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

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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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    1. Levitin, Gregory & Xing, Liudong & Dai, Yuanshun, 2018. "Optimal work distribution and backup frequency for two non-identical work sharing elements," Reliability Engineering and System Safety, Elsevier, vol. 170(C), pages 127-136.
    2. Berrade, M.D. & Scarf, P.A. & Cavalcante, C.A.V., 2018. "Conditional inspection and maintenance of a system with two interacting components," European Journal of Operational Research, Elsevier, vol. 268(2), pages 533-544.
    3. Jing, Zhao & Chen, Jianqiao & Li, Xu, 2019. "RBF-GA: An adaptive radial basis function metamodeling with genetic algorithm for structural reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 189(C), pages 42-57.
    4. G. Asha & A. Vincent Raja & Nalini Ravishanker, 2018. "Reliability modelling incorporating load share and frailty," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 34(2), pages 206-223, March.
    5. Moshe Shaked, 1984. "Extensions of the Freund Distribution with Applications in Reliability Theory," Operations Research, INFORMS, vol. 32(4), pages 917-925, August.
    6. Paul H. Kvam & Edsel A. Pena, 2005. "Estimating Load-Sharing Properties in a Dynamic Reliability System," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 262-272, March.
    7. Scrucca, Luca, 2013. "GA: A Package for Genetic Algorithms in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 53(i04).
    8. Zhang, Nan & Fouladirad, Mitra & Barros, Anne, 2017. "Maintenance analysis of a two-component load-sharing system," Reliability Engineering and System Safety, Elsevier, vol. 167(C), pages 67-74.
    9. Singh, Bhupendra & Gupta, Puneet Kumar, 2012. "Load-sharing system model and its application to the real data set," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(9), pages 1615-1629.
    10. Bin Liu & Min Xie & Way Kuo, 2016. "Reliability modeling and preventive maintenance of load-sharing systemswith degrading components," IISE Transactions, Taylor & Francis Journals, vol. 48(8), pages 699-709, August.
    11. Manuel Franco & Juana-María Vivo, 2018. "Genetic algorithms for parameter estimation in modelling of index returns," The European Journal of Finance, Taylor & Francis Journals, vol. 24(13), pages 1088-1099, September.
    12. 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.
    13. Cha, Ji Hwan & Finkelstein, Maxim & Levitin, Gregory, 2018. "Bivariate preventive maintenance of systems with lifetimes dependent on a random shock process," European Journal of Operational Research, Elsevier, vol. 266(1), pages 122-134.
    14. Dewei Wang & Chendi Jiang & Chanseok Park, 2019. "Reliability analysis of load-sharing systems with memory," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 25(2), pages 341-360, April.
    15. Arne Henningsen & Ott Toomet, 2011. "maxLik: A package for maximum likelihood estimation in R," Computational Statistics, Springer, vol. 26(3), pages 443-458, September.
    16. Chanseok Park, 2013. "Parameter estimation from load-sharing system data using the expectation–maximization algorithm," IISE Transactions, Taylor & Francis Journals, vol. 45(2), pages 147-163.
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    Cited by:

    1. 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).
    2. 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).
    3. 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).
    4. 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.

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