AbstractIn earthquake engineering, recorded accelerograms must be critically analyzed to predict the seismic behavior of structures under future earthquakes. Recent studies have highlighted that, in addition to amplitude, the spectral content of accelerograms also plays a key role in the seismic analysis of structural systems. Spectral content varies significantly from one accelerogram to another, even for records in the same soil category. It follows that in order to account for uncertainty about future seismic events, it is necessary to analyze an ensemble of recorded accelerograms and perform statistical calculations. To this aim, in this study, the spectral content of a large set of accelerograms recorded on rigid soil deposits was analyzed. Then, ground motion acceleration was modeled as a zero-mean stationary Gaussian random process, and statistical analysis was performed to characterize the main parameters of the pertinent power spectral density (PSD) function. Although the Chauvenet’s criterion was applied to discard outliers from the set of accelerograms, it was found that the main parameters of the power spectrum would be more appropriately defined in interval form. Therefore, seismic acceleration was characterized by an imprecise PSD function, which, unlike well-established power spectra with deterministic parameters, may be viewed as representative of the set of actual accelerograms recorded on rigid soil deposits. Finally, to assess structural safety, the imprecise PSD function of ground motion acceleration was embedded into the formulation of the classical first-passage problem. Due to the imprecision of the excitations, the reliability function of the selected extreme value stress process turned out to have an interval nature.