An efficient algorithm for computing the reliability of stochastic binary systems

This study addresses the problem of computing the reliability of stochastic binary systems. This computational problem is known as the problem of the union of a set of events, where each event is expressed as the product of a set of Boolean variables. It is assumed that each Boolean variable may take on either of two states: operative or failed. Computing the reliability of stochastic binary systems is known to be #P-complete. The computation remains #P-complete, even when all events have a cardinality two, and both elements of each event are selected from two disjoint sets. This study proposes a linear time algorithm to compute the reliability of stochastic binary systems when the events satisfy specific requirements.