Extending fault trees with continuous system variables

Fault Tree Analysis (FTA) is a widely adopted methodology where events are modeling the working/failure dichotomy of components and subsystems. However, system variables are often of continuous nature, and in some cases measured through a monitoring process. In this paper, we present an approach aimed at introducing continuous variables in a standard static fault tree (FT) formalism. We show how continuous variables can be tied to basic events in a FT, how to model probabilistic linear dependencies among them, and how influences of contextual information on system variables can be captured and modeled. We called the resulting formalism c-FT, and we propose a conversion of a c-FT into Hybrid Bayesian Networks (HBN); this allows us to exploit HBN inference algorithms, in order to perform the analyses of interest on the modeled system. As an experimental framework, we consider a model for a waste incinerator, and we present the results of specific analyses (from system reliability, to posterior probability of faulty situations) implemented through conversion of a c-FT into an HBN and by exploiting the MATLAB BNT Toolbox for inference.