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Parameter estimation from load-sharing system data using the expectation–maximization algorithm

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  • Chanseok Park

Abstract

This article considers a system of multiple components connected in parallel. As components fail one by one, the remaining working components share the total load applied to the system. This is commonly referred to as load sharing in the reliability engineering literature. This article considers the traditional approach to the modeling of a load-sharing system under the assumption of the existence of underlying hypothetical latent random variables. Using the Expectation–Maximization (EM) algorithm, a methodology is proposed to obtain the maximum likelihood estimates in such a model in the case where the underlying lifetime distribution of the components is lognormal or normal. The proposed EM method is also illustrated and substantiated using numerical examples. The estimates obtained using the EM algorithm are compared with those obtained using the Broyden–Fletcher–Goldfarb–Shanno algorithm, which falls under the class of numerical methods known as Newton or quasi-Newton methods. The results show that the estimates obtained using the proposed EM method always converge to a unique global maximizer, whereas the estimates obtained using the Newton-type method are highly sensitive to the choice of starting values and thus often fail to converge.

Suggested Citation

  • 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.
  • Handle: RePEc:taf:uiiexx:v:45:y:2013:i:2:p:147-163
    DOI: 10.1080/0740817X.2012.669878
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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. 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.
    3. 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.
    4. 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).
    5. Qin, Shuidan & Wang, Bing Xing & Tsai, Tzong-Ru & Wang, Xiaofei, 2023. "The prediction of remaining useful lifetime for the Weibull k-out-of-n load-sharing system," Reliability Engineering and System Safety, Elsevier, vol. 233(C).
    6. Tzong-Ru Tsai & Hua Xin & Chiun-How Kao, 2021. "Bayesian Estimation Based on Sequential Order Statistics for Heterogeneous Baseline Gompertz Distributions," Mathematics, MDPI, vol. 9(2), pages 1-21, January.
    7. 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.

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