Reliability Measures and Optimal Maintenance Policies for a Standby System with Repair Facilities Subject to Breakdown

The problem of determining optimal maintenance policies for a repairable standby system whose repair facilities are subject to random breakdowns is considered. The reliability measures of this system are derived by the discrete-state continuous-time Markov model, as well as by a more general probabilistic approach. The dynamic optimization problem is discussed and treated by a generalized version of Pontryagin's minimum principle based on an integral Hamiltonian functional. This is applied to the Markov model of the system for deriving both time-variable and fixed maintenance policies over the whole mission time. Then an appropriate cost function, involving a maintenance cost term and a down-time cost term, is minimized with respect to the vector repair rate function u(t) subject to the practical constraint 0 ⩽ u(t) ⩽ U, where U is a given upper repair rate limit. A particular nontrivial example is given.