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On information-based residual lifetime in survival models with delayed failures

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  • Cha, Ji Hwan
  • Finkelstein, Maxim

Abstract

At many practical instances, the initiating point events (e.g., shocks) affect an object not immediately, but after some random delay. These models were studied in the literature only for the case when an initial shock process is Poisson. In our paper, we generalize these results to a meaningful case of the generalized Polya process (GPP) of initial shocks that was recently introduced in the literature. Distinct from the Poisson process, the GPP possesses the property of dependent increments, which makes it much more attractive in applications. We derive the distribution of the time to failure for a system subject to the GPP with delays. Our main focus, however, is on analysis of the corresponding residual lifetime distribution that depends now on the full history (information) of the initiating shock process.

Suggested Citation

  • Cha, Ji Hwan & Finkelstein, Maxim, 2018. "On information-based residual lifetime in survival models with delayed failures," Statistics & Probability Letters, Elsevier, vol. 137(C), pages 209-216.
    • Handle: RePEc:eee:stapro:v:137:y:2018:i:c:p:209-216
    DOI: 10.1016/j.spl.2018.01.028
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    References listed on IDEAS

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    Cited by:

    1. Bautista, Lucía & Castro, Inma T. & Landesa, Luis, 2022. "Condition-based maintenance for a system subject to multiple degradation processes with stochastic arrival intensity," European Journal of Operational Research, Elsevier, vol. 302(2), pages 560-574.
    2. Antonio Di Crescenzo & Franco Pellerey, 2019. "Some Results and Applications of Geometric Counting Processes," Methodology and Computing in Applied Probability, Springer, vol. 21(1), pages 203-233, March.
    3. Junyuan Wang & Jimin Ye, 2022. "A new repair model and its optimization for cold standby system," Operational Research, Springer, vol. 22(1), pages 105-122, March.

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