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Simulations and predictions of future values in the time-homogeneous load-sharing model

Author

Listed:
  • Francesco Buono

    (Università di Napoli Federico II)

  • Jorge Navarro

    (Universidad de Murcia)

Abstract

In this paper, some properties of the order dependent time-homogeneous load-sharing model are obtained, including an algorithmic procedure to simulate samples from this model. Then, the problem of how to get predictions of the future failure times is analysed in a sample from censored data (early failures). Punctual predictions based on the median, the mean and the convolutions of exponential distributions are proposed and prediction bands are obtained. Some illustrative examples show how to apply the theoretical results. An application in the study of lifetimes of coherent systems is proposed as well.

Suggested Citation

  • Francesco Buono & Jorge Navarro, 2024. "Simulations and predictions of future values in the time-homogeneous load-sharing model," Statistical Papers, Springer, vol. 65(2), pages 661-685, April.
    • Handle: RePEc:spr:stpapr:v:65:y:2024:i:2:d:10.1007_s00362-023-01404-5
    DOI: 10.1007/s00362-023-01404-5
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    References listed on IDEAS

    as
    1. Zvi Schechner, 1984. "A load‐sharing model: The linear breakdown rule," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 31(1), pages 137-144, March.
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    3. Moshe Shaked & J. George Shanthikumar, 2015. "Multivariate conditional hazard rate functions – an overview," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 31(3), pages 285-296, May.
    4. Norros, Ilkka, 1985. "Systems weakend by failures," Stochastic Processes and their Applications, Elsevier, vol. 20(2), pages 181-196, September.
    5. Zhengcheng Zhang & Yonghong Yang & Xiujie Ji, 2020. "On stochastic behaviors of load-sharing parallel systems," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(22), pages 5392-5405, November.
    6. Sheldon M. Ross, 1984. "A model in which component failure rates depend on the working set," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 31(2), pages 297-300, June.
    7. Edmond Levy, 2022. "On the density for sums of independent exponential, Erlang and gamma variates," Statistical Papers, Springer, vol. 63(3), pages 693-721, June.
    8. Won Young Yun & Ji Hwan Cha, 2010. "A stochastic model for a general load‐sharing system under overload condition," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 26(5), pages 624-638, September.
    Full references (including those not matched with items on IDEAS)

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