TABLE OF CONTENTS In recent years, new algorithms concerning fault trees was proposed by Coudert and Madre [COU 92], [COU 94] designated under the term of binary decision diagrams (BDD). It is based on a kind of reduction of the factorization tree of Shannon, as tuned in the treatments of Boolean functions by Akers [AKE 78], and later by Bryant [BRY 87], [BRY 92]. With the aid of this new technique, a complete algorithmics (probabilistic assessment, logical analysis and calculation of the factors of importance) has already been proposed in the literatures [RAU 93], [ODE 95], [ODE 96].
The algorithms based on the BDD are exceptionally rapid. They have made possible the treatment of difficult test cases in a very short space of time (some seconds) instead of very long time periods (some hours, even some days) even with the most efficient traditional algorithms.
Nevertheless, it has to be noted that these algorithms have not altered the nature of the problem, which still continues to be NP-complete. As a result, there can be cases that are difficult to resolve, even with these algorithms.
Beginning from the tree developed by Shannon, we will proceed with its reduction starting, in principle, from the bottom towards the top, while eliminating the vertices that are not useful. We eliminate a vertex in the following two cases:
When its two children head for the same vertex, or
When it is equivalent to another...
