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Algebraic Analysis of Variants of Multi-State k -out-of- n Systems

Author

Listed:
  • Patricia Pascual-Ortigosa

    (Departamento de Matemáticas y Computación, Universidad de La Rioja, 26006 Logroño, Spain)

  • Eduardo Sáenz-de-Cabezón

    (Departamento de Matemáticas y Computación, Universidad de La Rioja, 26006 Logroño, Spain)

Abstract

We apply the algebraic reliability method to the analysis of several variants of multi-state k -out-of- n systems. We describe and use the reliability ideals of multi-state consecutive k -out-of- n systems with and without sparse, and show the results of computer experiments on these kinds of systems. We also give an algebraic analysis of weighted multi-state k -out-of- n systems and show that this provides an efficient algorithms for the computation of their reliability.

Suggested Citation

  • Patricia Pascual-Ortigosa & Eduardo Sáenz-de-Cabezón, 2021. "Algebraic Analysis of Variants of Multi-State k -out-of- n Systems," Mathematics, MDPI, vol. 9(17), pages 1-15, August.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:17:p:2042-:d:621648
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    References listed on IDEAS

    as
    1. Yu, Huan & Yang, Jun & Peng, Rui & Zhao, Yu, 2016. "Reliability evaluation of linear multi-state consecutively-connected systems constrained by m consecutive and n total gaps," Reliability Engineering and System Safety, Elsevier, vol. 150(C), pages 35-43.
    2. Bigatti, A.M. & Pascual-Ortigosa, P. & Sáenz-de-Cabezón, E., 2021. "A C++ class for multi-state algebraic reliability computations," Reliability Engineering and System Safety, Elsevier, vol. 213(C).
    3. David A. Butler, 1982. "Bounding the Reliability of Multistate Systems," Operations Research, INFORMS, vol. 30(3), pages 530-544, June.
    4. Levitin, Gregory & Xing, Liudong & Dai, Yuanshun, 2015. "Linear multistate consecutively-connected systems subject to a constrained number of gaps," Reliability Engineering and System Safety, Elsevier, vol. 133(C), pages 246-252.
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    Cited by:

    1. Wang, Chaonan & Wang, Shuli & Xing, Liudong & Guan, Quanlong, 2023. "Efficient performability analysis of dynamic multi-state k-out-of-n: G systems," Reliability Engineering and System Safety, Elsevier, vol. 237(C).

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