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Replacement model with random replacement time

Author

Listed:
  • Kanchan Jain

    (Panjab University)

  • Sudheesh K. Kattumannil

    (Indian Statistical Institute)

  • Anjana Rajagopal

    (Indian Statistical Institute)

Abstract

In this paper, we study a replacement model under which replacements take place not at fixed time but at random time T or upon failure. We study the properties of mean time to failure of the proposed model. Life times of two replacement models with different random replacement times have been compared using few stochastic orderings. A non-parametric test based on U-Statistics has been proposed for testing constancy of mean time to failure against NBUE alternative. The finite sample performance of the proposed test is evaluated through Monte Carlo simulation study. Finally, the proposed test procedure is illustrated using lifetime data of air conditioning equipment.

Suggested Citation

  • Kanchan Jain & Sudheesh K. Kattumannil & Anjana Rajagopal, 2023. "Replacement model with random replacement time," Statistical Papers, Springer, vol. 64(1), pages 1-15, February.
    • Handle: RePEc:spr:stpapr:v:64:y:2023:i:1:d:10.1007_s00362-022-01306-y
    DOI: 10.1007/s00362-022-01306-y
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    References listed on IDEAS

    as
    1. Toshio Nakagawa, 2014. "Random Maintenance Policies," Springer Series in Reliability Engineering, Springer, edition 127, number 978-1-4471-6575-0, June.
    2. Sudheesh K. Kattumannil & Deemat C. Mathew, 2015. "A Gini-based exact test for exponentiality against NBUE alternatives with censored observations," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 27(4), pages 503-515, December.
    3. Norbert Henze & Simos G. Meintanis, 2005. "Recent and classical tests for exponentiality: a partial review with comparisons," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 61(1), pages 29-45, February.
    4. Zhao, Xufeng & Al-Khalifa, Khalifa N. & Magid Hamouda, Abdel & Nakagawa, Toshio, 2017. "Age replacement models: A summary with new perspectives and methods," Reliability Engineering and System Safety, Elsevier, vol. 161(C), pages 95-105.
    5. Zhao, Xufeng & Nakagawa, Toshio, 2012. "Optimization problems of replacement first or last in reliability theory," European Journal of Operational Research, Elsevier, vol. 223(1), pages 141-149.
    6. Sudheesh K. Kattumannil & P. Anisha, 2019. "A simple non-parametric test for decreasing mean time to failure," Statistical Papers, Springer, vol. 60(1), pages 73-87, February.
    Full references (including those not matched with items on IDEAS)

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