Computing Optimal Repair Strategies by Means of NdRFT Modeling and Analysis

In this paper, the Non-deterministic Repairable Fault Tree (NdRFT) formalism is proposed: it allows the modeling of failures of complex systems in addition to their repair processes. Its originality with respect to other Fault Tree extensions allows us to address repair strategy optimization problems: in an NdRFT model, the decision as to whether to start or not a given repair action is non-deterministic, so that all the possibilities are left open. The formalism is rather powerful, it allows: the specification of self-revealing events, the representation of components degradation, the choice among local repair, global repair, preventive maintenance, and the specification of the resources needed to start a repair action. The optimal repair strategy with respect to some relevant system state function, e.g. system unavailability, can then be computed by solving an optimization problem on a Markov Decision Process derived from the NdRFT. Such derivation is obtained by converting the NdRFT model into an intermediate formalism called Markov Decision Petri Net (MDPN). In the paper, the NdRFT syntax and semantics are formally described, together with the conversion rules to derive from the NdRFT the corresponding MDPN model. The application of NdRFT is illustrated through examples.