A Novel Statistical Process Control Approach for PM2.5 Monitoring Using Time Series Modeling
This research seeks to create a novel control chart capable of managing autocorrelated time series data by proposing a modified Exponentially Weighted Moving Average (EWMA) approach tailored to processes following the ARMA(p,q) model, which also makes use of exponential white noise. The key methodological contribution involves an explicit formula to compute the Average Run Length (ARL), while the Numerical Integral Equation (NIE) approach is utilized for verification purposes. The proposed formula not only demonstrated 100% agreement with NIE results but also significantly reduced computational time, requiring less than 0.001 seconds per run, compared to the 3–4 seconds typically needed by NIE. To assess the performance, simulation experiments and real-world case studies on PM2.5 air pollution data from Nakhon Phanom, Nan, and Nonthaburi provinces in Thailand were conducted. Our modified control chart was better at identifying minimal changes than a standard EWMA chart, as shown by lower ARL1, SDRL1, AEQL, and optimal PCI values. The one-sided chart structure, designed to monitor upward shifts in pollutant levels, further supports its application in environmental surveillance. Overall, the study introduces a fast, accurate, and practical tool for quality control in autocorrelated environments, offering both analytical and computational advantages over existing methods.