on Systems and Control
Print ISSN: 1991-8763, E-ISSN: 2224-2856
Volume 20, 2025
Optimizing the EWMA Control Chart to Detect Changes in the Mean of a Long-Memory Seasonal Fractionally Integrated Moving Average and an Exogenous Variable Process with Exponential White Noise and its Application to Electrical Output Data
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Abstract: The exponentially weighted moving average (EWMA) control chart is frequently employed to monitor changes in process parameters. We developed a method to efficiently track minor changes sensitively, particularly when the data of the process are correlated. The average run length (ARL) is an essential metric employed to evaluate the efficacy of a control chart. Herein we provide exact formulas for the in-control ARL (ARL0) and out-of-control ARL (ARL1) for the mean of a long-memory seasonal fractionally integrated moving average with an exogenous variable model order ( ) process with exponential white noise on an EWMA control chart. The ARL results obtained using the exact formulas method were consistent with those using the classical numerical integral equation method. The sensitivity of the EWMA control chart to changes in the ARL of the mean of a process using the proposed and NIE methods with a low ARL1 value and various change levels was assessed in terms of the percentage difference in the expected ARL obtained using both methods, while the standard deviation of the RL (SDRL) was employed to assess the detected changes. Furthermore, the performances of the methods were evaluated temporally. In contrast, NIE also takes the time to display ARL1 results in seconds. The extensive simulation-based results indicate that the exact formulas approach performed better than the NIE method for all change levels in the mean of the process in terms of the results delivery time. An illustrative monitoring example using data on electricity production from natural gas is also provided to demonstrate the proposed method's practicability.
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Keywords: Exponentially weighted moving average (EWMA) control chart, average run length (ARL), long-memory or process, standard deviation of the run length (SDRL), exponential white noise, numerical integral equation method
Pages: 25-41
DOI: 10.37394/23203.2025.20.4