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Multi-State Joint Survival Signature for Multi-State Systems with Shared Multi-State Components

Author

Listed:
  • He Yi

    (Beijing University of Chemical Technology)

  • Narayanaswamy Balakrishnan

    (McMaster University)

  • Xiang Li

    (Beijing University of Chemical Technology)

Abstract

In this paper, the multi-state joint survival signature is proposed for two multi-state semi-coherent or mixed systems with shared independent and identically distributed (i.i.d.) multi-state components, and then its properties are studied along with the related multi-state joint signature. By using the idea of equivalent systems, generalized triangle rule for order statistics and the independence assumption of component lifetimes at different states, transformation formulas of multi-state joint survival signatures of different sizes are presented so that stochastic comparisons of multi-state semi-coherent or mixed system pairs that share different numbers of multi-state components can be carried out. For illustrating the theoretical results established here, some examples are presented. Finally, some concluding remarks are made.

Suggested Citation

  • He Yi & Narayanaswamy Balakrishnan & Xiang Li, 2023. "Multi-State Joint Survival Signature for Multi-State Systems with Shared Multi-State Components," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-18, March.
    • Handle: RePEc:spr:metcap:v:25:y:2023:i:1:d:10.1007_s11009-023-10023-4
    DOI: 10.1007/s11009-023-10023-4
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    References listed on IDEAS

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    1. Coolen-Maturi, Tahani & Coolen, Frank P.A. & Balakrishnan, Narayanaswamy, 2021. "The joint survival signature of coherent systems with shared components," Reliability Engineering and System Safety, Elsevier, vol. 207(C).
    2. Marichal, Jean-Luc & Mathonet, Pierre & Navarro, Jorge & Paroissin, Christian, 2017. "Joint signature of two or more systems with applications to multistate systems made up of two-state components," European Journal of Operational Research, Elsevier, vol. 263(2), pages 559-570.
    3. Ilya Gertsbakh & Yoseph Shpungin, 2012. "Multidimensional Spectra of Multistate Systems with Binary Components," Springer Series in Reliability Engineering, in: Anatoly Lisnianski & Ilia Frenkel (ed.), Recent Advances in System Reliability, chapter 0, pages 49-61, Springer.
    4. Francisco J. Samaniego, 2007. "System Signatures and their Applications in Engineering Reliability," International Series in Operations Research and Management Science, Springer, number 978-0-387-71797-5, March.
    5. Somayeh Ashrafi & Majid Asadi & Jorge Navarro, 2022. "Joint Reliability Function of Coherent Systems with Shared Heterogeneous Components," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1485-1502, September.
    6. Eryilmaz, Serkan & Coolen, Frank P.A. & Coolen-Maturi, Tahani, 2018. "Marginal and joint reliability importance based on survival signature," Reliability Engineering and System Safety, Elsevier, vol. 172(C), pages 118-128.
    7. Jorge Navarro & Francisco J. Samaniego & N. Balakrishnan & Debasis Bhattacharya, 2008. "On the application and extension of system signatures in engineering reliability," Naval Research Logistics (NRL), John Wiley & Sons, vol. 55(4), pages 313-327, June.
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    Cited by:

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