A New Method Based on An Absorbing Markov Chain to Determine the Optimal Preventive Maintenance Policy

Fallah Nezhad, Mohammad Saber; Kargar Shouroki, Mohammad Hossein

doi:10.22034/IJRRS.2025.8.2.5

A New Method Based on An Absorbing Markov Chain to Determine the Optimal Preventive Maintenance Policy

Document Type : Original Research Article

Authors

Mohammad Saber Fallah Nezhad ¹

Mohammad Hossein Kargar Shouroki ²

¹ Department of Industrial Engineering, Engineering Faculty, Yazd University, Yazd, Iran

² Department of Engineering, Meybod University, Meybod, Yazd, Iran

10.22034/IJRRS.2025.8.2.5

Abstract

In this paper, a machine with five operational states is considered. This machine starts working in state one at 100% nominal capacity. The machine’s performance decreases, and the machine enters states medium and bad, respectively. The operational process is modeled using a discrete Markov chain, a transition probability matrix is obtained, and the total cost of the system is evaluated considering costs, such as lost production cost, PM cost, as well as the operational costs of the machine entering each of the system states. The objective function is cost minimization. In this model, for different policies, the average cost of the production process is calculated, and the policy with the lowest production process cost is selected as the optimal maintenance and repair policy. Unlike many previous approaches that primarily rely on theoretical analysis or simplified modeling, the proposed framework employs a discrete-time absorbing Markov process to facilitate cost-based decision-making in maintenance and repair operations. By considering various functional states of equipment, transition probabilities between these states, and the associated costs of maintenance actions, the model offers optimal and implementable policies for short-term maintenance management. Key advantages of this model include its ability to simulate equipment behavior realistically, provide more accurate estimates of maintenance costs, and analyze practical strategies to minimize unplanned downtime and enhance operational efficiency.

Keywords

Discrete Markov Chain

Maintenance and Repair

Optimal Policy

Cost Minimization

Subjects

Maintenance engineering

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