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A method for computing probabilities of failure of structural components and systems is proposed. The approach is based on a radial‐space division technique in conjunction with automatic generation of unit centerline vectors. Based on this technique, the standard normal space is divided into active and passive subdomains. The probability contribution of each active subdomain to the total probability of failure is estimated by approximating the actual limit‐state hyper‐surface with a hypersphere segment centered on the actual hypersurface. The proposed method can solve with relatively high accuracy both component and system reliability problems involving nonlinearities and multiple extremum points of the probability density on the limit‐state hypersurface. A number of numerical examples involving linear and nonlinear performance functions of components and systems are presented. The results are in good agreement with exact solutions, probability bounds, multinormal approximations, and/or Monte Carlo simulations.
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Katsuki et al. (1994) studied this question.
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