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Bayesian non-parametric frailty model for dependent competing risks in a repairable systems framework

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  • Almeida, Marco Pollo
  • Paixão, Rafael S.
  • Ramos, Pedro L.
  • Tomazella, Vera
  • Louzada, Francisco
  • Ehlers, Ricardo S.

Abstract

The aim of this article is to analyze multiple repairable systems data under the presence of dependent competing risks. It is known that the dependence effect in this scenario influences the estimates of the model parameters. Hence, under the assumption that the cause-specific intensities follow a power law process (PLP), we propose a frailty-induced dependence approach to incorporate the dependence among the cause-specific recurrent processes. Moreover, the misspecification of the frailty distribution may lead to errors when estimating the parameters of interest. Because of this, we considered a nonparametric approach to model the frailty density using a Dirichlet process mixture prior, which offers more flexibility to provide consistent estimates for the PLP model, as well as insights about heterogeneity among the systems. We proposed an orthogonal parametrization for the PLP model parameters that allowed us to specify a joint prior distribution for the parameters that returned closed-form estimators for the posterior mean. Additionally, a hybrid MCMC sampler algorithm composed by Hamiltonian Monte Carlo and Gibbs sampling was built for computing the posterior estimates with respect to the frailty distribution. A simulation study was conducted to evaluate the efficiency of our estimates. This method was used to analyze a real dataset. Algorithms, code, and data are provided in supplementary material available online.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:reensy:v:204:y:2020:i:c:s0951832020306463
    DOI: 10.1016/j.ress.2020.107145
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    References listed on IDEAS

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    1. Peng, Weiwen & Shen, Lijuan & Shen, Yan & Sun, Qiuzhuang, 2018. "Reliability analysis of repairable systems with recurrent misuse-induced failures and normal-operation failures," Reliability Engineering and System Safety, Elsevier, vol. 171(C), pages 87-98.
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    3. 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.
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    6. Slimacek, Vaclav & Lindqvist, Bo Henry, 2017. "Nonhomogeneous Poisson process with nonparametric frailty and covariates," Reliability Engineering and System Safety, Elsevier, vol. 167(C), pages 75-83.
    7. Nafisah, Ibrahim & Shrahili, Mansour & Alotaibi, Naif & Scarf, Phil, 2019. "Virtual series-system models of imperfect repair," Reliability Engineering and System Safety, Elsevier, vol. 188(C), pages 604-613.
    8. Anupap Somboonsavatdee & Ananda Sen, 2015. "Parametric inference for multiple repairable systems under dependent competing risks," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 31(5), pages 706-720, September.
    9. Nailong Zhang & Qingyu Yang, 2015. "Optimal maintenance planning for repairable multi-component systems subject to dependent competing risks," IISE Transactions, Taylor & Francis Journals, vol. 47(5), pages 521-532, May.
    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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    Cited by:

    1. Zhou, Hang & Lopes Genez, Thiago Augusto & Brintrup, Alexandra & Parlikad, Ajith Kumar, 2022. "A hybrid-learning decomposition algorithm for competing risk identification within fleets of complex engineering systems," Reliability Engineering and System Safety, Elsevier, vol. 217(C).
    2. Zheng, Xiao-Wei & Li, Hong-Nan & Gardoni, Paolo, 2023. "Hybrid Bayesian-Copula-based risk assessment for tall buildings subject to wind loads considering various uncertainties," Reliability Engineering and System Safety, Elsevier, vol. 233(C).
    3. Alex Mota & Eder A. Milani & Vinicius F. Calsavara & Vera L. D. Tomazella & Jeremias Leão & Pedro L. Ramos & Paulo H. Ferreira & Francisco Louzada, 2021. "Weighted Lindley frailty model: estimation and application to lung cancer data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 27(4), pages 561-587, October.
    4. Brito, Éder S. & Tomazella, Vera L.D. & Ferreira, Paulo H., 2022. "Statistical modeling and reliability analysis of multiple repairable systems with dependent failure times under perfect repair," Reliability Engineering and System Safety, Elsevier, vol. 222(C).
    5. Zhang, Chunfang & Wang, Liang & Bai, Xuchao & Huang, Jianan, 2022. "Bayesian reliability analysis for copula based step-stress partially accelerated dependent competing risks model," Reliability Engineering and System Safety, Elsevier, vol. 227(C).
    6. Zhu, Xiaojun & Balakrishnan, N., 2022. "One-shot device test data analysis using non-parametric and semi-parametric inferential methods and applications," Reliability Engineering and System Safety, Elsevier, vol. 221(C).

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