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Comparisons of Multi-State Systems with Binary Components of Different Sizes

Author

Listed:
  • He Yi

    (Beijing University of Chemical Technology)

  • Narayanaswamy Balakrishnan

    (McMaster University)

  • Lirong Cui

    (Beijing Institute of Technology)

Abstract

The system signatures of multi-state coherent or mixed systems with i.i.d. (independent and identically distributed) binary-state components are considered in this paper. For any multi-state coherent or mixed system with m i.i.d. components, the signature of its equivalent system of size m + l can be written as a mixture of signatures of several multi-state vector k -out-of- m + l: F systems. This facilitates the comparison of two multi-state systems of different sizes upon transforming the signature of the system of smaller size to the signature of its equivalent system of larger size along the lines of Navarro et al. (2008) for the usual Samaniego signature. Some numerical examples are finally presented to illustrate all the results established here.

Suggested Citation

  • He Yi & Narayanaswamy Balakrishnan & Lirong Cui, 2021. "Comparisons of Multi-State Systems with Binary Components of Different Sizes," Methodology and Computing in Applied Probability, Springer, vol. 23(4), pages 1309-1321, December.
    • Handle: RePEc:spr:metcap:v:23:y:2021:i:4:d:10.1007_s11009-020-09805-x
    DOI: 10.1007/s11009-020-09805-x
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    References listed on IDEAS

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    1. 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.
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    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. He Yi & Lirong Cui, 2018. "A new computation method for signature: Markov process method," Naval Research Logistics (NRL), John Wiley & Sons, vol. 65(5), pages 410-426, August.
    5. 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, September.
    6. Michael R. Dugas & Francisco J. Samaniego, 2007. "On optimal system designs in reliability‐economics frameworks," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(5), pages 568-582, August.
    7. da Costa Bueno, Vanderlei, 2013. "A multistate monotone system signature," Statistics & Probability Letters, Elsevier, vol. 83(11), pages 2583-2591.
    8. Markos V. Koutras & Ioannis S. Triantafyllou & Serkan Eryilmaz, 2016. "Stochastic Comparisons Between Lifetimes of Reliability Systems with Exchangeable Components," Methodology and Computing in Applied Probability, Springer, vol. 18(4), pages 1081-1095, December.
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    Cited by:

    1. Jingwen Lu & He Yi & Xiang Li & Narayanaswamy Balakrishnan, 2023. "Joint Reliability of Two Consecutive-(1, l) or (2, k)-out-of-(2, n): F Type Systems and Its Application in Smart Street Light Deployment," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-26, March.
    2. Yi, He & Cui, Lirong & Balakrishnan, Narayanaswamy, 2021. "Computation of survival signatures for multi-state consecutive-k systems," Reliability Engineering and System Safety, Elsevier, vol. 208(C).
    3. He Yi & Lirong Cui & Narayanaswamy Balakrishnan & Jingyuan Shen, 2022. "Multi-Point and Multi-Interval Bounded-Covering Availability Measures for Aggregated Markovian Repairable Systems," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2427-2453, December.

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