ln structural design, taking into account uncertainties and errors allows to improve the estimation of failure risk. This work aims at controling the discretization error introduced by the finite element method in the reliability analysis. Two strategies are proposed to couple a kriging metamodel with Monte-Carlo estimators and discretization error estimators. The first strategy uses a posteriori estimators of the discretization error. lt is used to compute discretization error bounds on the probability of failure. The second strategy exploits a priori knowledge of the mesh convergence rate or the quantity of interest defining the failure of the structure. lt allows to extrapolate without discretization error this quantity of interest and the probability of failure. A posteriori estimation of the discretization error is then considered in the context of reliability assessment of structures used in the marine renewable energy (MRE) industry. One of the failure scenarios that need to be studied when deploying a structure at sea is fatigue due to cyclic loading. A new approach allowing to propagate bounds obtained on the local stress toward the fatigue damage of the structure is proposed.