Construction of Fractional Factorial Design Considering Accuracy and Robustness in the Estimation of Main Effects

Abstract

: The 𝐷𝐷 -optimal criterion evaluates the accuracy of estimators comprehensively, with assuming a model that describes the relationship between response and factors in appropriate manner. By using a design with high 𝐷𝐷 optimality level, we can estimate parameters accurately under the assumed model. However, it should be noted that there exists bias in the estimator if active factors and their interactions are not included in the model. In order to reduce the bias of estimators caused by not incorporating active two-factor interactions in the model, we construct experimental design considering both accuracy and robustness against the existence of interactions. This research constructs robust fractional factorial design against the existence of two-factor interactions by distributing low level of confounding on two-factor interactions into main effects. New designs considering robustness and accuracy are obtained by multiple criteria optimization with this new criterion of robustness and 𝐷𝐷 𝑓𝑓 criterion that is a sort of 𝐷𝐷 -optimality. Various algorithms for constructing optimal designs have been proposed such as 𝑘𝑘 exchange and coordinate exchange. This study use the column wise-pairwise algorithm because of the advantage that it can be applied to supersaturated design. Also, we carry out multiple criteria optimization with reference to the method proposed by a previous study. In this way, we obtained 16×15 and 12×16 design matrixes, which is more robust to the existence of two-factor interactions than the conventional design.