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Comparisons of Parallel Systems with Components Having Proportional Reversed Hazard Rates and Starting Devices

Author

Listed:
  • Narayanaswamy Balakrishnan

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

  • Ghobad Barmalzan

    (Department of Statistics, University of Zabol, Zabol 98615-538, Sistan and Baluchestan, Iran)

  • Sajad Kosari

    (Department of Mathematics, University of Zabol, Zabol 98615-538, Sistan and Baluchestan, Iran)

Abstract

In this paper, we consider stochastic comparisons of parallel systems with proportional reversed hazard rate (PRHR) distributed components equipped with starting devices. By considering parallel systems with two components that PRHR and starting devices, we prove the hazard rate and reversed hazard rate orders. These results are then generalized for such parallel systems with n components in terms of usual stochastic order. The establish results are illustrated with some examples.

Suggested Citation

  • Narayanaswamy Balakrishnan & Ghobad Barmalzan & Sajad Kosari, 2021. "Comparisons of Parallel Systems with Components Having Proportional Reversed Hazard Rates and Starting Devices," Mathematics, MDPI, vol. 9(8), pages 1-17, April.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:8:p:856-:d:535913
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    References listed on IDEAS

    as
    1. Chen Li & Xiaohu Li, 2019. "Stochastic comparisons of parallel and series systems of dependent components equipped with starting devices," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(3), pages 694-708, February.
    2. Xiaohu Li & Ming J. Zuo, 2004. "Preservation of stochastic orders for random minima and maxima, with applications," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(3), pages 332-344, April.
    3. Zhang, Yiying & Cai, Xiong & Zhao, Peng, 2019. "Ordering Properties Of Extreme Claim Amounts From Heterogeneous Portfolios," ASTIN Bulletin, Cambridge University Press, vol. 49(2), pages 525-554, May.
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