Some new designs for quantitative factors

D optimal designs are given for some incomplete quadratic models in linear regression The quadratic models are incomplete in the sense that not all quantitative factors have quadratic terms The experimental region is a q dimensional cube Two methods are developed to construct small designs for quantitative factors The rst method uses the new concept of design generator The second uses properties of D optimal designs for the incomplete quadratic model An application of a design with experiments is included Key words Phrases D optimal designs approximate theory linear regression incomplete quadratic models quantitative factors design generator orthogonality exact designs Many designs for quantitative factors have been developed during the past years They are very economical as regards the number of designs points needed in spite of the fact that many of these designs such as some response surface plans use levels for each facto