On preventive maintenance of systems subject to shocks

A system of identical components is subject to an external shock process, described by the number of shocks in each time interval. Each shock destroys one of the components with probability p and has no effect on a system with probability 1 − p . Signatures are defined and used for description of the system’s structure and for dealing with the corresponding optimal maintenance problems. Two optimal maintenance strategies are discussed. The first strategy is based on the obtained optimal number of a shock, after which the maintenance is performed unless the failure of a whole system occurs earlier. In the latter case the system is replaced. The second strategy is periodic when preventive maintenance is performed periodically with respect to the observed shock numbers. Several numerical examples are presented.