Reliability maximization in stochastic binary systems

Abstract

A Stochastic Binary System (SBS) is a mathematical model of multi-component on-off systems subject to random failures. This model is an extension of network reliability models (where the components are either nodes or links). The reliability maximization is a major network design problem, where the goal is to find the network that maximizes the reliability subject to budget constraints. Even though the problem is computationally hard, the scientific literature offers uniformly most-reliable graphs for specific cases, and necessary criteria for optimality. The concept of uniformly most-reliable stochastic binary system is here introduced. We discuss some basic aspects which must be taken into account to develop a theory of reliability maximization in this setting: computational complexity, necessary conditions for reliability maximization and shared results with the classical theory for network design.