In contrast to the traditional approach that computes the reliability index in the uncorrelated standard normal space (u-space), the reliability analysis that is simply realized in the original space (x-space, non-Gaussian type) would be more efficient for practical use, for example, with the Low and Tang's constrained optimization approach. On the other hand, a variant of Hasofer, Lind, Rackwits and Fiessler algorithm for first-order reliability method is derived in this paper. Also, the new algorithm is simply formulated in x-space and requires neither transformation of the random variables nor optimization tools. The algorithm is particularly useful for reliability analysis involving correlated non-Gaussian random variables subjected to implicit limit state function. The algorithm is first verified using a simple example with closed-form solution. With the aid of numerical differentiation analysis in x-space, it is then illustrated for a strut with complex support and for an earth slope with multiple failure modes, both cases involving implicit limit state surfaces. Copyright (c) 2015 John Wiley & Sons, Ltd.
