D-optimal response surface designs in the presence of random block effects

The purpose of this paper is to help the reader in designing D-optimal blocked experiments. The block effects are assumed to be random. Therefore, in general, the optimal designs depend on the extent to which observations within one block are correlated. An algorithm is presented that produces D-optimal designs for these cases. However, in three specific situations, the optimal design does not depend on the degree of correlation. These situations include some cases where the block size is greater than or equal to the number of model parameters, the case of minimum support designs and orthogonally blocked first-order designs. In addition, a relationship is established between the design of experiments with random block effects and the design of experiments with fixed block effects. Finally, it is shown that orthogonal blocking is an optimal design strategy.