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Performance variability management is an active research area in high-performance computing (HPC). We focus on input/output (I/O) variability. To study the performance variability, computer scientists often use grid-based designs (GBDs) to collect I/O variability data, and use mathematical approximation methods to build a prediction model. Mathematical approximation models could be biased particularly if extrapolations are needed. Space-filling designs (SFDs) and surrogate models such as Gaussian process (GP) are popular for data collection and building predictive models. The applicability of SFDs and surrogates in the HPC variability needs investigation. We investigate their applicability in the HPC setting in terms of design efficiency, prediction accuracy, and scalability. We first customize the existing SFDs so that they can be applied in the HPC setting. We conduct a comprehensive investigation of design strategies and the prediction ability of approximation methods. We use both synthetic data simulated from three test functions and the real data from the HPC setting. We then compare different methods in terms of design efficiency, prediction accuracy, and scalability. In synthetic and real data analysis, GP with SFDs outperforms in most scenarios. With respect to approximation models, GP is recommended if the data are collected by SFDs. If data are collected using GBDs, both GP and Delaunay can be considered. With the best choice of approximation method, the performance of SFDs and GBD depends on the property of the underlying surface. For the cases in which SFDs perform better, the number of design points needed for SFDs is about half of or less than that of the GBD to achieve the same prediction accuracy. SFDs that can be tailored to high dimension and non-smooth surface are recommended especially when large numbers of input factors need to be considered in the model.