Improved Dynamic Fault Tree modelling using Bayesian Networks

1. Background In modelling fault-tolerant systems , space state based approaches such as dynamic fault trees (DFTs) [4], have been shown to increase the power of traditional combinatorial models, like static fault trees (FTs) [9]. However, in practice, these approaches have severe limitations when dealing with the increasing complexity of component dependencies and failure behaviours of today’s real-time fault-tolerant systems. Two major limitations are: 1) the problem of space state explosion and 2) the inability to handle non-exponential failure distributions for some dynamic constructs. Bayesian Networks (BNs), and their extension for time-series modelling known as Dynamic Bayesian Networks (DBNs), [5], have shown to provide to a unified framework for reliability modelling and analysis of complex systems, [6]. In particular, the BN framework allows a compact representation of the temporal (and functional) dependencies among the system components and event-dependent failure behaviours characteristic of fault-tolerant systems, avoiding the state space explosion problem of the Markov Chain based approaches to DFT analysis, [3], [10]. In [8] we presented a new, effective and flexible event-based hybrid BN modelling method for Fault Tree analysis that scales up to large, complex dynamic systems. The new approach incorporates a recent powerful approximate inference algorithm for hybrid BNs, [7], based on a process of dynamic discretisation of the domain of all continuous variables in the BN, and the entropy error, as the basis for approximation. By combining the modelling capabilities of BNs with our dynamic discretisation inference algorithm we offer a unified technique for reliability analysis of large, safety critical systems, which overcomes most of the limitations of both space-state based reliability models and previous BN approaches. In our BN framework, continuous failure times with general parametric or empirical time-to-failure distributions occurring in practical applications, as well as discrete variables modelling the state of the system (or any subsystem) at a particular time instance, can be included in the model in a simple unified way. Approximated solutions for both static and dynamic constructs are obtained simultaneously, and so modularisation techniques, numerical integration and simulation methods are all unnecessary. Furthermore, Bayesian reliability data analysis can be easily carried out in our framework, allowing us to integrate information from multiple sources at different levels of granularity, as well as expert opinion. The approach offers a powerful framework for analysts and decision makers to successfully perform robust reliability as sessment. Sensitivity, uncertainty, diagnosis analysis, common cause failures, and warranty analysis can also be easily performed within this framework. All the example models in [8] were built and executed using the Bayesian Network tool AgenaRisk [1], in which the dynamic discretisation algorithm [7] is now implemented.