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Computationally Efficient and Numerically Stable Reliability Bounds for Repairable Fault-Tolerant Systems
March 2002 (vol. 51 no. 3)
pp. 254-268

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 $\rm C^{\prime\prime}$, 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.

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Index Terms:
fault-tolerant systems, repairable systems, reliability, continuous time Markov models, bounds, randomization
Citation:
J.A. Carrasco, "Computationally Efficient and Numerically Stable Reliability Bounds for Repairable Fault-Tolerant Systems," IEEE Transactions on Computers, vol. 51, no. 3, pp. 254-268, March 2002, doi:10.1109/12.990125
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