Abstract: A new method for computing the network two-terminal reliability was presented. The basic idea of the algorithm presented here relics on the notion of a frontal description of a graph. The innovation point is that the originality of the present work is in the application to the two-terminal and all-terminal reliability problem with close analysis of the complexity depending on the tree-width. We discussed methods to optimize the mean time to repair of the components. The method is valuable for optimizing network and assigning the mean time to repair.

Key words: Network reliability, Two-terminal reliability, Mttr, Mtbf