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Joint signatures of two or more semi-coherent systems with shared components

Author

Listed:
  • Yi, He
  • Balakrishnan, Narayanaswamy
  • Li, Xiang

Abstract

In this paper, for two or more semi-coherent systems with shared components, three signature measures–joint signature, joint survival signature and joint cumulative signature–are presented and their relationship to joint reliability and joint unreliability are also discussed. This relationship provides a joint (survival/cumulative) signature computational method which transforms related computation to the computation of joint reliability/unreliability of the systems. Based on that, further discussions on computation of the joint reliability are presented for two different types of consecutive-k systems, namely, linear (n, f, k): F systems and linear : F systems, by using finite Markov chain imbedding approach (FMCIA) in a new and novel way. Besides, for modular systems that can be regarded as a series/parallel connection of two groups of subsystems with shared components, their joint (survival/cumulative) signature is derived based on the joint survival/cumulative signatures of the subsystems, and this provides another computational method for joint signatures. Related results are applied to calculate joint signatures of a series/parallel connection of (n, f, k): F subsystems and : F subsystems by applying the two computational methods together. Finally, some potential applications and generalizations are mentioned.

Suggested Citation

  • Yi, He & Balakrishnan, Narayanaswamy & Li, Xiang, 2024. "Joint signatures of two or more semi-coherent systems with shared components," Reliability Engineering and System Safety, Elsevier, vol. 242(C).
    • Handle: RePEc:eee:reensy:v:242:y:2024:i:c:s0951832023006270
    DOI: 10.1016/j.ress.2023.109713
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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. 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. 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.
    4. He Yi & Narayanaswamy Balakrishnan & Lirong Cui, 2022. "On Dependent Multi-State Semi-Coherent Systems Based on Multi-State Joint Signature," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1717-1734, September.
    5. Yi, He & Balakrishnan, Narayanaswamy & Li, Xiang, 2023. "Reliability of three-dimensional consecutive k-type systems," Reliability Engineering and System Safety, Elsevier, vol. 233(C).
    6. Zarezadeh, S. & Mohammadi, L. & Balakrishnan, N., 2018. "On the joint signature of several coherent systems with some shared components," European Journal of Operational Research, Elsevier, vol. 264(3), pages 1092-1100.
    7. 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, December.
    8. Yin, Juan & Cui, Lirong & Balakrishnan, Narayanaswamy, 2022. "Reliability of consecutive-(k,l)-out-of-n: F systems with shared components under non-homogeneous Markov dependence," Reliability Engineering and System Safety, Elsevier, vol. 224(C).
    9. Leila Mohammadi, 2019. "The joint reliability signature of order statistics," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(19), pages 4730-4747, October.
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    11. 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.
    12. Gaofeng Da & Lvyu Xia & Taizhong Hu, 2014. "On Computing Signatures of k-out-of-n Systems Consisting of Modules," Methodology and Computing in Applied Probability, Springer, vol. 16(1), pages 223-233, March.
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