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Trend Autoregressive Model Exact Run Length Evaluation on a Two-Sided Extended EWMA Chart

Kotchaporn Karoon, Yupaporn Areepong*, Saowanit Sukparungsee

Department of Applied Statistics, King Mongkut's University of Technology, North Bangkok, Bangkok, 10800, Thailand

* Corresponding Author: Yupaporn Areepong. Email: email

Computer Systems Science and Engineering 2023, 44(2), 1143-1160.


The Extended Exponentially Weighted Moving Average (extended EWMA) control chart is one of the control charts and can be used to quickly detect a small shift. The performance of control charts can be evaluated with the average run length (ARL). Due to the deriving explicit formulas for the ARL on a two-sided extended EWMA control chart for trend autoregressive or trend AR(p) model has not been reported previously. The aim of this study is to derive the explicit formulas for the ARL on a two-sided extended EWMA control chart for the trend AR(p) model as well as the trend AR(1) and trend AR(2) models with exponential white noise. The analytical solution accuracy was obtained with the extended EWMA control chart and was compared to the numerical integral equation (NIE) method. The results show that the ARL obtained by the explicit formula and the NIE method is hardly different, but the explicit formula can help decrease the computational (CPU) time. Furthermore, this is also expanded to comparative performance with the Exponentially Weighted Moving Average (EWMA) control chart. The performance of the extended EWMA control chart is better than the EWMA control chart for all situations, both the trend AR(1) and trend AR(2) models. Finally, the analytical solution of ARL is applied to real-world data in the health field, such as COVID-19 data in the United Kingdom and Sweden, to demonstrate the efficacy of the proposed method.


Cite This Article

K. Karoon, Y. Areepong and S. Sukparungsee, "Trend autoregressive model exact run length evaluation on a two-sided extended ewma chart," Computer Systems Science and Engineering, vol. 44, no.2, pp. 1143–1160, 2023.

cc This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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