Abstract
In the present article, a simple method is developed for approximating the reliability of Markov chain imbeddable systems. The approximating formula reduces the problem to the reliability assessment of smaller systems with structure similar to the original systems. Two specific reliability structures which have attracted considerable research interest recently (r-within-consecutive-k-out-of-n system and two dimensional r-within-k 1 × k 2-out-of-n 1 × n 2 system) are studied by the new approach and numerical calculations are carried out, which reveal the high quality of our approximations. Several possible extensions and generalizations are also presented in brief.
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Boutsikas, M.V., Koutras, M.V. Reliability Approximation for Markov Chain Imbeddable Systems. Methodology and Computing in Applied Probability 2, 393–411 (2000). https://doi.org/10.1023/A:1010062218369
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DOI: https://doi.org/10.1023/A:1010062218369