Method for evaluating an extended Fault Tree to analyse the dependability of complex systems: Application to a satellite-based railway system

•New approach modelling critical events stemming from degraded-state duration.•Evaluating a repairable, multi-state & time duration dependent Fault Tree.•Practical solution for dependability analysis of a GNSS-based localisation.•Taking into account the local impacts on the GNSS-based localisation.

Evaluating dependability of complex systems requires the evolution of the system states over time to be analysed. The problem is to develop modelling approaches that take adequately the evolution of the different operating and failed states of the system components into account. The Fault Tree (FT) is a well-known method that efficiently analyse the failure causes of a system and serves for reliability and availability evaluations. As FT is not adapted to dynamic systems with repairable multi-state components, extensions of FT (eFT) have been developed. However efficient quantitative evaluation processes of eFT are missing. Petri nets have the advantage of allowing such evaluation but their construction is difficult to manage and their simulation performances are unsatisfactory. Therefore, we propose in this paper a new powerful process to analyse quantitatively eFT. This is based on the use of PN method, which relies on the failed states highlighted by the eFT, combined with a new analytical modelling approach for critical events that depend on time duration. The performances of the new process are demonstrated through a theoretical example of eFT and the practical use of the method is shown on a satellite-based railway system.