Selection of Second Order Models’ Design Using D-, A-, E-, T- Optimality Criteria

Abstract

There are numerous designs for fitting second order models that can be used in conjunction with the response surface methodology (RSM) technique in optimization processes, be it in agriculture, industries and so on. Some of the designs include the equiradial, Notz, San Cristobal, Koshal, Hoke, Central Composite and Factorial designs. However, RSM can only be applied in conjunction with a single design at a time. This research aimed at choosing a design out of the most widely employed designs for fitting 2nd order models involving 3 factors for optimization of French beans in conjunction with the RSM technique. The most commonly used designs for second order models were first identified as Box-Behnken designs, Hoke D2 and Hoke D6 designs, 3k factorial designs, CCD face centred, CCD rotatable and CCD spherical. Design matrices for these 7 designs were formed and augmented with 5 centre points (chosen through lottery methods), and information and optimal design matrices were formed. Then, for each design, the analysis of D-, A- E-, T- optimality (D-Determinant, A-Average Variance, E-Eigen Value and T-Trace) was carried out according to Pukelsheim’s definitions. The results were ranked for each criterion and the ranks corresponding to each design were averaged. The design chosen was Hoke D2 with the least average- 1.75. The Hoke D2 was found to be optimal in minimizing the variance of prediction and the most economical design among the seven. The findings are in agreement with other researchers and scientist that a design may be optimal in one criterion but fails in another criterion. Further, Hoke designs are in the class of the economical designs. It is recommended that more optimality criteria be applied and a wide range of designs be involved to see whether the results would still agree with these findings.