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 method is applied to a benchmark structure specifically designed to exhibit multiple failure modes and test the robustness and versatility of the method.