Time-domain computation of the reliability of standby systems with and without priority under general repair

In this paper, we consider a two-unit, non-identical cold standby system under general repair with or without priority. In the prioritized case, one unit in the system is designated to serve as standby only, that is, the standby unit is only utilized when the main unit has failed and is being repaired, whereas in the non-prioritized case, both units serve alternately as standby with each unit being put to standby mode when its repair is complete. The effect of each repair is modelled by a degree θ, 0≤θ≤1, where θ=0 means full repair (or full replacement) and θ=1 means minimal repair. For these cases, and for arbitrary distributions of the lifetimes and repair times of the units in the system, we obtain the reliability function in the time domain as opposed to the Laplace domain. Our functions utilize results from classical and generalized renewal theory results. We validated our formulas on various in-house standby configurations, as well as standby configurations occurring in coolant systems of nuclear power plants.