Algorithmic construction of RR-optimal designs for second-order response surface models

• An algorithm for constructing the RR-optimal designs for second-order models on the kk-cube is given.
• An algorithm for constructing the RR-optimal designs for second-order models on the kk-ball is given.
• The numerical results of RR-optimal designs for 2≤k≤252≤k≤25 are obtained by using the proposed algorithms.

The RR-optimality criterion introduced by Dette (1997) minimizes the volume of Bonferroni tt-intervals. The present paper is devoted to the construction of RR-optimal designs for second-order response surface models with k≥1k≥1 predictors. An equivalence theorem are given as an important tool for determining the RR-optimal designs. The algorithms are given for constructing the RR-optimal designs for second-order response surface models on the kk-dimensional unit cube and ball, respectively. Numerical results of the RR-optimal designs for 2≤k≤252≤k≤25 are obtained by using the proposed algorithms.