  The operation of a system, such as a vehicle, communication network or
automatic process, heavily depends on the correct operation of its components.
A Stochastic Binary System (SBS) mathematically models the behavior of on-off
systems, where the components are subject to probabilistic failures. Our goal
is to understand the reliability of the global system.
  The reliability evaluation of an SBS belongs to the class of NP-Hard
problems, and the combinatorics of SBS imposes several challenges. In a
previous work by the same authors, a special sub-class of SBSs called
"separable systems" was introduced. These systems accept an efficient
representation by a linear inequality on the binary states of the components.
However, the reliability evaluation of separable systems is still hard.
  A theoretical contribution in the understanding of separable systems is
given. We fully characterize separable systems under the all-terminal
reliability model, finding that they admit efficient reliability evaluation in
this relevant context.
