122 Int. J. Reliability and Safety, Vol. 4, Nos. 2/3, 2010 Copyright © 2010 Inderscience Enterprises Ltd. Spherical subset simulation (S 3 ) for solving non-linear dynamical reliability problems Lambros Katafygiotis* Department of Civil Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China Fax: + 852 2358 1534 Email: lambros@ust.hk *Corresponding author Sai Hung Cheung Department of Civil Engineering, California Institute of Technology, 1200 East California Boulevard, Pasadena, California, CA 91125, USA Email: sai@caltech.edu Ka-Veng Yuen Department of Civil and Environmental Engineering, University of Macau, Taipa, Macau, China Email: kvyuen@umac.mo Abstract: This paper presents a methodology for general non-linear reliability problems. It is based on dividing the failure domain into a number of appropriately selected subregions and calculating the failure probability as a sum of the probabilities for each subregion. The probability of each subregion is calculated as a product of factors, which can be estimated accurately by a relatively small number of samples generated according to the conditional distribution corresponding to the particular subregion. These samples are generated through Markov Chain Monte Carlo simulations using a slice-sampling-based algorithm proposed by the authors. The proposed method is robust and is suitable for high-dimensional problems. This is in contrast to popular importance sampling methods that often break down for high-dimensional problems. The method is found to be significantly more efficient than Monte Carlo simulations. The efficiency of the method is demonstrated with two examples involving 4000 and 1501 random variables. Keywords: spherical subset simulation; non-linear dynamic reliability; failure probability; MCMC; Markov Chain Monte Carlo. Reference to this paper should be made as follows: Katafygiotis, L., Cheung, S.H. and Yuen, K-V. (2010) ‘Spherical subset simulation (S 3 ) for solving non-linear dynamical reliability problems’, Int. J. Reliability and Safety, Vol. 4, Nos. 2/3, pp.122–138.