Application of binary decision diagrams for the analysis of consistent and non-consistent fault trees in the presence of uncertainties.

Summary In this thesis, we asked ourselves the following question: "What is the probability of occurrence of an undesirable event if the probabilities of occurrence of its basic events are imprecise? In other words, if these probabilities are given as intervals. In trying to answer this question we realized that the difficulty comes from the non-coherence of the fault tree structure, except that taking into account non-coherent fault trees creates a real computational challenge and answering this challenge was the main motivation of this thesis. On the other hand, non-coherent fault trees also create a challenge in the calculation of importance factors. Concerning this point, a research work is necessary, whether the probabilities of occurrence of the basic events are imprecise but also when they are precise. We propose two methods to calculate the probability of occurrence of an undesirable event. The first one is developed in the framework of the theory of belief functions and is based on binary decision diagrams. As for the second one, it is given in the framework of the theory of imprecise probabilities and it allows to give satisfactory results in a relatively short time (the same time that would have been taken if the probabilities were precise). We also propose a reinterpretation of the Birnbaum importance factor which is defined only for the basic events of a coherent fault tree. This reinterpretation allows to extend this factor in a trivial way to non-coherent fault trees.