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Extending minimal repair models for repairable systems: A comparison of dynamic and heterogeneous extensions of a nonhomogeneous Poisson process

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  • Asfaw, Zeytu Gashaw
  • Lindqvist, Bo Henry

Abstract

For many applications of repairable systems, the minimal repair assumption, which leads to nonhomogeneous Poisson processes (NHPP), is not adequate. We review and study two extensions of the NHPP, the dynamic NHPP and the heterogeneous NHPP. Both extensions are motivated by specific aspects of potential applications. It has long been known, however, that the two paradigms are essentially indistinguishable in an analysis of failure data. We investigate the connection between the two approaches for extending NHPP models, both theoretically and numerically in a data example and a simulation study.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:reensy:v:140:y:2015:i:c:p:53-58
    DOI: 10.1016/j.ress.2015.03.025
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    References listed on IDEAS

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    1. 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.
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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. Zhou, Xiaojun & Wu, Changjie & Li, Yanting & Xi, Lifeng, 2016. "A preventive maintenance model for leased equipment subject to internal degradation and external shock damage," Reliability Engineering and System Safety, Elsevier, vol. 154(C), pages 1-7.
    3. Wu, Shaomin & Scarf, Philip, 2017. "Two new stochastic models of the failure process of a series system," European Journal of Operational Research, Elsevier, vol. 257(3), pages 763-772.
    4. Chien, Yu-Hung, 2019. "The optimal preventive-maintenance policy for a NHPBP repairable system under free-repair warranty," Reliability Engineering and System Safety, Elsevier, vol. 188(C), pages 444-453.
    5. 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.
    6. Francisco Germán Badía & Sophie Mercier & Carmen Sangüesa, 2019. "Extensions of the Generalized Pólya Process," Methodology and Computing in Applied Probability, Springer, vol. 21(4), pages 1057-1085, December.
    7. Cha, Ji Hwan & Finkelstein, Maxim, 2016. "New shock models based on the generalized Polya process," European Journal of Operational Research, Elsevier, vol. 251(1), pages 135-141.

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