At a fixed intensity measure （IM） level, the accuracy of engineering demand parameter （EDP） prediction is jointly controlled by the number of ground-motion acceleration time histories and the corresponding conditional dispersion. In nonlinear time-history analysis, structural response predictions can exhibit substantial variability when ground-motion records are selected from a finite sample pool. Although seismic design codes worldwide specify minimum numbers of input ground motions, such requirements remain largely empirically derived and lack a unified quantitative framework linking record count, input uncertainty, and prediction accuracy. Structures with distinct dynamic characteristics also display varying sensitivity to ground-motion attributes. Compared with short-period systems, medium- and long-period structures are generally more sensitive to velocity- and displacement-related ground-motion features. Spectral acceleration at the fundamental period ［ S_a（T₁） ］ typically serves as a more efficient IM for short-period structures, whereas peak ground velocity （PGV） and Housner intensity （HI） are better suited for long-period counterparts. From the perspective of performance-based seismic demand assessment, the accuracy of EDP prediction is tightly coupled to the chosen IM; a more efficient IM can reduce the number of ground motions needed to meet a predefined target accuracy. Accordingly, the minimum number of input records should vary with a structure’s dynamic properties. Prior research has explored ground-motion sample sizes and their impacts on structural response evaluation, yet code provisions still rely predominantly on engineering experience. Existing work has largely focused on how record quantity, record selection schemes, and processing techniques affect the conditional mean of EDPs. By contrast, few systematic quantitative investigations have addressed IM-conditioned dispersion and associated sampling uncertainty under finite-sample conditions, as well as the quantification of the minimum number of ground motions required to achieve a target EDP prediction accuracy.

To fill this research gap, this study quantifies the interrelationships among IM-conditioned dispersion, sampling uncertainty, EDP prediction accuracy, and minimum sample size. A dataset comprising 3 969 unscaled ground-motion acceleration time histories is adopted. Four candidate IMs are considered: peak ground acceleration （PGA）, spectral acceleration at the fundamental period ［ S_a（T₁） ］ , peak ground velocity （PGV）, and Housner intensity （HI）. Two frame archetypes with contrasting dynamic properties are selected as case structures: a short-period frame with a fundamental period （T₁＝0.3 s）, and a medium-period frame with （T₁＝1.35 s）. IM–EDP seismic demand models are developed via nonlinear dynamic analyses, and IM-conditioned EDP dispersion is estimated from regression residuals. A repeated random sampling framework is then implemented to characterize the sampling distributions of conditional dispersion and relative prediction error under varying ground-motion sample sizes. Relative prediction error is adopted as the metric quantifying EDP prediction accuracy, while the median and 95th percentile interval are used to represent central tendency and sampling uncertainty, respectively.

The results reveal that sampling uncertainty in both conditional dispersion and relative prediction error gradually diminishes as the number of ground motions increases. For sample sizes exceeding 10 records, the influence of sampling uncertainty on EDP prediction accuracy can be reasonably neglected. When more than 20 ground motions are employed, the median of the conditional dispersion distribution stabilizes substantially; this indicates that the central tendency of conditional dispersion barely changes with further sample size growth, though sampling uncertainty persists. Beyond this threshold, increasing the number of ground motions no longer markedly alters the typical conditional dispersion level, but rather ensures that resultant EDP predictions satisfy the predefined accuracy criteria. When sampling uncertainty is explicitly accounted for and the acceptance criterion is defined such that 95% of relative prediction errors fall within a specified tolerance band （e.g., ±5%）, the optimal IM and corresponding minimum sample size can be determined for structures with different fundamental periods. For the short-period frame, ［ S_a（T₁） ］ emerges as the optimal IM, requiring a minimum of 5 ground motions. For the medium-period frame, HI constitutes the optimal IM, with a minimum sample size of no less than 80 records. These outcomes demonstrate that the optimal IM and required ground-motion quantity differ substantially for structures with distinct dynamic characteristics. More critically, EDP prediction accuracy is not solely controlled by sample size but dominated by IM selection. Once the characteristic conditional dispersion of a given IM is quantified, the minimum sample size required to achieve a target prediction accuracy can be readily calculated.

In summary, this study elucidates the inherent quantitative relationships among IM-conditioned dispersion, sample size, and EDP prediction accuracy under finite-sample and sampling uncertainty conditions. The findings provide a quantitative theoretical basis for selecting optimal intensity measures and determining the minimum number of ground-motion time histories required for nonlinear time-history analysis of structures with varied dynamic properties. This work can also improve the reliability and efficiency of seismic demand model calibration, seismic performance evaluation, and structural fragility function derivation.