Parametric fault trees with dynamic gates and repair boxes

A new approach is proposed to include s-dependencies in Fault Tree (FT) models. With respect to previous techniques, the approach presented in this paper is based on two peculiar powerful features. First, we adopt a parameterization technique, referred to as Parametric FT (PFT), to fold equal subtrees (or basic events) in order to resort to a more compact FT representation. It is shown that parameterization can be conveniently adopted as well for dynamic gates. Second, PFT can be modularized and each module translated into a High Level Colored Petri net in the form of a Stochastic Wellformed Net (SWN). SWN generate a lumped Markov chain and the saving in the dimension of the state space can be very substantial with respect to standard (non colored) Petri nets. Translation of PFT modules into SWN has proved to be very flexible, and various kinds of new dependencies can be easily accommodated. In order to exploit this flexibility a new primitive, called repair box, is introduced. A repair box, attached to an event, causes the starting of a repair activity of all the components that are failed as the event occurs. In contrast to all the previous FT based models, the addition of repair boxes enables our approach to model cyclic behaviors. We refer to the proposed approach as Dynamic Repairable PFT (DRPFT). A tool supporting DRPFT is briefly described and the tool is validated by analyzing a benchmark proposed recently in the literature for quantitative comparison (Ref. 12).