Challenges in Stochastic Binary Systems

Stochastic Binary Systems (SBS) are mathematical models of multi-component on-off systems subject to random failures on its components. In this abstract setting, an SBS can model a network, an information system or the operation of an industrial automatic process, among many others. Given the importance of its applications, recent works from the literature aim to understand the system reliability and combinatorics of some distinguished sub-classes of SBS. In this paper we revisit the progress in this field. The most challenging problems in the analysis and practice of SBS are also discussed.