The role of the design point for calculating failure probabilities in view of dimensionality and structural nonlinearities

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A survey on approaches for reliability-based optimization (2010, methodology): “Secondly, approximate reliability methods may not be applicable when the dimensionality of ζ is high, as discussed in Katafygiotis and Zuev (2008) and Valdebenito et al. (2010) .”
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.”
Adoption of a reliability approach for membrane structure analysis (2013, methodology): “Approximate reliability methods are required to make the problem tractable [25].”
The future of risk assessment (2018, background): “The high dimensionality in the inputs implies that the system conditions and scenarios to consider for simulating the system behavior for the identification of the CRs and/or for the estimation of the probability of their realizations [14,190], increase exponentially with the input space dimensions ”
MCMC algorithms for Subset Simulation (2015, methodology): “These methods result in approximations of the probability of failure, which may involve considerable errors especially in problems where the dimension 𝑛 of the random variable space is large or in problems with highly nonlinear limit-state functions (Rackwitz 2001, Valdebenito et al. 2010).”