Minimization of boolean sum of products with applications to the computation of reliability of general networks

The evaluation of the reliability of general networks is based on a few principles coming from the basic probability theory. The complexity of the networks inevitably requires the use of a computerised approach. Discussion leads to the long Boolean expressions (Boolean sum-of-products) which can include hundreds of product terms for fairly small networks. In this study a new binary vector method is presented for the computerised search of minimum ties of a general network. The resolved minimum ties are utilised in generating a network's probability space, i.e. set of points of success and points of failure. The data file of these points is interpreted as the network's Boolean system function. It provides basic information for the new minimisation algorithm of the Boolean SOP-expression which is discussed in detail. In addition to these computer algorithms a short reliability calculation program is presented for the verification of the former results. The developed methods are each, in turn, applied to several sample networks, and the results are compared and studied to ascertain the new algorithms.