An improved response surface method for the determination of failure probability and importance measures Sayan Gupta, C.S. Manohar* Department of Civil Engineering, Indian Institute of Science, Bangalore 560012, India Abstract The problem of response surface modeling of limit surface lying within two hyper spheres of prescribed radii is considered. The relevance of this problem in structural reliability analysis involving performance functions with multiple design points and/or multiple regions that make significant contributions to failure probability is discussed. The paper also proposes global measures of sensitivity of failure probability with respect to the basic random variables. The performance of the proposed improvements is examined by comparing simulation based results with results from the proposed procedure with reference to two specific structural reliability analysis problems. # 2003 Elsevier Ltd. All rights reserved. Keywords: Response surface method; Multiple design points; Structural reliability; Global importance measures; Fail- ure probability 1. Introduction Predicting reliability of real engineering structures is a challenging task, especially for structures with high reliability. A detailed modeling of the structure is necessary which implies that the structural analysis can be carried out principally through computational tools, such as finite ele- ment codes. The uncertainties in the structural and load properties are represented through a vector of random variables having specified joint probability distributions. A straightforward method for estimating the structural reliability is to carry out Monte Carlo simulations. This involves a large number of deterministic structural analysis for different realizations of the ran- dom variables. For an accurate estimate of the failure probability P f , the sample size, N, used in the simulation, must be at least of the order of 1/P f . For highly reliable complex structures, where the evaluation of each realization of performance function is computationally expensive, the direct Monte Carlo simulations is not a viable computational tool for estimating P f . Since the 0167-4730/03/$ - see front matter # 2003 Elsevier Ltd. All rights reserved. doi:10.1016/S0167-4730(03)00021-3 Structural Safety 26 (2004) 123–139 www.elsevier.com/locate/strusafe * Corresponding author. Tel.: +91-80-293-3121; fax: +9l-80-3600404. E-mail addresses: sayan@civil.iisc.ernet.in (S. Gupta), manohar@civil.iisc.ernet.in (C.S. Manohar).