Exact Average Run Length Evaluation on One-Sided and Two-Sided Extended EWMA Control Chart with Correlated Data

Q3 Mathematics

WSEAS Transactions on Mathematics Pub Date : 2023-11-09 DOI:10.37394/23206.2023.22.90

Phunsa Mongkoltawat, Yupaporn Areepong, Saowanit Sukparungsee

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Abstract

The Extended Exponentially Weighted Moving Average (Extended EWMA) control chart is one of the control charts that can rapidly detect a minor shift. Using the average run length (ARL), the control charts' effectiveness can be evaluated. This research aims to derive the explicit formulations for the ARL on one-sided and two-sided Extend EWMA control charts for the MA(1) model with exponential white noise, as they have not been previously presented. The analytical solution accuracy was determined and compared to the numerical integral equation (NIE) method. The results indicate that the ARL calculated using the explicit formula and the NIE method are nearly identical, demonstrating the validity of the explicit formula. In addition, this study is extended to compare the performance with the Exponentially Weighted Moving Average (EWMA) control chart. The results show that the Extended EWMA control chart has superior efficacy to the EWMA control chart. To demonstrate the efficacy of the proposed method, the analytical solution of ARL is finally applied to real-world data on Thailand's monthly fuel price.

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具有相关数据的单侧和双侧扩展EWMA控制图的精确平均行程评价

扩展指数加权移动平均(Extended EWMA)控制图是一种可以快速检测微小移动的控制图。利用平均运行长度(ARL)，可以评价控制图的有效性。本研究旨在推导出具有指数白噪声的MA(1)模型的单侧和双面扩展EWMA控制图上的ARL的显式公式，因为它们之前没有被提出。确定了解析解的精度，并与数值积分方程(NIE)法进行了比较。结果表明，用显式公式计算的ARL与用NIE方法计算的ARL基本一致，证明了显式公式的有效性。此外，本研究还扩展了与指数加权移动平均(EWMA)控制图的性能比较。结果表明，扩展后的EWMA控制图效果优于原有的EWMA控制图。为了证明所提出方法的有效性，最后将ARL的解析解应用于泰国每月燃料价格的实际数据。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

WSEAS Transactions on Mathematics Mathematics-Discrete Mathematics and Combinatorics

CiteScore

1.30

自引率

0.00%

发文量

期刊介绍： WSEAS Transactions on Mathematics publishes original research papers relating to applied and theoretical mathematics. We aim to bring important work to a wide international audience and therefore only publish papers of exceptional scientific value that advance our understanding of these particular areas. The research presented must transcend the limits of case studies, while both experimental and theoretical studies are accepted. It is a multi-disciplinary journal and therefore its content mirrors the diverse interests and approaches of scholars involved with linear algebra, numerical analysis, differential equations, statistics and related areas. We also welcome scholarly contributions from officials with government agencies, international agencies, and non-governmental organizations.