A compositional semantics for Repairable Fault Trees with general distributions

Fault Tree Analysis (FTA) is a prominent technique in industrial and scientific risk assessment. Repairable Fault Trees (RFT) enhance the classical Fault Tree (FT) model by introducing the possibility to describe complex dependent repairs of system components. Usual frameworks for analyzing FTs such as BDD, SBDD, and Markov chains fail to assess the desired properties over RFT complex models, either because these become too large, or due to cyclic behaviour introduced by dependent repairs. Simulation is another way to carry out this kind of analysis. In this paper we review the RFT model with Repair Boxes as introduced by Daniele Codetta-Raiteri. We present compositional semantics for this model in terms of Input/Output Stochastic Automata, which allows for the modelling of events occurring according to general continuous distribution. Moreover, we prove that the semantics generates (weakly) deterministic models, hence suitable for discrete event simulation, and prominently for Rare Event Simulation using the FIG tool

Rare Event Simulation for non-Markovian repairable Fault Trees

Dynamic Fault Trees (DFT) are widely adopted in industry to assess the dependability of safety-critical equipment. Since many systems are too large to be studied numerically, DFTs dependability is often analysed using Monte Carlo simulation. A bottleneck here is that many simulation samples are required in the case of rare events, e.g. in highly reliable systems where components fail seldomly. Rare Event Simulation (RES) provides techniques to reduce the number of samples in the case of rare events. We present a RES technique based on importance splitting, to study failures in highly reliable DFTs. Whereas RES usually requires meta-information from an expert, our method is fully automatic: by cleverly exploiting the fault tree structure we extract the so-called importance function. We handle DFTs with Markovian and non-Markovian failure and repair distributions (for which no numerical methods exist) and show the efficiency of our approach on several case studies

Rare event simulation with fully automated Importance splitting

Probabilistic model checking is a powerful tool for analysing probabilistic systems but it can only be efficiently applied to Markov models. Monte Carlo simulation provides an alternative for the generality of stochastic processes, but becomes infeasible if the value to estimate depends on the occurrence of rare events. To combat this problem, intelligent simulation strategies exist to lower the estimation variance and hence reduce the simulation time. Importance splitting is one such technique, but requires a guiding function typically defined in an ad hoc fashion by an expert in the field. We present an automatic derivation of the importance function from the model description. A prototypical tool was developed and tested on several Markov models, compared to analytically and numerically calculated results and to results of typical ad hoc importance functions, showing the feasibility and efficiency of this approach. The technique is easily adapted to general models like GSMPs.publishedVersionFil: Budde, Carlos Esteban. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina.Fil: Budde, Carlos Esteban. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina.Fil: D'Argenio, Pedro Ruben. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina.Fil: D'Argenio, Pedro Ruben. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina.Fil: Hermanns, Holger. Universität des Saarlandes. Fakultät für Mathematik und Informatik; Alemania.Ciencias de la Computació