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A C++ class for multi-state algebraic reliability computations

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  • Bigatti, A.M.
  • Pascual-Ortigosa, P.
  • Sáenz-de-Cabezón, E.

Abstract

We present the design and implementation of a C++ class for reliability analysis of multi-state systems using an algebraic approach based on monomial ideals. The class is implemented within the open-source CoCoALib library and provides functions to compute system reliability and bounds. The algorithms we present may be applied to general systems with independent components having identical or non-identical probability distributions.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:reensy:v:213:y:2021:i:c:s0951832021002817
    DOI: 10.1016/j.ress.2021.107751
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    References listed on IDEAS

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    1. Sáenz-de-Cabezón, Eduardo & Wynn, Henry P., 2011. "Computational algebraic algorithms for the reliability of generalized k-out-of-n and related systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(1), pages 68-78.
    2. Michael O. Ball & J. Scott Provan, 1988. "Disjoint Products and Efficient Computation of Reliability," Operations Research, INFORMS, vol. 36(5), pages 703-715, October.
    3. Lu, Shaoqi & Shi, Daimin & Xiao, Hui, 2019. "Reliability of sliding window systems with two failure modes," Reliability Engineering and System Safety, Elsevier, vol. 188(C), pages 366-376.
    4. Mo, Yuchang & Xing, Liudong & Amari, Suprasad V. & Bechta Dugan, Joanne, 2015. "Efficient analysis of multi-state k-out-of-n systems," Reliability Engineering and System Safety, Elsevier, vol. 133(C), pages 95-105.
    5. Michael O. Ball, 1979. "Computing Network Reliability," Operations Research, INFORMS, vol. 27(4), pages 823-838, August.
    6. Guanghan Bai & Zhigang Tian & Ming J. Zuo, 2018. "Reliability evaluation of multistate networks: An improved algorithm using state-space decomposition and experimental comparison," IISE Transactions, Taylor & Francis Journals, vol. 50(5), pages 407-418, May.
    7. BALL, Michael O., 1979. "Computing network reliability," LIDAM Reprints CORE 377, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    8. Chao Zhang & Tao Liu & Guanghan Bai, 2020. "An improved algorithm for reliability bounds of multistate networks," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(15), pages 3772-3791, August.
    9. Gregory Levitin, 2005. "The Universal Generating Function in Reliability Analysis and Optimization," Springer Series in Reliability Engineering, Springer, number 978-1-84628-245-4, June.
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    Cited by:

    1. 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.

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