Optimal design of a general warm standby system

Redundancy or standby is a technique that has been widely applied to improving system reliability and availability in the stage of system design. In this paper, we consider a standby system with two units in which the first unit (unit 1) starts its operation under active state and the other unit (unit 2) is under cold standby state at the starting point. After a specified time s (switching time), the state of unit 2 is changed to warm standby state and, as soon as the operating unit 1 fails, the state of unit 2 is changed to active state. If unit 1 fails before time s, the system fails. Units can fail at both active and warm standby states. A general method for modeling the standby system is adopted and system performance measures (system reliability and mean life) based on the proposed model are derived. Three models – a perfect switching model and two imperfect switching models – are considered in this paper. Two imperfect switching models include an imperfect switching probability and a preliminary warm-up period which is required for the change from cold standby state to warm standby state. We consider the problem of determining the optimal switching time which maximizes the expected system life and related allocation problem is also discussed. Some numerical examples are studied.