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Parameter estimation for the reliability of load-sharing systems

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  • Chanseok Park

Abstract

Consider a multi-component system connected in parallel. In this system, as components fail one by one, the total load or traffic applied to the system is redistributed among the remaining surviving components, which is commonly referred to as load-sharing. This develops parameter estimation methods for these type of systems. A closed-form Maximum Likelihood Estimator (MLE) and Best Unbiased Estimator (BUE) are provided under a general load-sharing rule when the underlying lifetime distribution of the components in the system is exponential. As an extension, it is assumed that the underlying lifetime distribution of the components is Weibull and it is shown that, after the shape parameter is estimated by solving the one-dimensional log-likelihood estimating equation, the closed-form MLE and conditional BUE of the rate parameter are easily obtained. The asymptotic distribution of the proposed MLE is also provided. Illustrative examples and Monte Carlo simulation results are also presented and these substantiate the proposed methods.

Suggested Citation

  • Chanseok Park, 2010. "Parameter estimation for the reliability of load-sharing systems," IISE Transactions, Taylor & Francis Journals, vol. 42(10), pages 753-765.
    • Handle: RePEc:taf:uiiexx:v:42:y:2010:i:10:p:753-765
    DOI: 10.1080/07408171003670991
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    Citations

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    Cited by:

    1. Pramendra Singh Pundir & Puneet Kumar Gupta, 2018. "Reliability Estimation in Load-Sharing System Model with Application to Real Data," Annals of Data Science, Springer, vol. 5(1), pages 69-91, March.
    2. Neha Choudhary & Abhishek Tyagi & Bhupendra Singh, 2022. "Analysing Load-Sharing System Model with Type-I and Type-II Failure Censored Data from Weibull Distribution," Annals of Data Science, Springer, vol. 9(4), pages 645-674, August.
    3. Azeem Ali & Sanku Dey & Haseeb Ur Rehman & Zeeshan Ali, 2019. "On Bayesian reliability estimation of a 1-out-of-k load sharing system model of modified Burr-III distribution," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 10(5), pages 1052-1081, October.
    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. 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.
    6. 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.
    7. de Paula, Cassio Pereira & Visnadi, Lais Bittencourt & de Castro, Helio Fiori, 2019. "Multi-objective optimization in redundant system considering load sharing," Reliability Engineering and System Safety, Elsevier, vol. 181(C), pages 17-27.
    8. Li, Der-Chiang & Lin, Liang-Sian, 2013. "A new approach to assess product lifetime performance for small data sets," European Journal of Operational Research, Elsevier, vol. 230(2), pages 290-298.
    9. Nezakati, Ensiyeh & Razmkhah, Mostafa, 2020. "Reliability analysis of a load sharing k-out-of-n:F degradation system with dependent competing failures," Reliability Engineering and System Safety, Elsevier, vol. 203(C).
    10. 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.
    11. Zhengcheng Zhang & Yonghong Yang & Danqing Li, 2022. "Estimation of parameters for load-sharing parallel systems under exponential Pareto distribution," Journal of Risk and Reliability, , vol. 236(2), pages 248-255, April.
    12. Levitin, Gregory & Xing, Liudong & Ben-Haim, Hanoch & Dai, Yuanshun, 2016. "Optimal task partition and state-dependent loading in heterogeneous two-element work sharing system," Reliability Engineering and System Safety, Elsevier, vol. 156(C), pages 97-108.
    13. 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.
    14. Kong, Yaonan & Ye, Zhisheng, 2017. "Goodness-of-fit tests in the multi-state Markov model," Reliability Engineering and System Safety, Elsevier, vol. 166(C), pages 16-24.

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