Please use this identifier to cite or link to this item: https://doi.org/10.1016/j.spl.2005.12.004
Title: On the dual reliability systems of ( n, f, k ) and 〈 n, f, k 〉
Authors: Cui, L.
Kuo, W.
Li, J.
Xie, M. 
Keywords: ( n, f, k ) and 〈 n, f, k 〉 systems
Consecutive system
Duality
Markov chain
Reliability
Issue Date: 1-Jun-2006
Source: Cui, L., Kuo, W., Li, J., Xie, M. (2006-06-01). On the dual reliability systems of ( n, f, k ) and 〈 n, f, k 〉. Statistics and Probability Letters 76 (11) : 1081-1088. ScholarBank@NUS Repository. https://doi.org/10.1016/j.spl.2005.12.004
Abstract: The ( n, f, k ) ( 〈 n, f, k 〉 ) system consists of n components ordered in a line or a circle and the system fails if and only if there exist at least f failed components or (and) at least k consecutive failed components. This type of models involves two common failure criteria of a system. In this paper, the duality of these systems is obtained and the proofs are given. We also obtain the recursive equations for the system reliability for these models. Furthermore, the finite Markov chain imbedding approach is employed to obtain some more compact reliability formulas for independent and Markov-dependent cases. © 2005 Elsevier B.V. All rights reserved.
Source Title: Statistics and Probability Letters
URI: http://scholarbank.nus.edu.sg/handle/10635/63219
ISSN: 01677152
DOI: 10.1016/j.spl.2005.12.004
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