Graph representation of logic differential calculus for reliability modeling of coherent binary state systems
Résumé
In reliability engineering a large class of models (fault trees, reliability block diagram, event trees, …) are founded on the structure function model often written as a Boolean polynomial. Based on the structure function, two approaches were recently proposed to analyze and asses the system reliability: logic differential calculus and graph models based on Hasse diagram. Logic differential calculus is a powerful mathematical methodology that allows the analyze of dynamic properties of Boolean functions by means of Direct Partial Boolean Derivatives. Hasse diagram is a graph representation of the partially order on the values of the state vector. The system states diagram, which is an extension of the Hasse diagram, allows the determination of a minimal disjoint Boolean polynomial as well as a direct computation of the system reliability. In this paper, we propose a new graph to represent Direct Partial Boolean Derivatives that allows us to compare both approaches of logic differential calculus and graph models in order to find correspondences between them. Thereafter these approaches are applied for computation of Birnbaum’s importance measure to determine the impact of critical components on the system reliability.