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A report on network decomposition method using Binary Decision Diagrams and manipulate Boolean functions for computing the reliability of networks such as computer, communications or power and its effectiveness is shown by several examples and experiments is presented.

A new algorithm is introduced to evaluate (non) coherent fault trees, obtaining exact lower and upper bounds on system unavailability, with a prespecified maximum error. The algorithm is based on the canonical normal form of the Boolean function, but overcomes the large number of terms needed, by using an intrinsic order criterion (IOC) to select the elementary states to evaluate.

The calculation of mean system-failure frequency (MSFF) with prescribed accuracy for good engineering designs using Bonferroni-type inequalities was analyzed. The shortening sum-of-products forms of the fault-tree Boolean-function was then theorized to avoid higher-order Bonferroni inequalities for approximate analysis. Upper and lower bounds for mincuts approximation were found through MSFF with the approximated values of system mean time to failure and mean time to repair.

The sum of disjoint products (SDP) approach for network reliability evaluation is examined with respect to implementing paths/cuts preprocessing for decreasing the computation time and the amount of generated SDP terms. The paths/cuts ordering is carried out via cardinality, lexicographic and Hamming distance techniques and their generalizations on 19 benchmark networks with paths ranging from four to 780 and cuts from four to 7376 using the Computer Aided Relilability Evaluator.