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Power–law nonhomogeneous Poisson process with a mixture of latent common shape parameters

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  • Chehade, Abdallah
  • Shi, Zunya
  • Krivtsov, Vasiliy

Abstract

Rapid developments in information technologies enabled recording big data environments in near real-time. Such big data environments provide an unprecedented opportunity for efficient event detection and therefore effective reliability models, but they also pose interesting challenges. One challenge is modeling the number of recurrent events for heterogeneous subpopulations with limited records. To address this challenge, a power–law nonhomogeneous Poisson process with machine learning capabilities is proposed. The scale parameter of the Poisson process is learned for each individual subpopulation. However, the shape parameter is learned for latent groups that each consists of multiple (internally homogenous) subpopulations. The proposed Poisson process collaboratively models multiple heterogeneous subpopulations; therefore, it allows transferring knowledge between subpopulations and diminishes the chances of overfitting. Simulation and real-life case studies showed the high modeling accuracy of the proposed approach.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:reensy:v:203:y:2020:i:c:s0951832020305986
    DOI: 10.1016/j.ress.2020.107097
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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.
    2. Maxim Finkelstein, 2008. "Failure Rate Modelling for Reliability and Risk," Springer Series in Reliability Engineering, Springer, number 978-1-84800-986-8, June.
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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. Chehade, Abdallah & Hassanieh, Wael & Krivtsov, Vasiliy, 2024. "SeqOAE: Deep sequence-to-sequence orthogonal auto-encoder for time-series forecasting under variable population sizes," Reliability Engineering and System Safety, Elsevier, vol. 247(C).

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