Computationally efficient and numerically stable reliability bounds for repairable fault-tolerant systems
The transient analysis of large continuous time Markov reliability models of repairable fault-tolerant systems is computationally expensive due to model stiffness, In this paper, 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-r, 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.
reliability bounds fault-tolerant systems continuous time markov models randomization repairable systems