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

• Main Authors: Peang-or Yeesa, Patchanok Srisuradetchai, John J. Borkowski
• Format: Article
• Language: English
• Published: Prince of Songkla University 2020-12-01
• Series: Songklanakarin Journal of Science and Technology (SJST)
• Subjects: experimental design; d-optimality; weak heredity; genetic algorithm
• Online Access: https://rdo.psu.ac.th/sjstweb/journal/42-6/13.pdf

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.