Optimal Third Order Rotatable Designs Constructed from Balanced Incomplete Block Design (BIBD)

In the design of experiments for estimating statistical models, optimal designs allow parameters to be estimated without bias and with minimum variance. Optimal designs are experimental designs that are generated based on a particular optimality criterion and are generally optimal only for a specific statistical model. The purpose of this study therefore was to investigate the optimality criteria for third order rotatable designs (TORD) constructed from balanced incomplete block design (BIBD). Specifically the study obtained alphabetic optimality criteria for specific TORD in three, four, five and six factors. From the existing TORD constructed using BIBD, the design matrix, moment matrix and information matrix considering full parameter system were obtained. Evaluation of the alphabetic optimality criteria was done. However, all the designs under investigation were found to be E-optimal. E-optimality maximizes the minimum eigenvalue of the information matrix. Optimum TORD from BIBD can be applied in real life experiments.