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Reliability of a 2‐dimensional k‐within‐consecutive‐r × s‐out‐of‐m × n:F system

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  • Tomoaki Akiba
  • Hisashi Yamamoto

Abstract

A 2‐dimensional rectangular (cylindrical) k‐within‐consecutive‐r × s‐out‐of‐m × n:F system is the rectangular (cylindrical) m × n‐system if the system fails whenever k components in a r × s‐submatrix fail. This paper proposes a recursive algorithm for the reliability of the 2‐dimensional k‐within‐consecutive‐r × s‐out‐m × n:F system, in the rectangular case and the cylindrical case. This algorithm requires min (O(mkr(n−s)), O(nks(m−r))), and O(mkrn) computing time in the rectangular case and the cylindrical case, respectively. The proposed algorithm will be demonstrated and some numerical examples will be shown. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48: 625–637, 2001.

Suggested Citation

  • Tomoaki Akiba & Hisashi Yamamoto, 2001. "Reliability of a 2‐dimensional k‐within‐consecutive‐r × s‐out‐of‐m × n:F system," Naval Research Logistics (NRL), John Wiley & Sons, vol. 48(7), pages 625-637, October.
    • Handle: RePEc:wly:navres:v:48:y:2001:i:7:p:625-637
    DOI: 10.1002/nav.1038
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    References listed on IDEAS

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    1. Yeh Lam & Yuan Lin Zhang, 2000. "Repairable consecutive‐k‐out‐of‐n: F system with Markov dependence," Naval Research Logistics (NRL), John Wiley & Sons, vol. 47(1), pages 18-39, February.
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    Cited by:

    1. Hisashi Yamamoto & Tomoaki Akiba, 2005. "Evaluating methods for the reliability of a large 2‐dimensional rectangular k‐within‐consecutive‐(r, s)‐out‐of‐(m, n):F system," Naval Research Logistics (NRL), John Wiley & Sons, vol. 52(3), pages 243-252, April.
    2. Lin, Cong & Zeng, Zhaoyang & Zhou, Yan & Xu, Ming & Ren, Zhanyong, 2019. "A lower bound of reliability calculating method for lattice system with non-homogeneous components," Reliability Engineering and System Safety, Elsevier, vol. 188(C), pages 36-46.

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