R - Optimal Design Algorithm For Quadratic Response Surface Model

The R- optimality criterion introduced by Dette [JRSS, B,59(1997),97-110] minimizes the volume of Bonferroni t- intervals, and it is invariance on linearly transformed design spaces. The present paper is devoted to how to construct the R- optimal designs for second-order response surface models with k≥1 predictors. An equivalence theorem are given as an important tool for determining the R- optimal designs in methodology of optimal designs.The algorithms are given for constructing the R- optimal designs for second-order response surface models on the k- dimensional unit cube and ball, respectively, by the constraint condition from R- optimal designs. At the same time obtains the numerical solution of the R- optimal design when 2≤k≤25. According to the result above, calculate the D- efficiency of R- optimum design and we can find that the efficiency of second-order response surface in the cube is not less than 97%, and it is closing to one when k is increas-ing. Meanwhile, the efficiency in unit ball is not less than 94%, it is closing to one too.There is much loss in efficiency in using the general rounded designs, when the sample size is small. Therefore, rounds R- optimal approximate design by means of Adams method and shows the result for k= 2,3,4 when sample size is n. Compares the rounded ap-proximate design with R- optimum design, it will obtain that R- efficiency is good when k= 2,3,4. And R- efficiency will increases by adding sample point. Meanwhile, com-pares it with D- optimal design, and calculates the efficiency, we can find that efficiency of rounded approximate design remained above 92%.