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Practical extensions to NHPP application in repairable system reliability analysis

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  • Krivtsov, Vasiliy V.

Abstract

An overwhelming majority of publications on Nonhomogeneous Poisson Process (NHPP) considers just two monotonic forms of the NHPP's rate of occurrence of failures (ROCOF): the log-linear model the power law model. In this paper, we propose to capitalize on the fact that NHPP's ROCOF formally coincides with the hazard function of the underlying lifetime distribution. Therefore, the variety of parametric forms for the hazard functions of traditional lifetime distributions (lognormal, Gumbel, etc.) could be used as the models for the ROCOF of respective NHPPs. Moreover, the hazard function of a mixture of underlying distributions could be used to model the non-monotonic ROCOF. Parameter estimation of such ROCOF models reduces to the estimation of the cumulative hazard function of the underlying lifetime distribution. We use real-world automotive data to illustrate the point.

Suggested Citation

  • Krivtsov, Vasiliy V., 2007. "Practical extensions to NHPP application in repairable system reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 92(5), pages 560-562.
    • Handle: RePEc:eee:reensy:v:92:y:2007:i:5:p:560-562
    DOI: 10.1016/j.ress.2006.05.002
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    Cited by:

    1. Chehade, Abdallah & Savargaonkar, Mayuresh & Krivtsov, Vasiliy, 2022. "Conditional Gaussian mixture model for warranty claims forecasting," Reliability Engineering and System Safety, Elsevier, vol. 218(PB).
    2. Prataviera, Fábio & Ortega, Edwin M.M. & Cordeiro, Gauss M. & Pescim, Rodrigo R. & Verssani, Bruna A.W., 2018. "A new generalized odd log-logistic flexible Weibull regression model with applications in repairable systems," Reliability Engineering and System Safety, Elsevier, vol. 176(C), pages 13-26.
    3. de Oliveira, Cícero Carlos Felix & Firmino, Paulo Renato Alves & Cristino, Cláudio Tadeu, 2019. "A tool for evaluating repairable systems based on Generalized Renewal Processes," Reliability Engineering and System Safety, Elsevier, vol. 183(C), pages 281-297.
    4. Krivtsov, V. & Yevkin, O., 2013. "Estimation of G-renewal process parameters as an ill-posed inverse problem," Reliability Engineering and System Safety, Elsevier, vol. 115(C), pages 10-18.

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