Title :
Probabilistic Algebraic Analysis of Fault Trees With Priority Dynamic Gates and Repeated Events
Author :
Merle, Guillaume ; Roussel, Jean-Marc ; Lesage, Jean-Jacques ; Bobbio, Andrea
Author_Institution :
LURPA, Ecole Normale Super. de Cachan, Cachan, France
fDate :
3/1/2010 12:00:00 AM
Abstract :
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.
Keywords :
Boolean algebra; Markov processes; fault trees; probability; Boolean operators; Markov model; failure distribution; priority dynamic fault trees; priority dynamic gates; probabilistic algebraic analysis; repeated events; Algebraic approach; cut sequence sets; dynamic fault tree; qualitative analysis;
Journal_Title :
Reliability, IEEE Transactions on
DOI :
10.1109/TR.2009.2035793