An Approximate Algorithm for Evaluation of Semi-Markov Reliability Models

Reliability models of fault tolerant control systems (FTCS) are described by semi-Markov models when sequential tests are used for failure detection and identification (FDI). The transient analysis of these semi-Markov chains are of interest because the steady state behaviour is trivial. The relatively rare occurence of the failure events compared to the fast decisions by the FDI tests allow time-scale decomposition of these models. This leads to an aggregated state model which is approximately Markovian in character in the limit when the failure rates approach zero. An aggregate non-homogeneous Markov model is considered over the transient period of interest and an algorithm to compute the transition rates from the aggregated states is described. From the aggregated model, the state probability distribution of the original semi-Markov model can be derived by a disaggregation step.