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Unobserved heterogeneity in the power law nonhomogeneous Poisson process

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  • Asfaw, Zeytu Gashaw
  • Lindqvist, Bo Henry

Abstract

A study of possible consequences of heterogeneity in the failure intensity of repairable systems is presented. The basic model studied is the nonhomogeneous Poisson process with power law intensity function. When several similar systems are under observation, the assumption that the corresponding processes are independent and identically distributed is often questionable. In practice there may be an unobserved heterogeneity among the systems. The heterogeneity is modeled by introduction of unobserved gamma distributed frailties. The relevant likelihood function is derived, and maximum likelihood estimation is illustrated. In a simulation study we then compare results when using a power law model without taking into account heterogeneity, with the corresponding results obtained when the heterogeneity is accounted for. A motivating data example is also given.

Suggested Citation

  • Asfaw, Zeytu Gashaw & Lindqvist, Bo Henry, 2015. "Unobserved heterogeneity in the power law nonhomogeneous Poisson process," Reliability Engineering and System Safety, Elsevier, vol. 134(C), pages 59-65.
    • Handle: RePEc:eee:reensy:v:134:y:2015:i:c:p:59-65
    DOI: 10.1016/j.ress.2014.10.005
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    References listed on IDEAS

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    1. Cha, Ji Hwan & Finkelstein, Maxim, 2014. "Some notes on unobserved parameters (frailties) in reliability modeling," Reliability Engineering and System Safety, Elsevier, vol. 123(C), pages 99-103.
    2. James Vaupel & Kenneth Manton & Eric Stallard, 1979. "The impact of heterogeneity in individual frailty on the dynamics of mortality," Demography, Springer;Population Association of America (PAA), vol. 16(3), pages 439-454, August.
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    Cited by:

    1. Zhao, Heng & Liu, Zixian & Li, Mei & Liang, Lijun, 2022. "Optimal monitoring policies for chronic diseases under healthcare warranty," Socio-Economic Planning Sciences, Elsevier, vol. 84(C).
    2. Almeida, Marco Pollo & Paixão, Rafael S. & Ramos, Pedro L. & Tomazella, Vera & Louzada, Francisco & Ehlers, Ricardo S., 2020. "Bayesian non-parametric frailty model for dependent competing risks in a repairable systems framework," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    3. Asfaw, Zeytu Gashaw & Lindqvist, Bo Henry, 2015. "Extending minimal repair models for repairable systems: A comparison of dynamic and heterogeneous extensions of a nonhomogeneous Poisson process," Reliability Engineering and System Safety, Elsevier, vol. 140(C), pages 53-58.
    4. Bodunrin Brown & Bin Liu & Stuart McIntyre & Matthew Revie, 2023. "Reliability evaluation of repairable systems considering component heterogeneity using frailty model," Journal of Risk and Reliability, , vol. 237(4), pages 654-670, August.
    5. Zhou, Yu & Kou, Gang & Xiao, Hui & Peng, Yi & Alsaadi, Fawaz E., 2020. "Sequential imperfect preventive maintenance model with failure intensity reduction with an application to urban buses," Reliability Engineering and System Safety, Elsevier, vol. 198(C).
    6. Chehade, Abdallah & Shi, Zunya & Krivtsov, Vasiliy, 2020. "Power–law nonhomogeneous Poisson process with a mixture of latent common shape parameters," Reliability Engineering and System Safety, Elsevier, vol. 203(C).
    7. Liu, Xingheng & Vatn, Jørn & Dijoux, Yann & Toftaker, Håkon, 2020. "Unobserved heterogeneity in stable imperfect repair models," Reliability Engineering and System Safety, Elsevier, vol. 203(C).
    8. Rezgar Zaki & Abbas Barabadi & Javad Barabady & Ali Nouri Qarahasanlou, 2022. "Observed and unobserved heterogeneity in failure data analysis," Journal of Risk and Reliability, , vol. 236(1), pages 194-207, February.
    9. Rezgar Zaki & Abbas Barabadi & Ali Nouri Qarahasanlou & A. H. S. Garmabaki, 2019. "A mixture frailty model for maintainability analysis of mechanical components: a case study," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 10(6), pages 1646-1653, December.
    10. Slimacek, Vaclav & Lindqvist, Bo Henry, 2016. "Nonhomogeneous Poisson process with nonparametric frailty," Reliability Engineering and System Safety, Elsevier, vol. 149(C), pages 14-23.

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