Optimal maintenance of deteriorating equipment using semi-Markov decision processes and linear programming

This paper considers a mathematical model analysing the deterioration of system equipment and available maintenance options. Under specific conditions on costs and transition probabilities of the model, the issue of ideal maintenance of the equipment by assuming that preventive maintenance, condition-based maintenance, and the replacement times of the equipment follow known continuous probability distributions is explored. A semi-Markov decision process formulation is provided for this model and computational analysis is possible by applying well-known Markov decision algorithms. A linear programming approach is also presented with appropriate constraints established for the equipment's maintenance and repair times. Various numerical results are also presented for the validation of the model. The motivation for this paper is to develop a realistic framework for determining decisions about the type of maintenance, possible replacement, or the continuation of operation of deteriorating equipment. The above decisions are taken within a framework of time constraints for equipment maintenance and replacement. Such limitations in the implementation of these actions are very crucial for all maintenance management systems. The purpose of this paper is to make the described model a useful tool for maintenance managers who plan and implement optimal maintenance policies within an environment of variable time constraints.