Efficiency of Custom A-, D-, and I- Optimal Designs Relative to CCD, BBD, and MCCD

Abstract

The efficiencies of custom A-, D-, and I-optimal designs are compared with the CCDs, BBDs, and MCCDs on standard and non-standard second-order models using the D-, G-, and A-efficiency metrics. Custom A-, D-, and I-optimal designs are constructed for the standard models but for the non-standard model, custom A-, D-, and I-designs with sample sizes 13, 15, 21, and 25 respectively are adapted from Iwundu and Israel (2024). The results of the evaluation of the designs are presented. The results show that for standard models, custom A-, D-, and I-optimal designs performed as well as the CCD but outperformed the BBD. Specifically, the D-optimal designs are more D-efficient. The A-, and I-optimal have the same result as the CCD for the three variables. For non-standard models, custom A-, D-, and I-optimal designs have larger efficiency values than the CCDs, BBDs, and MCCDs for specified design sizes. The D-optimal designs have larger D- and G-efficiency values. A-optimal designs have larger A-efficiency values and in most cases have the same efficiency value as the I-optimal design. Thus, custom designs can be adopted in the design of experiments for reliable and consistent results that meet experimental objectives.