Quality or safety requirements on a product necessitate to take scattering influences into account. These influences can be external (random loads or operation conditions) or inherent in the product itself (like scattering material properties or production tolerances). If the failure rate is small, as it is typical for safety considerations, then the usual framework, which is also established by codes (Eurocode EN 1990 ), is the probabilistic safety assessment. The variance-based robustness evaluation, or sigma-level approach, (Equation 4–1), may not be sufficient, since it is just a one-dimensional consideration and relies on the assumption of normal distribution.

Within the framework of probabilistic safety assessment or reliability analysis, the scattering influences are modelled as random variables, which are defined by distribution type, stochastic moments and mutual correlations, see Definition of Uncertainties. The result of the analysis is the complementary of reliability, the probability of failure, which can be represented on a logarithmic scale.

In the following sections, the definition of the probability of failure will be given first. optiSLang offers a variety of methods to compute it, with different ranges of application, which will be introduced then.