It is of great interest to assess during the operation of a dynamic system whether it is expected to satisfy specified performance objectives.To do this, the failure probability (or its complement, robust reliability) of the system when it is subjected to dynamic excitation is computed. The word ‘failure’ is used here to refer to unsatisfactory performance of the system. In this paper, we are interested in using system data to update the robust failure probability that any particular response of a linear structural dynamic system exceeds a specified threshold during the time when the system is subjected to future Gaussian dynamic excitation. Computation of the robust reliability takes into account uncertainties from structural modeling in addition to the modeling of the uncertain excitation that the structure will experience during its lifetime. The updating is based on partial modal data from the structure. By exploiting the properties of linear dynamics, a new approach based on stochastic simulation methods is proposed, to update the robust reliability of the structure. The efficiency of the proposed approach is illustrated by a numerical example involving a linear elastic structural model of a building.