A. Alban, H. Darji, A. Imamura, and M. K. Nakayama, Efficient Monte Carlo methods for estimating failure probabilities, Reliability Engineering and System Safety, vol.165, pp.376-394, 2017.
DOI : 10.1016/j.ress.2017.04.001

A. N. Avramidis and J. R. Wilson, Correlation-induction techniques for estimating quantiles in simulation, Operations Research, vol.46, pp.574-591, 1998.
DOI : 10.1145/224401.224614

URL : http://repository.lib.ncsu.edu/bitstream/1840.4/4541/1/1995_0038.pdf

R. R. Bahadur, A note on quantiles in large samples, Annals of Mathematical Statistics, vol.37, issue.3, pp.577-580, 1966.
DOI : 10.1214/aoms/1177699450

URL : https://doi.org/10.1214/aoms/1177699450

P. Billingsley, Probability and Measure, 1995.

D. A. Bloch and J. L. Gastwirth, On a simple estimate of the reciprocal of the density function, Annals of Mathematical Statistics, vol.39, pp.1083-1085, 1968.

F. Chu and M. K. Nakayama, Confidence intervals for quantiles when applying variance-reduction techniques, ACM Transactions On Modeling and Computer Simulation, vol.22, issue.2, 2012.
DOI : 10.1145/2133390.2133394

R. Cranley and T. N. Patterson, Randomization of number theoretic methods for multiple integration, SIAM Journal on Numerical Analysis, vol.13, issue.6, pp.904-914, 1976.

D. A. Dube, R. R. Sherry, J. R. Gabor, and S. M. Hess, Application of risk informed safety margin characterization to extended power uprate analysis, Reliability Engineering and System Safety, vol.129, pp.19-28, 2014.

Z. He and X. Wang, Convergence of randomized quasi-Monte Carlo sampling for value-at-risk and conditional value-atrisk, 2017.

X. Jin and A. X. Zhang, Reclaiming quasi-Monte Carlo efficiency in portfolio value-at-risk simulation through Fourier transform, Management Science, vol.52, issue.6, pp.925-938, 2006.
DOI : 10.1287/mnsc.1060.0505

P. Jorion, Value at Risk: The New Benchmark for Managing Financial Risk, 2007.

F. Y. Kuo and D. Nuyens, Application of quasi-monte carlo methods to elliptic PDEs with random diffusion coefficients -a survey of analysis and implementation, Foundations of Computational Mathematics, vol.16, issue.6, pp.1631-1696, 2016.

Y. Lai and K. S. Tan, Simulation of nonlinear portfolio value-at-risk by monte carlo and quasi-monte carlo methods, Financial Engineering and Applications, 2006.

P. Ecuyer, D. Munger, and B. Tuffin, On the distribution of integration error by randomly-shifted lattice rules, Electronic Journal of Statistics, vol.4, pp.950-993, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00793293

C. Lemieux, Monte Carlo and Quasi-Monte Carlo Sampling. Series in Statistics, 2009.

C. Lemieux, P. , and L. Ecuyer, Selection criteria for lattice rules and other low-discrepancy point sets, Mathematics and Computers in Simulation, vol.55, issue.1-3, pp.139-148, 2001.
DOI : 10.1016/s0378-4754(00)00254-8

W. Loh, On the asymptotic distribution of scrambled net quadrature, Annals of Statistics, vol.31, issue.4, pp.1282-1324, 2003.

M. K. Nakayama, Estimating a failure probability using a combination of variance-reduction tecniques, Proceedings of the 2015 Winter Simulation Conference, pp.621-632, 2015.

H. Niederreiter, Random Number Generation and Quasi-Monte Carlo Methods, vol.63, 1992.

A. B. Owen, Randomly permuted (t,m,s)-nets and (t,s)-sequences, Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing: Lecture Notes in Statistics, vol.106, pp.299-317, 1995.
DOI : 10.1007/978-1-4612-2552-2_19

A. B. Owen, Monte Carlo variance of scrambled net quadrature, SIAM Journal of Numerical Analysis, vol.34, pp.1884-1910, 1997.

A. B. Owen, Scrambled net variance for integrals of smooth functions, Annals of Statistics, vol.25, issue.4, pp.1541-1562, 1997.

A. B. Owen, Scrambling Sobol' and Niedeerreiter-Xing points, Journal of Complexity, vol.14, issue.4, pp.466-489, 1998.
DOI : 10.1006/jcom.1998.0487

URL : https://doi.org/10.1006/jcom.1998.0487

A. Papageorgiou and S. H. Paskov, Deterministic simulation for risk management, Journal of Portfolio Management, vol.25, issue.5, pp.122-127, 1999.
DOI : 10.3905/jpm.1999.319698

R. J. Serfling, Approximation Theorems of Mathematical Statistics, 1980.

R. R. Sherry, J. R. Gabor, and S. M. Hess, Pilot application of risk informed safety margin characterization to a total loss of feedwater event, Reliability Engineering and System Safety, vol.117, pp.65-72, 2013.

I. H. Sloan and S. Joe, Lattice Methods for Multiple Integration, 1994.
DOI : 10.1016/0377-0427(85)90012-3

URL : https://doi.org/10.1016/0377-0427(85)90012-3

B. Tuffin, On the use of low discrepancy sequences in Monte Carlo methods, Monte Carlo Methods and Applications, vol.2, issue.4, pp.295-320, 1996.

B. Tuffin, Variance reduction order using good lattice points in Monte Carlo methods, Computing, vol.61, issue.4, pp.371-378, 1998.

B. Tuffin, Randomization of quasi-monte carlo methods for error estimation: Survey and normal approximation, Monte Carlo Methods and Applications, vol.10, issue.3-4, pp.617-628, 2004.

U. , Nuclear Regulatory Commission. Final safety evaluation for WCAP-16009-P, revision 0, "realistic large break LOCA evaluation methodology using automated statistical treatment of uncertainty method (AS-TRUM), Nuclear Regulatory Commission, 2005.

U. , Nuclear Regulatory Commission. Acceptance criteria for emergency core cooling systems for light-water nuclear power reactors. Title 10, Code of Federal Regulations §50, NRC, vol.46, 2010.

U. , Nuclear Regulatory Commission. Applying statistics. U.S. Nuclear Regulatory Commission Report NUREG-1475, 2011.