Hybrid model of maintenance effect under the influence of Discrete-Time Markov Chain

Abstract

Maintenance outcomes in real-world industrial settings are inherently stochastic, varying among better-than-minimal, minimal, and worse-than-minimal effects due to factors such as technician expertise, environmental conditions, and component wear. Traditional repairable system models—including the Non-Homogeneous Poisson Process (NHPP), Generalized Pólya Process (GPP), and Extended Generalized Pólya Process (EGPP)—rely on deterministic repair assumptions that fail to capture this variability, leading to inaccurate reliability predictions and suboptimal maintenance decisions. To overcome these limitations, this paper proposes a hybrid model incorporating EGPP, NHPP, and GPP within a Discrete-Time Markov Chain (DTMC) framework. The model dynamically represents probabilistic transitions between repair effects via a state-dependent transition matrix and integrates them into a weighted mixed failure rate function, reflecting the true evolution of system reliability. Based on this model, a periodic replacement strategy is developed to minimize long-term cost rates. Experimental validation confirms that the proposed approach significantly enhances predictive accuracy and cost efficiency compared to conventional models, offering a more realistic and adaptable foundation for maintenance optimization in industrial applications.