Computationally efficient and numerically stable reliability bounds for repairable fault-tolerant systems

Abstract

The transient analysis of large continuous time Markov reliability models of repairable fault-tolerant systems is computationally expensive due to model stiffness. We develop and analyze a method to compute bounds for a measure defined on a particular, but quite wide class of continuous time Markov models, encompassing both exact and bounding continuous time Markov reliability models of fault-tolerant systems. The method is numerically stable and computes the bounds with well-controlled and specifiable-in-advance error. Computational effort can be traded off with bounds accuracy. For a class of continuous time Markov models, class C, including typical failure/repair reliability models with exponential failure and repair time distributions and repair in every state with failed components, the method can yield reasonably tight bounds at a very small computational cost. The method builds upon a recently proposed numerical method for the transient analysis of continuous time Markov models called regenerative randomization.