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

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An efficient method for the estimation of structural reliability intervals with random sets, dependence modeling and uncertain inputs (2014, background): “[2,41–46], the focus of present paper is the determination of the reliability intervals under uncertain input variables by means of Monte Carlo simulation.”
Sequential importance sampling for structural reliability analysis (2016, background): “However, it has been discussed [19, 20] that in settings involving a large number of random variables, IS based on such densities may fail to describe the important region, leading to a dramatic increase of the variance of the resulting estimate.”
A survey on approaches for reliability-based optimization (2010, methodology): “An important characteristic of several advanced simulation methods is that they are specially designed for addressing reliability problems involving a large number of uncertain parameters (Katafygiotis and Zuev, 2008; Valdebenito et al, 2010).”
Uncertainty analysis of complex structural systems (2009, background): “Moreover, in [42] the challenges related with high-dimensional reliability problems, addressed in [35, 43], are described in detail.”