WSEAS Transactions on Systems and Control
Print ISSN: 1991-8763, E-ISSN: 2224-2856
Volume 18, 2023
Approximating the ARL of Changes in the Mean of a Seasonal Time Series Model with Exponential White Noise Running on a CUSUM Control Chart
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Abstract: Control charts comprise an excellent statistical process control tool for monitoring industrial processes. Especially, the CUSUM control chart is very sensitive to small-to-moderate process parameter changes. The proposed approach utilizes the numerical integral equation (NIE) method to approximate the average run length (ARL) of changes in the mean of a seasonal time series model with underlying exponential white noise running on a CUSUM control chart. This was achieved by solving a system of linear equations and integration through partitioning and summation using the area under the curve of a function obtained by applying the Gauss-Legendre quadrature. A numerical study was conducted to compare the capabilities of the ARL derivations obtained using the NIE method and explicit formulas to detect changes in the mean of a long-memory model with exponential white noise running on a CUSUM control chart. The results reveal that the performances of both were comparable in terms of the accuracy percentage, which was greater than 95%, meaning that the ARL values were highly consistent. Thus, the NIE method can be used to validate ARL results for this situation.
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Keywords: CUSUM control chart, average run length (ARL), exponential white noise, process, numerical integral equation (NIE)
Pages: 370-381
DOI: 10.37394/23203.2023.18.39