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On the q-Weibull distribution for reliability applications: An adaptive hybrid artificial bee colony algorithm for parameter estimation

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  • Xu, Meng
  • Droguett, Enrique López
  • Lins, Isis Didier
  • das Chagas Moura, Márcio

Abstract

The q-Weibull model is based on the Tsallis non-extensive entropy [22] and is able to model various behaviors of the hazard rate function, including bathtub curves, by using a single set of parameters. Despite its flexibility, the q-Weibull has not been widely used in reliability applications partly because of the complicated parameters estimation. In this work, the parameters of the q-Weibull are estimated by the maximum likelihood (ML) method. Due to the intricate system of nonlinear equations, derivative-based optimization methods may fail to converge. Thus, the heuristic optimization method of artificial bee colony (ABC) is used instead. To deal with the slow convergence of ABC, it is proposed an adaptive hybrid ABC (AHABC) algorithm that dynamically combines Nelder-Mead simplex search method with ABC for the ML estimation of the q-Weibull parameters. Interval estimates for the q-Weibull parameters, including confidence intervals based on the ML asymptotic theory and on bootstrap methods, are also developed. The AHABC is validated via numerical experiments involving the q-Weibull ML for reliability applications and results show that it produces faster and more accurate convergence when compared to ABC and similar approaches. The estimation procedure is applied to real reliability failure data characterized by a bathtub-shaped hazard rate.

Suggested Citation

  • Xu, Meng & Droguett, Enrique López & Lins, Isis Didier & das Chagas Moura, Márcio, 2017. "On the q-Weibull distribution for reliability applications: An adaptive hybrid artificial bee colony algorithm for parameter estimation," Reliability Engineering and System Safety, Elsevier, vol. 158(C), pages 93-105.
    • Handle: RePEc:eee:reensy:v:158:y:2017:i:c:p:93-105
    DOI: 10.1016/j.ress.2016.10.012
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    References listed on IDEAS

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    Cited by:

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    3. Zhang, Fode & Ng, Hon Keung Tony & Shi, Yimin, 2018. "On alternative q-Weibull and q-extreme value distributions: Properties and applications," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 1171-1190.
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    5. Xiang Jia & Saralees Nadarajah & Bo Guo, 2020. "Inference on q-Weibull parameters," Statistical Papers, Springer, vol. 61(2), pages 575-593, April.
    6. Baker, Rose, 2019. "New survival distributions that quantify the gain from eliminating flawed components," Reliability Engineering and System Safety, Elsevier, vol. 185(C), pages 493-501.
    7. Ahmad, Abd EL-Baset A. & Ghazal, M.G.M., 2020. "Exponentiated additive Weibull distribution," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
    8. Zhu, Tiefeng, 2020. "Reliability estimation for two-parameter Weibull distribution under block censoring," Reliability Engineering and System Safety, Elsevier, vol. 203(C).
    9. Reyes-Santias, Francisco & Reboredo, Juan C. & de Assis, Edilson Machado & Rivera-Castro, Miguel A., 2021. "Does length of hospital stay reflect power-law behavior? A q-Weibull density approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 568(C).

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