Abstract A statistical approach for time-variant system reliability problems is developed and investigated. The basic proposal is to use a response surface, characterised by a statistical model of the mixed type, to represent the capacity in an analytical limit-state function. The fragility function of the system is then calculated by FORM analysis, with the constructed empirical limit-state function as input. The methodology is applied in the assessment of a 3D RC frame structure. The application allows a number of detailed implementation issues to be clarified, and confirms the robustness and versatility of the method.