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Gumbel mixture modelling for multiple failure data

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  • Nagode, Marko
  • Oman, Simon
  • Klemenc, Jernej
  • Panić, Branislav

Abstract

The Gumbel mixture model is a popular tool for modelling extreme events with mixed formation mechanisms. The lack of a shape parameter in the Gumbel distribution makes it somewhat less practical for mixture modelling compared to the Weibull distribution, which is widely used in structural reliability and safety applications. Since the Gumbel distribution has two forms (i.e., left- and right-skewed), we describe it as a three-parameter distribution. The additional parameter ξ∈{−1,1} is used to control the skewness of the Gumbel distribution. The maximum likelihood parameter estimation procedure for the proposed Gumbel mixture model is derived. Based on the simulation study, we confirmed that 1) the estimation procedure can successfully estimate the parameters of the mixture model, and 2) the proposed three-parameter Gumbel distribution has advantages over the state of the art in mixture modelling using different parametric families. An illustrative real-world example is also considered. Climbing rope failure was observed as a function of two random variables, and two competing failure modes were found. The experiment and subsequent mixture modelling provided further insight into the degradation of climbing ropes. Finally, the proposal is implemented in the freely available R package rebmix.

Suggested Citation

  • Nagode, Marko & Oman, Simon & Klemenc, Jernej & Panić, Branislav, 2023. "Gumbel mixture modelling for multiple failure data," Reliability Engineering and System Safety, Elsevier, vol. 230(C).
    • Handle: RePEc:eee:reensy:v:230:y:2023:i:c:s0951832022005610
    DOI: 10.1016/j.ress.2022.108946
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    References listed on IDEAS

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    1. Almalki, Saad J. & Nadarajah, Saralees, 2014. "Modifications of the Weibull distribution: A review," Reliability Engineering and System Safety, Elsevier, vol. 124(C), pages 32-55.
    2. Xu, Zhaoyi & Saleh, Joseph Homer, 2021. "Machine learning for reliability engineering and safety applications: Review of current status and future opportunities," Reliability Engineering and System Safety, Elsevier, vol. 211(C).
    3. Puppo, L. & Pedroni, N. & Maio, F. Di & Bersano, A. & Bertani, C. & Zio, E., 2021. "A Framework based on Finite Mixture Models and Adaptive Kriging for Characterizing Non-Smooth and Multimodal Failure Regions in a Nuclear Passive Safety System," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    4. Chehade, Abdallah & Savargaonkar, Mayuresh & Krivtsov, Vasiliy, 2022. "Conditional Gaussian mixture model for warranty claims forecasting," Reliability Engineering and System Safety, Elsevier, vol. 218(PB).
    5. Asadi, Zohreh Soltani & Melchers, Robert E., 2017. "Extreme value statistics for pitting corrosion of old underground cast iron pipes," Reliability Engineering and System Safety, Elsevier, vol. 162(C), pages 64-71.
    6. Branislav Panić & Jernej Klemenc & Marko Nagode, 2020. "Optimizing the Estimation of a Histogram-Bin Width—Application to the Multivariate Mixture-Model Estimation," Mathematics, MDPI, vol. 8(7), pages 1-30, July.
    7. Ducros, Florence & Pamphile, Patrick, 2018. "Bayesian estimation of Weibull mixture in heavily censored data setting," Reliability Engineering and System Safety, Elsevier, vol. 180(C), pages 453-462.
    8. Franko, Mitja & Nagode, Marko, 2015. "Probability density function of the equivalent stress amplitude using statistical transformation," Reliability Engineering and System Safety, Elsevier, vol. 134(C), pages 118-125.
    9. Yu, Weichao & Huang, Weihe & Wen, Kai & Zhang, Jie & Liu, Hongfei & Wang, Kun & Gong, Jing & Qu, Chunxu, 2021. "Subset simulation-based reliability analysis of the corroding natural gas pipeline," Reliability Engineering and System Safety, Elsevier, vol. 213(C).
    10. Branislav Panić & Jernej Klemenc & Marko Nagode, 2020. "Improved Initialization of the EM Algorithm for Mixture Model Parameter Estimation," Mathematics, MDPI, vol. 8(3), pages 1-29, March.
    11. Gómez, Yolanda M. & Bolfarine, Heleno & Gómez, Héctor W., 2019. "Gumbel distribution with heavy tails and applications to environmental data," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 157(C), pages 115-129.
    12. Lu, Zhenzhou & Xinyao Li,, 2018. "Failure-mode importance measures in structural system with multiple failure modes and its estimation using copulaAuthor-Name: He, Liangli," Reliability Engineering and System Safety, Elsevier, vol. 174(C), pages 53-59.
    13. Ye, Zhenggeng & Yang, Hui & Cai, Zhiqiang & Si, Shubin & Zhou, Fuli, 2021. "Performance evaluation of serial-parallel manufacturing systems based on the impact of heterogeneous feedstocks on machine degradation," Reliability Engineering and System Safety, Elsevier, vol. 207(C).
    14. Adumene, Sidum & Khan, Faisal & Adedigba, Sunday & Zendehboudi, Sohrab, 2021. "Offshore system safety and reliability considering microbial influenced multiple failure modes and their interdependencies," Reliability Engineering and System Safety, Elsevier, vol. 215(C).
    15. Kang, Dongbum & Ko, Kyungnam & Huh, Jongchul, 2015. "Determination of extreme wind values using the Gumbel distribution," Energy, Elsevier, vol. 86(C), pages 51-58.
    16. Dai, Baorui & Xia, Ye & Li, Qi, 2022. "An extreme value prediction method based on clustering algorithm," Reliability Engineering and System Safety, Elsevier, vol. 222(C).
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