On a general standby system and its optimization

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 times, the system fails. Units can fail at both active and warm standby states. A general method for modeling the standby system is adopted and, based on it, system performance measures (system reliability and mean life) are derived. We consider the problem of determining optimal switching time which maximizes the expected system life. Some numerical examples are studied.