The introduction of reliability assessment methods in safety analysis of composite structures increased the complexity and the efficiency of failure evaluation methodologies proposed in the literature. In this paper, an approach based on surrogate modelling of first ply failure to obtain the reliability of the whole composite structure is proposed and analysed. This approach overcomes the expensive costs associated with exhaustive local reliability evaluation. The errors introduced by approximations used in structural reliability assessment of composite structures are studied within the context of robust design. The identification of different failure modes and its importance in reliability analysis are outlined and discussed.