Modelling and Inference for Networks with Repairable Redundant Subsystems

We consider the problem of modelling the reliability of a network of subsystems where each subsystem has redundancy and is repairable. The motivation for this work is large-scale telecommunications networks. The time to failure of the subsystem hardware is modeled by an appropriate Markov process and is hence a phase-type distribution. The network structure defines a failure rule in terms of the states of the subsystems, allowing computation by Monte Carlo simulation of the time to failure distribution for the network. This is illustrated by some simple examples. When data on the reliability of the subsystems are available, this can be incorporated via a Bayesian inference approach to modify the prediction of network reliability.