A new reliability parameter and algorithm for active network

To solve the problem that existing reliability parameters can't measure the connection probability from the source terminal to percentage of terminals in a specific terminal set for active networks, a new active network reliability parameter of source-to-k-out-of-N-terminal reliability (S(k/N)T reliability) was proposed. The definition and expression of the new parameter were described. The relationships between the new parameter and the classic reliability parameters for active networks were discussed. Based on inclusion-exclusion principle, an exact algorithm was given to calculate the new parameter. The connection requirement of the S(k/N)T reliability was transferred to that of SKT reliability which was an operative path from source terminal to every terminal in some specified node set. The K trees reflecting connectivity of SKT reliability was established. Based on inclusion-exclusion principle, the S(k/N)T reliability was calculated to obtain the new reasonability parameter and the algorithm, and verified with a case. The results show that the S(k/N)T reliability is an important metrics in engineering. Based on inclusion-exclusion principle, the algorithm is suitable for two-state system with failure independence assumption under the considerations of terminal and link failure.