and reliability studies in the science of materials. 

From a strictly statistical standpoint, the above description may also be considered when the distribution $G$ is of some special form, namely when the conditional distribution of $R$ given $\{R>x\}$ has a functional form which differs from that of $G$ only through some changes of the parameters. In this case, simulation under these conditional distributions can be performed for adaptive choice of the thresholds $x_{l}$’s, substituting the above sequence of trials. This sequential procedure allows to estimate iteratively the initial parameters of $G$ and to obtain $q_{1-\alpha }$ combining corresponding quantiles of the conditional distributions above thresholds, a method named splitting. In this method, we will choose sequentially the $%
x_{l}$’s in a way that $q_{1-\alpha }$ will be obtained easily from the last distribution of $x$ conditioned upon $\{R>x_{m}\}.$

In safety issues or in pharmaceutical control, the focus is usually set on the behavior of a variable of interest (strength, maximum tolerated dose) for small (or even very small) levels. In these settings the above considerations turn to be equivalently stated through a clear change of variable, considering the inverse of the variable of interest. As an example which is indeed 