Central composite designs are widely used in practice for factor screening and building response surface models. We study two classes of new composite designs. The first class consists of a 2-level factorial design and a 3-level orthogonal array; the second consists of a 2-level factorial and a 3-level definitive screening design. We derive bounds of their efficiencies for estimating all and part of the parameters in a second-order model and obtain some general theoretical results. New

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... designs are constructed. They are more efficient than central composite designs and other existing designs. Supplementary materials are available online.