Analysis and optimal design of systems operating in a random environment and having a rescue option

Abstract

ABSTRACTThe paper presents a model for a system exposed to a random environment characterized by the Poisson shock processes. A subset of the system components ℜM is required for a mission completion. Failures of some components of this subset terminate a mission, whereas failures of other components are not terminal and allow for a rescue operation that is activated immediately upon failure. This operation is performed by a subset ℜR of the system components and succeeds if all components from ℜR survive all shocks occurring until its completion. The subsets ℜM and ℜR overlap. The duration of the rescue operation depends on the time of its activation. The components that are engaged only in the rescue operation remain in the warm standby mode during the primary mission. An approach for obtaining the mission success and the system survival probabilities is developed and an algorithm for the corresponding numerical computation is presented. An example analyzing the tradeoff between these two probabilities and illustrating optimization of the system protection design is given.