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A generalized Freund bivariate model for a two-component load sharing system

Author

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  • Franco, Manuel
  • Vivo, Juana-Maria
  • Kundu, Debasis

Abstract

Motivated by reliability systems whose components fail one by one and share a common load, this work provides a generalized Freund bivariate class of distributions for modeling the two component lifetimes of a parallel redundant system. When a component fails, such load-sharing systems can be repaired meanwhile the surviving one endures the total load, modifying its two-dimensional lifetime model, which is of interest in maintenance and stress-strength reliability modeling. The proposed model is based on the overload of the surviving component after the first failure, causing both the proportional failure rate parameters and the baseline distribution of the component to change. A genetic algorithm is employed to find the maximum likelihood estimation, and a simulation study illustrates its implementation and efficiency. Applications in three real engineering data sets are carried out, revealing the usefulness of the proposed class for modeling the load-sharing effect.

Suggested Citation

  • Franco, Manuel & Vivo, Juana-Maria & Kundu, Debasis, 2020. "A generalized Freund bivariate model for a two-component load sharing system," Reliability Engineering and System Safety, Elsevier, vol. 203(C).
    • Handle: RePEc:eee:reensy:v:203:y:2020:i:c:s0951832020305974
    DOI: 10.1016/j.ress.2020.107096
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    References listed on IDEAS

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    16. Zhang, Jianchun & Zhao, Yu & Ma, Xiaobing, 2019. "A new reliability analysis method for load-sharing k-out-of-n: F system based on load-strength model," Reliability Engineering and System Safety, Elsevier, vol. 182(C), pages 152-165.
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    1. Manuel Franco & Juana-María Vivo & Debasis Kundu, 2020. "A Generator of Bivariate Distributions: Properties, Estimation, and Applications," Mathematics, MDPI, vol. 8(10), pages 1-30, October.
    2. Abba, Badamasi & Wang, Hong & Bakouch, Hassan S., 2022. "A reliability and survival model for one and two failure modes system with applications to complete and censored datasets," Reliability Engineering and System Safety, Elsevier, vol. 223(C).
    3. Zhao, Sangqi & Wei, Yian & Li, Yang & Cheng, Yao, 2026. "A multi-agent reinforcement learning (MARL) framework for designing an optimal state-specific hybrid maintenance policy for a series k-out-of-n load-sharing system," Reliability Engineering and System Safety, Elsevier, vol. 265(PA).
    4. Brown, Bodunrin & Liu, Bin & McIntyre, Stuart & Revie, Matthew, 2022. "Reliability analysis of load-sharing systems with spatial dependence and proximity effects," Reliability Engineering and System Safety, Elsevier, vol. 221(C).
    5. Wang, Han & Liao, Haitao & Ma, Xiaobing, 2022. "Stochastic Multi-phase Modeling and Health Assessment for Systems Based on Degradation Branching Processes," Reliability Engineering and System Safety, Elsevier, vol. 222(C).
    6. Zhang, Nan & Yi, Xiangjian & Ma, Yiqi & Cai, Kaiquan, 2026. "Reliability assessment and maintenance optimization of a load-sharing system considering dependent failure rates and component heterogeneity," Reliability Engineering and System Safety, Elsevier, vol. 269(C).

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