A method is presented to efficiently approximate the failure probabili
ty of structures subjected to time-variant loads, where the system of
loads and structure may have uncertain parameters. The method uses res
ponse surface methodology in conjunction with the fast integration tec
hnique suggested by Wen and Chen, to provide a limit-state formulation
that is computationally simple to solve based on a small number of re
sponse time histories. The system reliability may then be quickly comp
uted by first-order reliability method (FORM)/second-order reliability
method (SORM) or Monte Carlo simulation. Sensitivity analysis is perf
ormed to determine the effect on the failure probability of changes to
the system parameters, which can be important when determining whethe
r uncertainty in a given system parameter is significant. An empirical
measure of the accuracy of the response surface approximation is pres
ented.