Developed ARL by Integral Equation Solutions to Monitor Changes under Autocorrelated Data for the DEWMA Chart

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作者：
Areepong, Yupaporn [1 ]
Karoon, Kotchaporn [2 ]
机构：
[1] Applied Statistics Department, King Mongkut’s University of Technology North Bangkok, Bangkok,10800, Thailand
[2] Mathematics Department, Research Center for Academic Excellence in Mathematics, Naresuan University, Phitsanulok,65000, Thailand
来源：
IAENG International Journal of Applied Mathematics | 2024年 / 54卷 / 08期
关键词：
The DEWMA control chart was developed as a useful tool to monitor the process mean quickly under autocorrelated data. The Average Run Length (ARL) metric; which is designed for control charts; is intended for measuring the ability of the control chart. In this work; an analytical Integral Equation or explicit ARL will be developed for data on the DEWMA control chart that are characterized by a quadratic trend AR(1) model. Banach’s fixed point theorem was used to proved its uniqueness and existence after it was generated by the second form of the Fredholm integral equation. It has evolved compared to the ARL obtained via the Numerical Integral Equation (numerical IE) approach and looked at in connection with the EWMA chart; which has shown to have superior detection capabilities. The AEQL and RMI metrics were used to confirm their ability. Furthermore; real-world data from the relevant domains of finance and economics was used to test this suggested technique. © (2024); (International Association of Engineers). All rights reserved;
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页码：1631 / 1642
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