EXACT AND TRUNCATED COMPUTATIONS OF PRIME IMPLICANTS OF COHERENT AND NONCOHERENT FAULT-TREES WITHIN ARALIA

Aralia is a Binary Decision Diagram (BDD) package extended to handle f ault trees. It is currently developed at the University of Bordeaux as a part of a partnership between university laboratories and several F rench companies. BDD's are the state of the art data structure to hand le boolean functions. They have been recently used with success in the framework of safety and reliability analysis. The aim of this paper i s to present how prime implicants (minimal cuts) of coherent and non-c oherent fault trees are computed within Aralia. The used algorithms ar e mainly those proposed by J. C. Madre and O. Coudert on the one hand and A. Rauzy on the other hand. We introduce the notion of minimal p-c uts that is a sound extension of the notion of minimal cuts to the cas e of non-coherent fault trees. We propose two BDD based algorithms to compute them. We show how to modify these algorithms in order to compu te only prime implicants (or minimal p-cuts) whose orders are less tha n a given constant or whose probabilities are greater than a given thr eshold. We report experiments showing that this improves significantly the methodology for this allows fast, accurate and incremental approx imations of the desired result. (C) 1997 Elsevier Science Limited.