Application of EWMA Control Chart for Analyzing Changes in SAR(P)L Model with Quadratic Trend
9
Issued Date
2025-06-01
Resource Type
ISSN
23322071
eISSN
23322144
Scopus ID
2-s2.0-105010351315
Journal Title
Mathematics and Statistics
Volume
13
Issue
3
Start Page
163
End Page
174
Rights Holder(s)
SCOPUS
Bibliographic Citation
Mathematics and Statistics Vol.13 No.3 (2025) , 163-174
Suggested Citation
Polyeam D., Phanyaem S. Application of EWMA Control Chart for Analyzing Changes in SAR(P)L Model with Quadratic Trend. Mathematics and Statistics Vol.13 No.3 (2025) , 163-174. 174. doi:10.13189/ms.2025.130305 Retrieved from: https://repository.li.mahidol.ac.th/handle/123456789/111282
Title
Application of EWMA Control Chart for Analyzing Changes in SAR(P)L Model with Quadratic Trend
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Abstract
The Exponentially Weighted Moving Average (EWMA) control chart is widely implemented in applications in various fields, such as finance, medicine, engineering, and others. In real-world applications such as hospital admissions, share prices, and daily rainfall, data often exhibits both seasonal autocorrelation patterns and quadratic trend characteristics. Therefore, the application of EWMA control charts for detecting changes in processes offers significant advantages. The average run length (ARL) is commonly used as the standard criterion for measuring the efficiency of control charts. Hence, the accurate calculation of average run length with minimal processing time is an essential element of this research. This paper focuses on proposing an explicit formula for the ARL of the EWMA chart when the observations follow a seasonal autoregressive model of order P (SAR(P)<inf>L</inf>) with quadratic trend. The proof for deriving the explicit formula of the ARL uses Fredholm's integral equation method. The application of Banach's Fixed Point Theorem provides a guarantee for solution uniqueness. Additionally, the performance of the proposed explicit formula is compared with the approximate ARL derived from Numerical Integral Equation methods, which consist of the Midpoint rule, the Trapezoidal rule, the Simpson's rule, and the Gaussian rule. The efficiency of the explicit formula of ARL is evaluated using two criteria: absolute percentage difference and the computational (CPU) time. The results obtained indicate that the ARL from the explicit formula is close to the numerical integral equation with an absolute percentage difference of less than 0.001. The proposed explicit formula has a minimal CPU time of about 0.001 seconds, while the Midpoint and Trapezoidal rules take 2-3 seconds. The Simpson’s and Gaussian rules require the longest times, approximately 9-10 seconds. A key finding of this study was that the explicit formulas performed better than the numerical integral equation methods in terms of CPU time. As a result, both the proposed explicit formulas and the numerical integral equation methods have emerged as viable alternatives for determining the ARL of the EWMA control chart.