Optimality Criteria for Third order rotatable designs constructed through balanced incomplete block design

Abstract

In the design and analysis of experiments for estimating statistical models, optimal designs allow parameters to be estimated with minimum variance. These designs are generated based on a particular optimality criterion and are generally optimal only for a specific statistical model. The purpose of this study 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. A general method of evaluating alphabetic optimality for TORD constructed using BIBD in k-factors was determined. Further a compound optimality for D- and T- was evaluated for TORD constructed from BIBD. From the existing TORD constructed using BIBD, the design matrix, and moment matrix considering full parameter system were used. The existing methods were utilized to evaluate alphabetic optimality and DT-optimality for the designs from their information matrices. Evaluation of alphabetic optimality was done and D-, A-, T-, E-, I- and G- optimal designs were obtained. The study evaluated DT- compound optimality and determined DT- optimal design. A general method of evaluating alphabetic optimality for TORD constructed from BIBD in k-factors was also determined. In conclusion, the study showed that the designs’ optimal values decreased with the increase in the number of factors for D-, G- and T- optimality. However, all the designs under investigation were found to be E-optimal. The values of DT-optimality increases as the number of factors increase implying that DT-compound optimality is appropriate for design with few factors. The study recommends the application of optimum designs in the design and analysis of field experiments