Availability of deteriorating system under inspection and maintenance strategies

In this paper, a Markov model is used to derive the steady state availability of a system that undergoes several stages of degradation, and is subject to random failures at each stage. Upon failure, partial repair is carried out in order to restore the system to its operational stage just before failure. In addition, an inspection is carried out at each of the degraded stages, where one of the following three maintenance actions may be taken: do nothing (leave the system as it is); minimal maintenance (restore the system to the previous degraded state, as bad as old); replacement (perfect repair returning the system to its initial state, as good as new). An analytical expression for the asymptotic availability for the system is derived.