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Likelihood-based representation of epistemic uncertainty due to sparse point data and/or interval data

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  • Sankararaman, Shankar
  • Mahadevan, Sankaran

Abstract

This paper presents a likelihood-based methodology for a probabilistic representation of a stochastic quantity for which only sparse point data and/or interval data may be available. The likelihood function is evaluated from the probability density function (PDF) for sparse point data and the cumulative distribution function for interval data. The full likelihood function is used in this paper to calculate the entire PDF of the distribution parameters. The uncertainty in the distribution parameters is integrated to calculate a single PDF for the quantity of interest. The approach is then extended to non-parametric PDFs, wherein the entire distribution can be discretized at a finite number of points and the probability density values at these points can be inferred using the principle of maximum likelihood, thus avoiding the assumption of any particular distribution. The proposed approach is demonstrated with challenge problems from the Sandia Epistemic Uncertainty Workshop and the results are compared with those of previous studies that pursued different approaches to represent and propagate interval description of input uncertainty.

Suggested Citation

  • Sankararaman, Shankar & Mahadevan, Sankaran, 2011. "Likelihood-based representation of epistemic uncertainty due to sparse point data and/or interval data," Reliability Engineering and System Safety, Elsevier, vol. 96(7), pages 814-824.
    • Handle: RePEc:eee:reensy:v:96:y:2011:i:7:p:814-824
    DOI: 10.1016/j.ress.2011.02.003
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    References listed on IDEAS

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    1. Zaman, Kais & Rangavajhala, Sirisha & McDonald, Mark P. & Mahadevan, Sankaran, 2011. "A probabilistic approach for representation of interval uncertainty," Reliability Engineering and System Safety, Elsevier, vol. 96(1), pages 117-130.
    2. Elkan F. Halpern & Milton C. Weinstein & Maria G.M. Hunink & G. Scott Gazelle, 2000. "Representing Both First- and Second-order Uncertainties by Monte Carlo Simulation for Groups of Patients," Medical Decision Making, , vol. 20(3), pages 314-322, July.
    3. Baudrit, C. & Dubois, D., 2006. "Practical representations of incomplete probabilistic knowledge," Computational Statistics & Data Analysis, Elsevier, vol. 51(1), pages 86-108, November.
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    Cited by:

    1. Ling, You & Mahadevan, Sankaran, 2013. "Quantitative model validation techniques: New insights," Reliability Engineering and System Safety, Elsevier, vol. 111(C), pages 217-231.
    2. Wang, Zhenqiang & Jia, Gaofeng, 2020. "Augmented sample-based approach for efficient evaluation of risk sensitivity with respect to epistemic uncertainty in distribution parameters," Reliability Engineering and System Safety, Elsevier, vol. 197(C).
    3. Sankararaman, Shankar & Mahadevan, Sankaran, 2015. "Integration of model verification, validation, and calibration for uncertainty quantification in engineering systems," Reliability Engineering and System Safety, Elsevier, vol. 138(C), pages 194-209.
    4. Mi, Jinhua & Li, Yan-Feng & Peng, Weiwen & Huang, Hong-Zhong, 2018. "Reliability analysis of complex multi-state system with common cause failure based on evidential networks," Reliability Engineering and System Safety, Elsevier, vol. 174(C), pages 71-81.
    5. Wang, Yuhao & Liu, Yongming, 2020. "Bayesian entropy network for fusion of different types of information," Reliability Engineering and System Safety, Elsevier, vol. 195(C).
    6. Cheng, Lei & Lu, Zhenzhou & Zhang, Leigang, 2015. "Application of Rejection Sampling based methodology to variance based parametric sensitivity analysis," Reliability Engineering and System Safety, Elsevier, vol. 142(C), pages 9-18.
    7. Mi, Jinhua & Li, Yan-Feng & Yang, Yuan-Jian & Peng, Weiwen & Huang, Hong-Zhong, 2016. "Reliability assessment of complex electromechanical systems under epistemic uncertainty," Reliability Engineering and System Safety, Elsevier, vol. 152(C), pages 1-15.
    8. VanDerHorn, Eric & Mahadevan, Sankaran, 2018. "Bayesian model updating with summarized statistical and reliability data," Reliability Engineering and System Safety, Elsevier, vol. 172(C), pages 12-24.
    9. Xiang Peng & Xiaoqing Xu & Jiquan Li & Shaofei Jiang, 2021. "A Sampling-Based Sensitivity Analysis Method Considering the Uncertainties of Input Variables and Their Distribution Parameters," Mathematics, MDPI, vol. 9(10), pages 1-18, May.
    10. Mi, Jinhua & Lu, Ning & Li, Yan-Feng & Huang, Hong-Zhong & Bai, Libing, 2022. "An evidential network-based hierarchical method for system reliability analysis with common cause failures and mixed uncertainties," Reliability Engineering and System Safety, Elsevier, vol. 220(C).
    11. Su, Xiaoyan & Mahadevan, Sankaran & Xu, Peida & Deng, Yong, 2014. "Inclusion of task dependence in human reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 128(C), pages 41-55.
    12. Tohme, Tony & Vanslette, Kevin & Youcef-Toumi, Kamal, 2020. "A generalized Bayesian approach to model calibration," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    13. Sankararaman, S. & Mahadevan, S., 2013. "Separating the contributions of variability and parameter uncertainty in probability distributions," Reliability Engineering and System Safety, Elsevier, vol. 112(C), pages 187-199.
    14. N-C Xiao & H-Z Huang & Z Wang & Y Li & Y Liu, 2012. "Reliability analysis of series systems with multiple failure modes under epistemic and aleatory uncertainties," Journal of Risk and Reliability, , vol. 226(3), pages 295-304, June.

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