A fundamental component of safety assessment is the appropriate representation and incorporation of uncertainty. A procedure for handling hybrid uncertainties in stochastic mechanics problems is presented. The procedure can be used for determining the bounds on failure probability for cases where failure probability is a monotonic function of the fuzzy variables. The procedure is illustrated through an example problem of safety assessment of a nuclear power plant piping component against stress corrosion cracking, considering the stochastic evolution of stress corrosion cracks with time. It is found that the bounds obtained enclose the values of failure probability obtained from probabilistic analyses.

There is a need to use probability distributions with power-law decaying tails to describe the large variations exhibited by some of the physical phenomena. The Weierstrass Random Walk (WRW) shows promise for modeling such phenomena. The theory of anomalous diffusion is now well established. It has found number of applications in Physics, Chemistry and Biology. However, its applications are limited in structural mechanics in general, and structural engineering in particular. The aim of this paper is to present some mathematical preliminaries related to WRW that would help in possible applications. In the limiting case, it represents a diffusion process whose evolution is governed by a fractional partial differential equation. Three applications of superdiffusion processes in mechanics, illustrating their effectiveness in handling large variations, are presented.