Stationary availability of a semi-Markov system with random maintenance (Q2744951)

This paper deals with the question: is it worth preventively maintaining a machine or is it better to wait until it breaks down to repair it (if possible)? More precisely, the author considers a repairable system with a finite state space that evolves in time according to a semi-Markov process. The system is stopped for preventive maintaining at random times for a random duration. The main problem is to find the preventive maintenance policy that optimizes the stationary availability, i.e. the availability when the system reaches its steady state. The key moment for calculating is the fact that the system evolves according to a semi-regenerative process. Via numerical examples the author observes that for optimization of the maintenance policy the problem may be restricted to the study of maintenance actions at deterministic times. The author also proves this fact for certain special cases and conjectures that this will always be true. NEWLINENEWLINENEWLINEAlso a few criteria to optimize the deterministic maintenance policies are proposed. In particular, if the initial system has an increasing failure rate, the maintenance actions improve the stationary availability if and only if they are not too long on average, compared to the repairs. On the contrary, if the initial system has a decreasing failure rate, the maintenance policy lowers the stationary availability.