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Exact Run Length Evaluation on Extended EWMA Control Chart for Autoregressive Process

Kotchaporn Karoon, Yupaporn Areepong*, Saowanit Sukparungsee

Department of Applied Statistics, Faculty of Applied Science, King Mongkut’s University of Technology NorthBangkok, Bangkok, 10800, Thailand

* Corresponding Author: Yupaporn Areepong. Email:

(This article belongs to this Special Issue: Soft Computing Methods for Intelligent Automation Systems)

Intelligent Automation & Soft Computing 2022, 33(2), 743-759.


Extended Exponentially Weighted Moving Average (Extended EWMA or EEWMA) control chart is one of the control charts which can quickly detect a small shift. The average run length (ARL) measures the performance of control chart. Due to the derivation of the explicit formulas for ARL on the EEWMA control chart for the autoregressive AR(p) process has not previously been reported. The aim of the article is to derive explicit formulas of ARL using a Fredholm integral equation of the second kind on EEWMA control chart for Autoregressive process, as AR(2) and AR(3) processes with exponential white noise. The accuracy of the solution obtained with the EEWMA control chart was compared to the numerical integral equation (NIE) method and extended to compare performance with Cumulative Sum (CUSUM) and Exponentially Weighted Moving Average (EWMA) control charts. The results show that the ARL obtained by the explicit formula and the NIE method are hardly different but ARL of explicit formula is less the computational (CPU) time than ARL of NIE method. The performance of EEWMA control chart is better than the CUSUM and EWMA control charts for all situations except when the large shift sizes the EEWMA control chart performed as well as the EWMA control chart for AR(2) and AR(3) processes. And then, the EEWMA control chart is also extended to compare efficiency of EEWMA control chart with various λ. An exponential smoothing parameter of 0.05 is recommended. In addition, the simulation study, and efficacy illustration with real data on new COVID-19 cases in Thailand and Vietnam provided similar results.


Cite This Article

K. Karoon, Y. Areepong and S. Sukparungsee, "Exact run length evaluation on extended ewma control chart for autoregressive process," Intelligent Automation & Soft Computing, vol. 33, no.2, pp. 743–759, 2022.

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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