Simplifying semi-Markov fault recovery models

The author presents computational techniques that extend and relate several approximation methods in reliability prediction and performance analysis. The approximation methods considered are those that tackle the problems that arise when a Markov or semi-Markov model has a mix of very slow rates and very fast rates. It is shown that the heuristic rule approximation from performance analysis and the instantaneous jump approximation from reliability modeling are mathematically equivalent. That is, the two methods alter the probabilities in the same way. The results obtained permit the computation of the probabilities and moments of complex fault recovery and system repair models. The results are useful when analyzing highly reliable or high-performance systems, and they are relevant for several reliability prediction packages and for a model reduction method in performance analysis