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Nonparametric Bayesian reliability analysis of masked data with dependent competing risks

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  • Liu, Bin
  • Shi, Yimin
  • Ng, Hon Keung Tony
  • Shang, Xiangwen

Abstract

The characteristic of dependence widely exists among different failure modes of systems, which brings extra difficulty for the reliability analysis. In this paper, a nonparametric Bayesian analysis method is proposed for dependent masked data under accelerated lifetime test with censoring. Using the copula function, the dependence structure is constructed among the competing failure modes which can be viewed as the components in a series system. By establishing the transformational relationship between the subsurvival functions and the survival functions, the estimators of components’ reliability can be derived from the nonparametric Bayesian estimators of the subsurvival functions when a Dirichlet multivariate process prior is considered. A simulation study is given to illustrate the effectiveness of the proposed methods and the influence of the degree of dependence on the performance of the estimation procedure. It is shown that the dependence between failure modes should not be ignored because ignoring the dependence may lead to serious errors. A numerical example based on a life test of rolling ball bearings is presented as an application of the proposed methodology.

Suggested Citation

  • Liu, Bin & Shi, Yimin & Ng, Hon Keung Tony & Shang, Xiangwen, 2021. "Nonparametric Bayesian reliability analysis of masked data with dependent competing risks," Reliability Engineering and System Safety, Elsevier, vol. 210(C).
    • Handle: RePEc:eee:reensy:v:210:y:2021:i:c:s095183202100065x
    DOI: 10.1016/j.ress.2021.107502
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    References listed on IDEAS

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    1. Genest, Christian & Rémillard, Bruno & Beaudoin, David, 2009. "Goodness-of-fit tests for copulas: A review and a power study," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 199-213, April.
    2. Joe, Harry, 2005. "Asymptotic efficiency of the two-stage estimation method for copula-based models," Journal of Multivariate Analysis, Elsevier, vol. 94(2), pages 401-419, June.
    3. Jing Cai & Yimin Shi & Yongjin Zhang, 2020. "Robust Bayesian analysis for parallel system with masked data under inverse Weibull lifetime distribution," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(6), pages 1422-1434, March.
    4. Kojadinovic, Ivan & Yan, Jun, 2010. "Comparison of three semiparametric methods for estimating dependence parameters in copula models," Insurance: Mathematics and Economics, Elsevier, vol. 47(1), pages 52-63, August.
    5. Cui, Lirong & Wu, Bei, 2019. "Extended Phase-type models for multistate competing risk systems," Reliability Engineering and System Safety, Elsevier, vol. 181(C), pages 1-16.
    6. Julien Worms & Rym Worms, 2018. "Extreme value statistics for censored data with heavy tails under competing risks," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(7), pages 849-889, October.
    7. Salinas-Torres, Victor H. & de Bragança Pereira, Carlos A. & Tiwari, Ram C., 1997. "Convergence of Dirichlet Measures Arising in Context of Bayesian Analysis of Competing Risks Models," Journal of Multivariate Analysis, Elsevier, vol. 62(1), pages 24-35, July.
    8. Cheng-Hung Hu & Robert Plante & Jen Tang, 2012. "Step-stress accelerated life tests: a proportional hazards–based non-parametric model," IISE Transactions, Taylor & Francis Journals, vol. 44(9), pages 754-764.
    9. Gao, Hongda & Cui, Lirong & Qiu, Qingan, 2019. "Reliability modeling for degradation-shock dependence systems with multiple species of shocks," Reliability Engineering and System Safety, Elsevier, vol. 185(C), pages 133-143.
    10. Gong, Changqing & Frangopol, Dan M., 2020. "Time-variant hull girder reliability considering spatial dependence of corrosion growth, geometric and material properties," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
    11. Lin, Kunsong & Chen, Yunxia & Xu, Dan, 2017. "Reliability assessment model considering heterogeneous population in a multiple stresses accelerated test," Reliability Engineering and System Safety, Elsevier, vol. 165(C), pages 134-143.
    12. Ancha Xu & Shirong Zhou, 2017. "Bayesian analysis of series system with dependent causes of failure," Statistical Theory and Related Fields, Taylor & Francis Journals, vol. 1(1), pages 128-140, January.
    13. Huard, David & Evin, Guillaume & Favre, Anne-Catherine, 2006. "Bayesian copula selection," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 809-822, November.
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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. 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).

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