ABSTRACT
A solution of the Fokker–Planck–Kolmogorov equation (FPE) provides a complete characterization of the nonlinear response by the probability density function. For reliability analysis where the probability density function in the tail region plays a central role, such a solution provides the basis for a credible reliability assessment in quantitative terms. The chapter focuses on to the case of random loading. Uncertainties of the structural parameters can be treated in a further step by determining the stochastic response conditional on certain structural parameters. The approach is based on determining the limit state function by the commonly used structural analysis procedure. In this context the limit state function is defined as the transition from the safe to the unsafe state. The alternative approach is the analytical assessment of the expected risk. To decide whether or the risk associated with a new technological system to be introduced is acceptable, it may be compared with the risk associated with those of existing technologies.
