Performance Evaluation of HWMA Control Chart based on AR(p) with Trend Model to Detect Shift Process Mean

Q3 Economics, Econometrics and Finance

WSEAS Transactions on Business and Economics Pub Date : 2024-01-26 DOI:10.37394/23207.2024.21.50

R. Sunthornwat, Y. Areepong, S. Sukparungsee

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引用次数: 0

Abstract

The main goal of this study is to establish explicit solutions for the average run length (ARL) of the Homogenously Weighted Moving Average control chart when subjected to autoregressive with trend process. The accuracy of the explicit formula for the ARL is evaluated in comparison to the numerical integral equation method. To evaluate the two approaches, the accuracy percentage was employed. A determination is carried out of the HWMA control chart’s effectiveness using the median run length (MRL), the standard deviation of run length (SDRL), and the average run length (ARL). A comprehensive comparison is performed between the HWMA control chart, the Extended Exponentially Weighted Moving Average (EEWMA), and the cumulative sum (CUSUM) control charts with mean process shifts to illustrate the design and implementation of the HWMA control chart. As criteria for various values of design parameters, the performance of these control charts can also be evaluated using the relative mean index (RMI), the average extra quadratic loss (AEQL), and the performance comparison index (PCI). To evaluate the effectiveness of our explicit formula approach, we employ this formula on copper price data.

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基于带有趋势模型的 AR（p）的 HWMA 控制图的性能评估，以检测移动过程均值

本研究的主要目标是建立同源加权移动平均控制图在受自回归趋势过程影响时的平均运行长度（ARL）的显式解法。通过与数值积分方程法进行比较，评估了平均运行长度显式公式的准确性。为了评估这两种方法，采用了准确率百分比。使用运行长度中位数（MRL）、运行长度标准偏差（SDRL）和平均运行长度（ARL）确定 HWMA 控制图的有效性。对 HWMA 控制图、扩展指数加权移动平均（EEWMA）控制图和带有平均过程偏移的累积和（CUSUM）控制图进行了综合比较，以说明 HWMA 控制图的设计和实施。作为不同设计参数值的标准，这些控制图的性能还可以使用相对平均指数 (RMI)、平均二次外损失 (AEQL) 和性能比较指数 (PCI) 进行评估。为了评估显式公式方法的有效性，我们在铜价数据中使用了该公式。

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 Business and Economics Economics, Econometrics and Finance-Economics and Econometrics

CiteScore

1.50

自引率

0.00%

发文量

180

期刊介绍： WSEAS Transactions on Business and Economics publishes original research papers relating to the global economy. We aim to bring important work using any economic approach to a wide international audience and therefore only publish papers of exceptional scientific value that advance our understanding of finances. The research presented must transcend the limits of case studies, while both experimental and theoretical studies are accepted. While its main emphasis is economic, it is a multi-disciplinary journal and therefore its content mirrors the diverse interests and approaches of scholars involved with the international dimensions of business, economics, finance, history, law, marketing, management, political science, and related areas. It also welcomes scholarly contributions from officials with government agencies, international agencies, and non-governmental organizations.