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Advantages of variance reduction techniques in establishing confidence intervals for quantiles

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  • Grabaskas, Dave
  • Nakayama, Marvin K.
  • Denning, Richard
  • Aldemir, Tunc

Abstract

Over the past two decades, U.S. nuclear power plant regulation has increasingly depended on best-estimate plus uncertainty safety analyses. As a result of the shift to best-estimate analyses, the distribution of the output metric must be compared against a regulatory goal, rather than a single, conservative value. This comparison has historically been conducted using a 95% one-sided confidence interval for the 0.95-quantile of the output distribution, which is usually found following the technique of simple random sampling using order statistics (SRS-OS). While SRS-OS has certain statistical advantages, there are drawbacks related to the available sampling schemes and the accuracy and precision of the resulting value. Recent work has shown that it is possible to establish asymptotically valid confidence intervals for a quantile of the output of a model simulated using variance reduction techniques (VRTs). These VRTs can provide more informative results than SRS-OS. This work compares SRS-OS and the VRTs of antithetic variates and Latin hypercube sampling through several experiments, designed to replicate conditions found in nuclear safety analyses. This work is designed as an initial investigation into the use of VRTs as a tool to satisfy nuclear regulatory requirements, with hope of expanded analyses of VRTs in the future.

Suggested Citation

  • Grabaskas, Dave & Nakayama, Marvin K. & Denning, Richard & Aldemir, Tunc, 2016. "Advantages of variance reduction techniques in establishing confidence intervals for quantiles," Reliability Engineering and System Safety, Elsevier, vol. 149(C), pages 187-203.
    • Handle: RePEc:eee:reensy:v:149:y:2016:i:c:p:187-203
    DOI: 10.1016/j.ress.2015.12.015
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    References listed on IDEAS

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    1. Falk, Michael, 1986. "On the estimation of the quantile density function," Statistics & Probability Letters, Elsevier, vol. 4(2), pages 69-73, March.
    2. Athanassios N. Avramidis & James R. Wilson, 1998. "Correlation-Induction Techniques for Estimating Quantiles in Simulation Experiments," Operations Research, INFORMS, vol. 46(4), pages 574-591, August.
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    Cited by:

    1. Zheng, Xiaoyu & Tamaki, Hitoshi & Sugiyama, Tomoyuki & Maruyama, Yu, 2022. "Dynamic probabilistic risk assessment of nuclear power plants using multi-fidelity simulations," Reliability Engineering and System Safety, Elsevier, vol. 223(C).
    2. Alban, Andres & Darji, Hardik A. & Imamura, Atsuki & Nakayama, Marvin K., 2017. "Efficient Monte Carlo methods for estimating failure probabilities," Reliability Engineering and System Safety, Elsevier, vol. 165(C), pages 376-394.
    3. Wu, Shengnan & Zhang, Laibin & Zheng, Wenpei & Liu, Yiliu & Lundteigen, Mary Ann, 2019. "Reliability modeling of subsea SISs partial testing subject to delayed restoration," Reliability Engineering and System Safety, Elsevier, vol. 191(C).
    4. Yijie Peng & Chun-Hung Chen & Michael C. Fu & Jian-Qiang Hu & Ilya O. Ryzhov, 2021. "Efficient Sampling Allocation Procedures for Optimal Quantile Selection," INFORMS Journal on Computing, INFORMS, vol. 33(1), pages 230-245, January.
    5. Sanchez-Saez, F. & Sánchez, A.I. & Villanueva, J.F. & Carlos, S. & Martorell, S., 2018. "Uncertainty analysis of a large break loss of coolant accident in a pressurized water reactor using non-parametric methods," Reliability Engineering and System Safety, Elsevier, vol. 174(C), pages 19-28.

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