Approximate semi-Markov chain reliability models

A property observed in high-reliability fault-tolerant control systems is the relatively rare occurrence of component failures compared to the frequent occurrence of redundancy-management decision events. This property leads to a temporal decomposition of the semi-Markov chain reliability model into two time scales: a slow time scale for failure events and a fast time scale for FDI (failure detection and isolation) events. Conditions are described under which a perturbed semi-Markov chain can be approximated by an enlarged Markov process, the parameters of which derive from the parameters of the semi-Markov chain. Two simple semi-Markov reliability models of a single-component monitoring system are examined