@Article{csse.2023.025420,
AUTHOR = {Kotchaporn Karoon, Yupaporn Areepong, Saowanit Sukparungsee},
TITLE = {Trend Autoregressive Model Exact Run Length Evaluation on a Two-Sided Extended EWMA Chart},
JOURNAL = {Computer Systems Science and Engineering},
VOLUME = {44},
YEAR = {2023},
NUMBER = {2},
PAGES = {1143--1160},
URL = {http://www.techscience.com/csse/v44n2/48255},
ISSN = {},
ABSTRACT = {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 (<i>ARL</i>). Due to the deriving explicit formulas for the <i>ARL</i> 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 <i>ARL</i> 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 <i>ARL</i> 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 <i>ARL</i> 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.},
DOI = {10.32604/csse.2023.025420}
}