TY  - EJOU
AU  - Supharakonsakun, Yadpirun 
AU  - Areepong, Yupaporn 
AU  - Silpakob, Korakoch 

TI  - Explicit ARL Computational for a Modified EWMA Control Chart in Autocorrelated Statistical Process Control Models
T2  - Computer Modeling in Engineering \& Sciences

PY  - 2025
VL  - 145
IS  - 1
SN  - 1526-1506

AB  - 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)<sub>L</sub> 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)<sub>L</sub> 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.
KW  - Statistical process control; average run length; modified EWMA control chart; autocorrelated data; SARMA process; computational modeling; real-time monitoring

DO  - 10.32604/cmes.2025.067702