A Proposed Inscribed-Doehlert Design for three-factor Spherical N-Point Design: Variation in Model Parameter Estimation
Abstract
This study considered and proposed three Factor Spherical N-point Design as applied to Variation in Model Parameter Estimation. Two quadratic models were considered: one contained all the parameters while the other model excluded the three interaction term s. The Box-Behnken, Central Composite Circumscribed, Central Composite Inscribed and Doehlert Designs were studied for these two quadratic models using the D-optimality criterion, Sum of Square Errors and Grand Means of the Designs. The study also proposed a 14-point Design from the Central Composite Inscribed and the Doehlert Designs. We found out that the determinant values of all the designs studied were higher for reduced model than for the full model and that the designs with smaller determinants usually produce larger Sum of Square Errors. We also ascertained that, as the centre points increase, the determinants of all the designs decrease for the full model, while the Box-Behnken Design has equal determinants for 1 and 2 centre points for the reduced model. The study found out that Box-Behnken Design was a better design for reduced model on the basis of Sum of Square Errors other than Central Composite Circumscribed design. Also, we found out that the reduced quadratic model was a better model for the three factor Spherical Second-Order Designs. The proposed design was found to be better than all the standard designs so far studied, because it gave smaller values of the sum of square errors and also better values of the AIC (Akaike Information Criterion) and SBC (Schwartz Bayesian Criterion) for both models and for all the 5 centre points added.
Keywords
Inscribed-Doehlert designBox Behnken designDoehlert design and Central
Composite design
References
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