In structural safety the computation of the probability of failure obviously requires the knowledge of the joint density function of the basic variables x. In some cases, however, only the marginal distributions and, perhaps, the correlation matrix are known, with the consequence that approximate models for the joint density function should be applied [36]. A more frequent situation is that even the marginal densities remain unknown, due to the insufficiency of experimental evidence [115] and hence only low order marginal and joint moments can be confidently estimated. In such situation the estimation of the reliability as (7.1) $$R = \int\limits_s {f\underline x \left( x \right)dx}$$ can only be performed on some strong assumptions, such as the linearity of the limit state function and the Gaussian behavior of the basic variables, because this model is entirely defined in terms of second order moment information. Since this is evidently a disputable decision, some authors propose to measure the reliability in terms of an index, which affords a meaningful value for design, as it measures the extent of the safe domain in some sense. It is specially useful when the statistical information on the basic variables is reduced, normally consisting of second-order marginal and cross moments of the basic variables.