Open Access

ARTICLE

Explicit ARL Computational for a Modified EWMA Control Chart in Autocorrelated Statistical Process Control Models

Yadpirun Supharakonsakun¹, Yupaporn Areepong², Korakoch Silpakob^3,*

1 Department of Applied Mathematics and Statistics, Phetchabun Rajabhat University, Phetchabun, 67000, Thailand
2 Department of Applied Statistics, King Mongkut’s University of Technology North Bangkok, Bangkok, 10800, Thailand
3 Department of Educational Testing and Research, Buriram Rajabhat University, Buriram, 31000, Thailand

* Corresponding Author: Korakoch Silpakob. Email:

(This article belongs to the Special Issue: Scientific Computing and Its Application to Engineering Problems)

Computer Modeling in Engineering & Sciences 2025, 145(1), 699-720. https://doi.org/10.32604/cmes.2025.067702

Received 09 May 2025; Accepted 28 September 2025; Issue published 30 October 2025

Abstract

This study presents an innovative development of the exponentially weighted moving average (EWMA) control chart, explicitly adapted for the examination of time series data distinguished by seasonal autoregressive moving average behavior—SARMA(1,1)_L under exponential white noise. Unlike previous works that rely on simplified models such as AR(1) or assume independence, this research derives for the first time an exact two-sided Average Run Length (ARL) formula for the Modified EWMA chart under SARMA(1,1)_L conditions, using a mathematically rigorous Fredholm integral approach. The derived formulas are validated against numerical integral equation (NIE) solutions, showing strong agreement and significantly reduced computational burden. Additionally, a performance comparison index (PCI) is introduced to assess the chart’s detection capability. Results demonstrate that the proposed method exhibits superior sensitivity to mean shifts in autocorrelated environments, outperforming existing approaches. The findings offer a new, efficient framework for real-time quality control in complex seasonal processes, with potential applications in environmental monitoring and intelligent manufacturing systems.

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