An approach of reliability assessment of systems based on graphs models

Abstract

This paper presents an approach to assess the systems reliability based on graphs models. The Hasse diagram is a graph representation of the order relation between the system components' states. Using the monotony property of the structure function, an ordered graph is defined from the classical Hasse diagram by taking into account only the tie-sets of the system. Supplementary, this ordered graph can be built from the only knowledge of the minimal tie-sets, or for any Boolean formula representing the structure function of the system. Browsing paths from the minimal tie-sets to the maxima of the ordered graph, a weight is associated to each node. The dynamically changing of the nodes weight during the research paths allows us an algorithm development to directly determine the reliability polynomial of coherent systems. Thereafter, this approach is extended to non coherent systems for obtaining their reliability polynomial based on the paths starting from a new concept of terminal tie-sets. Performances of these algorithms are also identified.