Fractional factorial designs for Fourier-cosine models

Fourier-cosine models, rooted in the discrete cosine transformation, are widely used in numerous applications in science and engineering. Because the selection of design points where data are collected greatly affects the modeling process, we study the choice of fractional factorial designs for fitting Fourier-cosine models. We propose a new type of generalized resolution and provide a framework for the construction of fractional factorial designs with the maximum generalized resolution. The construction applies level permutations to regular designs with a novel nonlinear transformation. A series of theoretical results are developed to characterize the properties of the level-permuted designs. Based on the theory, we further provide efficient methods for constructing designs with high resolutions without any computer search. Examples are given to show the advantages of the constructed designs over existing ones.