Direct construction of three-level designs with less β-aberration

Abstract

The β-wordlength pattern has been justified as an appropriate criterion for measuring designs with quantitative factors. However, construction methods of designs with less β-aberration have not been fully investigated. In this paper, some properties of β-wordlength pattern for three-level designs will be firstly provided, and then a direct construction method is proposed to generate three-level designs with using 2-level orthogonal arrays. Subsequently, two methods of level rearrangement are discussed to reduce the β 3 and β 4 of the resultant designs. Moreover, the advantages of these two methods are also compared. Finally, numerical examples are presented to illustrate the effectiveness of the proposed methods.