Modeling Interactions for Inoperability Management: from Fault Tree Analysis (FTA) to Dynamic Bayesian Network (DBN)

Abstract

This paper considers the problem of modeling the mechanism of inoperability propagation within a network of complex systems (a production unit, a transportation system, an energy supply system, etc.). We are particularly interested in modeling one of the main attributes of complexity that is interaction; indeed, interactions between systems in a network or components in a system have the effect of propagating and perhaps even amplifying local inoperabilities. Two types of interactions are considered: influence that can be described by an acyclic hierarchical relationships graph of the interacting systems or components and interdependence for which the graphical representation of relationships allows loops. Hierarchy is mainly functional or structural and is analyzed and established in this communication using fault tree analysis (FTA) as the underlying mathematical tools whereas interdependence is apprehended through dynamic Bayesian network (DBN) by considering that effects are delayed. The ultimate DBN model (obtained in two steps: (1) a static Bayesian network (BN) isomorphic to the FTA model and then (2) DBN model by introducing delayed interdependence effects) of a complex system can serve as a decision support system for many risk related scenarios analysis and/or activities such as predictive maintenance.