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Optimal Grouping of Dependent Components in Parallel-Series and Series-Parallel Systems with Independent Subsystems Equipped with Starting Devices

Author

Listed:
  • Narayanaswamy Balakrishnan

    (Department of Mathematics and Statistics, McMaster University, Hamilton, ON L8S 4L8, Canada)

  • Ghobad Saadat Kia (Barmalzan)

    (Department of Basic Science, Kermanshah University of Technology, Kermanshah 6715685420, Iran)

  • Aliakbar Hosseinzadeh

    (Department of Mathematics, University of Zabol, Zabol 3585698613, Iran)

  • Mostafa Sattari

    (Department of Mathematics, University of Zabol, Zabol 3585698613, Iran)

Abstract

In this paper, we consider parallel-series and series-parallel systems comprising dependent components that are drawn from a heterogeneous population consisting of m different subpopulations, and each subsystem is equipped with a starter device. We also make the assumption that the components within each subpopulation are dependent, while the subsystems themselves are independent. The joint distribution of these subsystems is modeled using an Archimedean copula. Our research considers a general setting in which each subpopulation has a different Archimedean copula for its dependence. By adopting this general setup, we investigate the stochastic, hazard rate, and reversed hazard rate orders between these systems. Furthermore, we provide several numerical examples to demonstrate all the theoretical results established in this study. These results broaden the scope of the known results in the existing literature.

Suggested Citation

  • Narayanaswamy Balakrishnan & Ghobad Saadat Kia (Barmalzan) & Aliakbar Hosseinzadeh & Mostafa Sattari, 2023. "Optimal Grouping of Dependent Components in Parallel-Series and Series-Parallel Systems with Independent Subsystems Equipped with Starting Devices," Mathematics, MDPI, vol. 11(17), pages 1-19, August.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:17:p:3718-:d:1228210
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    References listed on IDEAS

    as
    1. Levitin, Gregory & Amari, Suprasad V., 2009. "Optimal load distribution in series–parallel systems," Reliability Engineering and System Safety, Elsevier, vol. 94(2), pages 254-260.
    2. Sun, Mu-Xia & Li, Yan-Fu & Zio, Enrico, 2019. "On the optimal redundancy allocation for multi-state series–parallel systems under epistemic uncertainty," Reliability Engineering and System Safety, Elsevier, vol. 192(C).
    3. Zhao, Peng & Zhang, Yiying & Li, Long, 2015. "Redundancy allocation at component level versus system level," European Journal of Operational Research, Elsevier, vol. 241(2), pages 402-411.
    4. Zhao, Peng & Chan, Ping Shing & Ng, Hon Keung Tony, 2012. "Optimal allocation of redundancies in series systems," European Journal of Operational Research, Elsevier, vol. 220(3), pages 673-683.
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