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

On the Interpretation of χ 2 from Contingency Tables, and the Calculation of P

R. A. Fisher · Journal Of The Royal Statistical Society · 1922 · 2.9K citations

Natural Sciences, Biostatistics, Mathematics +13

Estimation of small failure probabilities in high dimensions by subset simulation

Siu‐Kui Au, James L. Beck · Probabilistic Engineering Mechanics · 2001 · 2.4K citations

Business, Biostatistics, Probability Theory +15

Important sampling in high dimensions

Siu‐Kui Au, James L. Beck · Structural Safety · 2002 · 369 citations

Natural Sciences, Physics, Statistics +3

Design-point excitation for non-linear random vibrations

Heonsang Koo, Armen Der Kiureghian, Kazuya Fujimura · Probabilistic Engineering Mechanics · 2005 · 98 citations

Engineering, Mechanical Engineering, Computational Structural Analysis +13

Application of spherical subset simulation method and auxiliary domain method on a benchmark reliability study

Lambros S. Katafygiotis, Sai Hung Cheung · Structural Safety · 2007 · 72 citations

Computing, Computational Engineering, Mechanical Engineering +16