Geometric insight into the challenges of solving high-dimensional reliability problems

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	Year	Citations
On the Interpretation of χ 2 from Contingency Tables, and the Calculation of P R. A. Fisher Journal Of The Royal Statistical Society Statisticsχ 2Contingency Tables	1922	2.8K
Estimation of small failure probabilities in high dimensions by subset simulation Siu‐Kui Au, James L. Beck Probabilistic Engineering Mechanics Reliability EngineeringSmall Failure ProbabilitiesHigh DimensionsEngineeringReliability Modelling	2001	2.3K
Important sampling in high dimensions Siu‐Kui Au, James L. Beck Structural Safety Geometric ModelingEngineeringData ScienceNatural SciencesHigher Dimensional Problem	2002	360
Design-point excitation for non-linear random vibrations Heonsang Koo, Armen Der Kiureghian, Kazuya Fujimura Probabilistic Engineering Mechanics EngineeringVibrationsPhysicsMechanical SystemsRandom Vibration	2005	96
Application of spherical subset simulation method and auxiliary domain method on a benchmark reliability study Lambros S. Katafygiotis, Sai Hung Cheung Structural Safety ReliabilityNumerical AnalysisReliability EngineeringEngineeringReliability Modelling	2007	70
A normal approximation for the chi-square distribution Luisa Canal Computational Statistics & Data Analysis Density EstimationEngineeringClassical ApproximationChi-square DistributionMathematical Statistic	2004	53

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