In this study, two reliability computational algorithms which respectively utilize a factoring method are proposed for a system represented by reliability block diagram. First, vertex factoring algorithm is proposed. In this algorithm, a reliability block diagram is considered as a network graph with vertex reliabilities. Second algorithm is mainly concerned with conversion of a reliabilities block diagram into a network graph with edge reliabilities. In this algorithm, the independence of edges is preserved by eliminating replicated edges, and in computing the reliability of a converted network graph, existing edge factoring algorithm is applied. The efficiency of two algorithms are compared for example systems with respect to computing times. The results shows that the second algorithm is shown to be more efficient than the first algorithm.