Optimal replacement and reactivation in warm standby systems performing random duration missions

Abstract

Reliability modeling and optimization of warm standby systems have attracted considerable research attentions in the past decade due to their wide use in diverse critical applications. The existing works have mostly assumed that the activation of a standby element is triggered by the failure of the online operating element. This paper advances the state of the art by modeling a new type of warm standby systems subject to preventive replacements (PR) and element reactivation during its uncertain mission time. According to pre-determined PR schedule and element activation sequence, the online element is replaced with a standby element before its failure, and any element may be activated or reactivated multiple times during the mission. The mission succeeds if none of the activated elements fails before (i.e., while in the standby mode) or during its operation. A probabilistic method is proposed to evaluate the mission success probability for the considered warm standby system. The optimal PR scheduling problem is then formulated and solved, maximizing the mission success probability. Impacts of different system model parameters on the mission success probability and on the optimization solutions are examined through two examples, including a homogeneous and a heterogeneous warm standby system.