WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 24, 2025
Integral Equation Method for ARL on New Modified EWMA Chart in Change-Point Detection Problems
Authors: ,
Abstract: This research proposes an explicit formula for the Average Run Length (ARL) on a new modified EWMA (new MEWMA) control chart. This study proposes a mathematical algorithm for determining the ARL of a new MEWMA control chart for detecting autocorrelated processes for zero-state. The integral equation method is called Fredholm Integral Equations of the second kind can be effectively employed to calculate ARL. Banach’s fixed point theorem is utilized to demonstrate the existence and uniqueness of the ARL solution. A process for constructing one-sided and two-sided new MEWMA control charts is presented, and the results were compared to the accuracy with numerical integral equations relying on various quadrature rules. This algorithm will utilize the autoregressive with the exogenous variables model (ARX(p,r)) and apply the algorithm to examine empirical data in the economic area. The effectiveness of control charts can be further evaluated using the expected average run length and the expected standard deviation of run length measures. Our analysis indicates that the new MEWMA control chart surpasses the MEWMA and EWMA control charts in performance. Comparisons are conducted for varying magnitudes of the process mean shift and varied levels of autocorrelation.
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Keywords: Average Run Length, change-point detection, zero-state, Autoregressive with exogenous variable model, new Modified Exponentially Weighted Moving Average, control charts
Pages: 268-288
DOI: 10.37394/23206.2025.24.26