Abstract
Many large engineering systems can be viewed (or imbedded) as a series system in time. In this paper, we introduce the structure of a repairable system and the reliabilities of these large systems are studied systematically by studying the ergodicities of certain non-homogeneous Markov chains. It shows that if the failure probabilities of components satisfy certain conditions, then the reliability of the large system is approximately exp (-β) for some β>0. In particular, we demonstrate how the repairable system can be used for studying the reliability of a large linearly connected system. Several practical examples of large consecutive-k-out-of-n:F systems are given to illustrate our results. The Weibull distribution is derived under our natural set-up.
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This research work was partially supported by the National Science Council of the Republic of China.
This work was supported in part by the Natural Sciences and Engineering Research Council of Canada under Grant A-9216, and by the National Science Council of the Republic of China.
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Chao, M.T., Fu, J.C. A limit theorem of certain repairable systems. Ann Inst Stat Math 41, 809–818 (1989). https://doi.org/10.1007/BF00057742
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DOI: https://doi.org/10.1007/BF00057742