Probabilistic Algebraic Analysis of Fault Trees With Priority Dynamic Gates and Repeated Events

Guillaume Merle (1) , Jean-Marc Roussel (1) , Jean-Jacques Lesage (1) , Andrea Bobbio (2)

1 LURPA - Laboratoire Universitaire de Recherche en Production Automatisée
2 Dipartimento di Informatica

This paper focuses on a sub-class of Dynamic Fault Trees (DFTs), called Priority Dynamic Fault Trees (PDFTs), containing only static gates, and Priority Dynamic Gates (Priority-AND, and Functional Dependency) for which a priority relation among the input nodes completely determines the output behavior. We define events as temporal variables, and we show that, by adding to the usual Boolean operators new temporal operators denoted BEFORE and SIMULTANEOUS, it is possible to derive the structure function of the Top Event with any cascade of Priority Dynamic Gates, and repetition of basic events. A set of theorems are provided to express the structure function in a sum-of-product canonical form, where each product represents a set of cut sequences for the system. We finally show through some examples that the canonical form can be exploited to determine directly and algebraically the failure probability of the Top Event of the PDFT without resorting to the corresponding Markov model. The advantage of the approach is that it provides a complete qualitative description of the system, and that any failure distribution can be accommodated.

Mots clés: Algebraic approach; cut sequence sets; dynamic fault tree; qualitative analysis

Domaines: Automatique / Robotique

Guillaume Merle, Jean-Marc Roussel, Jean-Jacques Lesage, Andrea Bobbio. Probabilistic Algebraic Analysis of Fault Trees With Priority Dynamic Gates and Repeated Events. IEEE Transactions on Reliability, 2010, 59 (1), pp. 250-261. ⟨10.1109/TR.2009.2035793⟩. ⟨hal-00480014⟩