A Convolution Universal Generating Function Method for Evaluating the Symbolic One-to-All-Target-Subset Reliability Function of Acyclic Multi-State Information Networks

The acyclic multi-state information network (AMIN) is an extension of the multi-state network without having to satisfy the flow conservation law. A very straightforward convolution universal generating function method (CUGFM) is developed to find the exact symbolic one-to-all-target-subset reliability function of AMIN. The correctness and computational complexity of the proposed algorithm will be proven. Two illustrative examples demonstrate the power of the proposed CUGFM to solve the exact symbolic reliability functions of the one-to-all-target-subset AMIN problem more efficiently than the best-known UGFM.