Optimal Maintenance Policies for Multi-State k-out-of-n: G Systems under R1-R2 Bernoulli Vacations: A MMAP-Based Modeling Framework

J. E. Ruiz Castro, M. Dawabsha

Modern industrial efficiency relies on the modeling and optimization of complex reliability systems. This work presents a model for a monitored multi-state k-out-of-n:G system with repairable and non-repairable failures. We integrate condition-based preventive maintenance and an R1-R2 Bernoulli vacation policy for the repair facility. Using matrix-analytic methods and Markovian Arrival Processes, we develop transient and steady-state analyses, deriving key performance measures. Costs and rewards are incorporated to analyze the trade-off between availability and operational costs via a Pareto-based multi-objective optimization. A numerical example demonstrates the model's versatility for designing optimal service policies.

Acknowledgements. Supported by Government of Andalusia (FQM-307) and Spanish Ministry of Science, Innovation and Universities (PID2023-149087NB-I00/AEI/10.13039/501100011033), co-funded by ERDF. First author supported by IMAG–María de Maeztu (CEX2020-001105-M)

Palabras clave: Markovian Arrival Processes, Preventive Maintenace, Multi-state k-out-of-n:G system, Vacation Policy

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