Sensitivity Analysis of Continuous Time Bayesian Network Reliability Models

We show how to perform sensitivity analysis on continuous time Bayesian networks (CTBNs) as applied specifically to reliability models. Sensitivity analysis of these models can be used, for example, to measure how uncertainty in the failure rates impact the reliability of the modeled system. The CTBN can be thought of as a type of factored Markov process that separates a system into a set of interdependent subsystems. The factorization allows CTBNs to model more complex systems than single Markov processes. However, the state-space of the CTBN is exponential in the number of subsystems. Therefore, existing methods for sensitivity analysis of Markov processes, when applied directly to the CTBN, become intractable. Sensitivity analysis of CTBNs, while borrowing from techniques for Markov processes, must be adapted to take advantage of the factored nature of the network if it is to remain feasible. To address this, we show how to extend the perturbation realization method for Markov processes to the CTBN. We show how to exploit the conditional independence structure of the CTBN to perform perturbation realization separately for different subnetworks, making the technique able to handle larger networks. This in turn allows the CTBN to model more complex systems while keeping sensitivity analysis of the model tractable.