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On hazard rate processes

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  • Y. Kebir

Abstract

Hazard rate processes are discussed in the context of doubly stochastic Poisson processes. We derive an explicit expression for the reliability function corresponding to an increasing hazard rate processes with independent increments. Also, bounds are obtained for the reliability function of a system with a general hazard rate process.

Suggested Citation

  • Y. Kebir, 1991. "On hazard rate processes," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(6), pages 865-876, December.
    • Handle: RePEc:wly:navres:v:38:y:1991:i:6:p:865-876
    DOI: 10.1002/nav.3800380606
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    References listed on IDEAS

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    1. Mark Brown & Sheldon M. Ross, 1982. "The observed hazard and multicomponent systems," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 29(4), pages 679-683, December.
    2. Elja Arjas, 1981. "The Failure and Hazard Processes in Multivariate Reliability Systems," Mathematics of Operations Research, INFORMS, vol. 6(4), pages 551-562, November.
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    Cited by:

    1. Cha, Ji Hwan & Finkelstein, Maxim, 2016. "Justifying the Gompertz curve of mortality via the generalized Polya process of shocks," Theoretical Population Biology, Elsevier, vol. 109(C), pages 54-62.
    2. Botosaru, Irene, 2011. "A Duration Model with Dynamic Unobserved Heterogeneity," TSE Working Papers 11-262, Toulouse School of Economics (TSE), revised Nov 2013.
    3. Hazra, Nil Kamal & Finkelstein, Maxim & Cha, Ji Hwan, 2022. "On a hazard (failure) rate process with delays after shocks," Statistics & Probability Letters, Elsevier, vol. 181(C).
    4. Finkelstein, M. S., 2003. "A model for spatial survival," Statistics & Probability Letters, Elsevier, vol. 62(4), pages 371-378, May.
    5. Peng, Shizhe & Jiang, Wei & Huang, Wenpo & Luo, Qinglin, 2024. "The impact of gamma usage processes on preventive maintenance policies under two-dimensional warranty," Reliability Engineering and System Safety, Elsevier, vol. 242(C).
    6. Botosaru, Irene, 2020. "Nonparametric analysis of a duration model with stochastic unobserved heterogeneity," Journal of Econometrics, Elsevier, vol. 217(1), pages 112-139.
    7. Ji Hwan Cha & Maxim Finkelstein, 2018. "On a New Shot Noise Process and the Induced Survival Model," Methodology and Computing in Applied Probability, Springer, vol. 20(3), pages 897-917, September.
    8. Sophie Mercier & Carmen Sangüesa, 2023. "A general multivariate lifetime model with a multivariate additive process as conditional hazard rate increment process," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(1), pages 91-129, January.
    9. Antonio Di Crescenzo & Franco Pellerey, 1998. "On lifetimes in random environments," Naval Research Logistics (NRL), John Wiley & Sons, vol. 45(4), pages 365-375, June.
    10. Ji Hwan Cha & Jie Mi, 2011. "On a Stochastic Survival Model for a System Under Randomly Variable Environment," Methodology and Computing in Applied Probability, Springer, vol. 13(3), pages 549-561, September.
    11. Cha, Ji Hwan & Finkelstein, Maxim, 2013. "The failure rate dynamics in heterogeneous populations," Reliability Engineering and System Safety, Elsevier, vol. 112(C), pages 120-128.

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