Balancing mission success probability and risk of system loss by allocating redundancy in systems operating with a rescue option

Abstract

In many real-world safety-critical applications, a rescue procedure aimed at saving a system can be activated after its failure to execute a primary mission. For such systems, it is essential to keep the balance between the mission success probability and the system survival probability, as both of these contradicting metrics are extremely important in practice. This balance is achieved in the paper by solving the corresponding constrained redundancy optimization problem utilizing the innovative algorithmic approach. The developed methodology is applied to multicomponent systems with overlapping sets of components involved in primary and rescue phases of a mission, respectively. Each component is a subsystem that consists of parallel heterogeneous elements. The random environment in which the system operates is modeled by the Poisson shock process, whereas each shock can result in failures with given probabilities. The detailed numerical example illustrating optimal redundancy solutions is presented. Further directions for generalizations and applications of the obtained results are discussed.