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Reliability of a toroidal connected-(r,s)-out-of-(m,n):F lattice system

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  • Taishin Nakamura
  • Hisashi Yamamoto
  • Tomoaki Akiba

Abstract

This article focuses on a toroidal connected-( r,s )-out-of-( m,n ):F lattice system, which has m vertical circles and n horizontal circles, and the components are deployed at their intersections. This system fails if and only if the system has an ( r , s ) sub-matrix where all components fail. It might be used to evaluate the reliability of a system with a toroidal structure, for example, toroidal storage tanks and neutron accelerators. The purpose of this article is to efficiently compute the reliability of the toroidal connected-( r,s )-out-of-( m,n ):F lattice system. First, we propose a recursive method and then develop two kinds of algorithms based on this method. We apply an idea of preparing a set in a pre-processing phase to one algorithm, and consequently, the algorithm with the idea requires the extra memory space but has better time complexity compared with the other one. Finally, we investigate the efficiency of the two algorithms through numerical experiments.

Suggested Citation

  • Taishin Nakamura & Hisashi Yamamoto & Tomoaki Akiba, 2022. "Reliability of a toroidal connected-(r,s)-out-of-(m,n):F lattice system," Journal of Risk and Reliability, , vol. 236(2), pages 329-338, April.
    • Handle: RePEc:sae:risrel:v:236:y:2022:i:2:p:329-338
    DOI: 10.1177/1748006X19893533
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    References listed on IDEAS

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    1. 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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    Cited by:

    1. Yi, He & Balakrishnan, Narayanaswamy & Li, Xiang, 2023. "Reliability of three-dimensional consecutive k-type systems," Reliability Engineering and System Safety, Elsevier, vol. 233(C).
    2. Zhang, Changzhen & Yang, Jun & Li, Mingjia & Wang, Ning, 2024. "Reliability analysis of a two-dimensional linear consecutive-(r,s)-out-of-(m,n): F repairable system," Reliability Engineering and System Safety, Elsevier, vol. 242(C).

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    1. Yi, He & Balakrishnan, Narayanaswamy & Li, Xiang, 2023. "Reliability of three-dimensional consecutive k-type systems," Reliability Engineering and System Safety, Elsevier, vol. 233(C).

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