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On Dependent Multi-State Semi-Coherent Systems Based on Multi-State Joint Signature

Author

Listed:
  • He Yi

    (Beijing University of Chemical Technology)

  • Narayanaswamy Balakrishnan

    (McMaster University)

  • Lirong Cui

    (Qingdao University)

Abstract

In this paper, by considering two multi-state semi-coherent systems sharing some components, we define the multi-state joint signature. Then, some properties of this multi-state joint signature are discussed in detail, and some preservation results are established in terms of stochastic ordering. A south-east shift order for comparing the multi-state joint signature matrices is then discussed. Finally, some numerical examples are presented for illustrating all the theoretical results established here.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metcap:v:24:y:2022:i:3:d:10.1007_s11009-021-09877-3
    DOI: 10.1007/s11009-021-09877-3
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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.
    2. Levitin, G. & Gertsbakh, I. & Shpungin, Y., 2011. "Evaluating the damage associated with intentional network disintegration," Reliability Engineering and System Safety, Elsevier, vol. 96(4), pages 433-439.
    3. Subhash Kochar & Hari Mukerjee & Francisco J. Samaniego, 1999. "The “signature” of a coherent system and its application to comparisons among systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 46(5), pages 507-523, August.
    4. 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.
    5. 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.
    6. Reed, Sean, 2017. "An efficient algorithm for exact computation of system and survival signatures using binary decision diagrams," Reliability Engineering and System Safety, Elsevier, vol. 165(C), pages 257-267.
    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, September.
    8. Mariusz Bieniek & Marco Burkschat & Tomasz Rychlik, 2020. "Comparisons of the Expectations of System and Component Lifetimes in the Failure Dependent Proportional Hazard Model," Methodology and Computing in Applied Probability, Springer, vol. 22(1), pages 173-189, March.
    9. Yandan Yang & Hon Keung Tony Ng & Narayanaswamy Balakrishnan, 2019. "Expectation–maximization algorithm for system-based lifetime data with unknown system structure," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 103(1), pages 69-98, March.
    10. Navarro, Jorge & Rychlik, Tomasz, 2007. "Reliability and expectation bounds for coherent systems with exchangeable components," Journal of Multivariate Analysis, Elsevier, vol. 98(1), pages 102-113, January.
    11. 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.
    12. Arcones M. A. & Kvam P. H. & Samaniego F. J., 2002. "Nonparametric Estimation of a Distribution Subject to a Stochastic Precedence Constraint," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 170-182, March.
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    1. Yi, He & Balakrishnan, Narayanaswamy & Li, Xiang, 2024. "Joint reliability of linear consecutive k-type systems with shared components in a zigzag structure," Reliability Engineering and System Safety, Elsevier, vol. 241(C).

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