This paper reviews the mathematical foundation of the importance sampling technique and
discusses two general classes of methods to construct the importance sampling density (or …

Passive systems are fundamental for the safe development of Nuclear Power Plant (NPP)
technology. The accurate assessment of their reliability is crucial for their use in the nuclear …

Very efficient sampling algorithms have been proposed to estimate rare event probabilities,
such as Importance Sampling or Importance Splitting. Even if the number of samples …

Abstract Crude Monte-Carlo or quasi Monte-Carlo methods are well suited to characterize
events of which associated probabilities are not too low with respect to the simulation …

Reliability assessment in presence of epistemic uncertainty leads to consider the failure
probability as a quantity depending on the state of knowledge about uncertain input …

Running a reliability analysis on engineering problems involving complex numerical models
can be computationally very expensive, requiring advanced simulation methods to reduce …

Reliability-oriented sensitivity analysis methods have been developed for understanding the
influence of model inputs relative to events which characterize the failure of a system (eg, a …

Abstract An Adaptive Metamodel-Based Subset Importance Sampling (AM-SIS) approach,
previously developed by the authors, is here employed to assess the (small) functional …

This introduction recalls the considerable socio-economic challenges associated with
extreme natural hazards. The possibilities of statistical quantification of past hazards and …

In solving simulation-based stochastic root-finding or optimization problems that involve rare
events, such as in extreme quantile estimation, running crude Monte Carlo can be …