| The standard design practice treats factor screening and response surface exploration as different objectives and thus employs different designs (e.g., fractional designs and central composite designs respectively). A unified approach is proposed that can achieve both in a single design. Its main advantage over response surface methodologies is the economy derived from using a single to achieve both objectives. Its rationale is based on a two-stage analysis strategy, which performs factor screening, identifies a few significant factors, and then fits a response surface for these factors. What designs can facilitate both factor screening and response exploration? Contrary to a classical observation of Box and Wilson (1951), 3 designs can be utilized to achieve both objectives. The orthogonality properties of 3 designs make them qualified for factor screening. A criterion called eligible projection is proposed to evaluate the performance of 3 designs after significant factors are identified. For response surface exploration, we use model isomorphism (a generalization of combinatorial isomorphism) to further classify 3 designs. They are quite efficient for estimating first and second order effects in terms of D- and G-criteria. Corresponding properties of nonregular three-level designs, like OA(18,3 ) and OA(36,3 ), are also studied. Both are more efficient than the regular 3 designs for estimating first and second order effects. A new method is developed to construct novel nonregular 3 designs that are better than regular 3 designs in terms of screening and response surface exploration. |