An enumeration algorithm for combinatorial problems of the reliability analysis of binary coherent systems

In this paper the problem of the generation of all elements of a system of sets is investigated and a backtrack algorithm (A1) is given solving this problem. The algorithm is applied to combinatorial problems of reliability: A t-graph is interpreted as a binary coherent system ℝ5S and the system function of ℝ5S is represented as the sum of Boolean orthogonal products. This approach is a simple and efficient alternative to a method suggested by Satyanarayana and N. Hagstrom. A directed p-graph is also interpreted as a binary coherent system ℝ5S and both the minimal cuts of ℝ5S and the cocycles of G are determined.