Algebraic Expression of the Structure Function of a subclass of Dynamic Fault Trees

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 subclass of Dynamic Fault Trees (DFTs), called Priority Dynamic Fault Trees (PDFTs), containing only static gates and Priority Dynamic Gates (PAND and FDEP) 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. We finally show through an example that the canonical form can be exploited in order 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 this approach is that it provides a complete qualitative description of the system and that any failure distribution can be accommodated.

Mots clés: Dynamic Fault Tree; Algebraic approach; Qualitative analysis; Quantitative analysis

Domaines: Automatique / Robotique

Guillaume Merle, Jean-Marc Roussel, Jean-Jacques Lesage, Andrea Bobbio. Algebraic Expression of the Structure Function of a subclass of Dynamic Fault Trees. 2nd IFAC Workshop on Dependable Control of Discrete Systems (DCDS'09), Jun 2009, Bari, Italy. pp.129-134. ⟨hal-00394459⟩