A weighted D-optimality criterion for constructing model-robust designs in the presence of block effects

Abstract

It is generally known that blocking can reduce unexplained variation, and in response surface designs block sizes can be pre-specified. This paper proposes a novel way of weighting D-optimality criteria obtained from all possible models to construct robust designs with blocking factors and addresses the challenge of uncertainty as to whether a first-order model, an interaction model, or a second-order model is the most appropriate choice. Weighted D-optimal designs having 2 and 3 variables with 2, 3, and 4 blocks are compared with corresponding standard D-optimal designs in terms of the DN -efficiencies. Effects of blocking schemes are also investigated. Both an exchange algorithm (EA) and a genetic algorithm (GA) are employed to generate the model-robust designs. The results show that the proposed Dw -optimality criterion can be a good alternative for researchers as it can create robust designs across the set of potential models.

Keywords

• experimental design
• d-optimality
• weak heredity
• genetic algorithm