WSEAS Transactions on Systems
Print ISSN: 1109-2777, E-ISSN: 2224-2678
Volume 24, 2025
The Exact Solution of ARL using an Integral Equation on the DMEWMA Chart for the SAR(P)L Process for Mean Shift Detection
Authors: ,
Abstract: The main objective of this investigation is to prove the explicit formula for the average run length (ARL) of the modified double exponentially weighted moving average (DMEWMA) control chart in the context of a seasonal regression process. The explicit formula is compared to the numerical integral equation (NIE) method, with the percentage of accuracy serving as the evaluation metric for both approaches. Furthermore, the performance of the DMEWMA control chart is assessed by calculating the standard deviation of the run length (SDRL) and the median run length (MRL). To demonstrate the design and application of the DMEWMA control chart, a comparison is conducted with the modified exponentially weighted moving average (MEWMA) and the exponentially weighted moving average (EWMA) control charts under conditions of mean process shift. Key metrics such as EARL, ESDRL, and EMRL are utilized to measure the performance of these control charts across several design parameter configurations. To evaluate the explicit formula’s practical effectiveness, it is applied to real-world data, specifically the production index for biofuel gasohol 91, to detect process variations. This case study highlights the efficiency and reliability of the DMEWMA control chart in monitoring and identifying shifts in the process mean.
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Keywords: Average Run Length, Seasonal Autoregressive, Double Modified Exponentially Weighted Moving Average, zero-state, change point detection, Integral equation
Pages: 388-402
DOI: 10.37394/23202.2025.24.34