Availability analysis and maintenance modelling for inspected Markov systems with down time threshold

Practically, many repairable systems are subject to neglected failures, i.e. if some failures can be repaired promptly they will not affect system availability. This paper investigates the availability and optimal maintenance policy for inspected Markov systems with down time threshold. Based on practical applications, a down time threshold is introduced. If a down time of the system is less than a given threshold, then the system may be considered as operating during the down time, i.e. the down time could be neglected. Otherwise, if a down time is longer than the given threshold, then the system is considered as operating from the beginning of the system failure until the down time exceeding the threshold, i.e. the down time could be delayed. Incorporating the down time threshold, the instantaneous and steady-state availabilities of the system are derived. Furthermore, a maintenance model is formulated to find the optimal inspection interval, T^*, which minimizes the long-run average cost rate. A numerical example for ventilator system is presented to demonstrate the application of the developed approach.