An Aliasing Measure of Factor Effects in Three-Level Regular Designs

For three-level regular designs, the confounding from the perspectives of both factor and component effects leads to different results. The aliasing properties of factor effects are more significant than the latter in the experimental model. In this paper, a new three-level aliasing pattern is proposed to evaluate the degree of aliasing among different factors. Based on the classification pattern, a new criterion is introduced for choosing optimal three-level regular designs. Then, we analyze the relationship between the criterion and the existing criteria, including general minimum lower-order confounding, entropy, minimum aberration, and clear effects. The results show that the classification patterns of other criteria can be expressed as functions of our proposed pattern. Further, an aliasing algorithm is provided, and all 27-run, some of the 81-run, and 243-run three-level designs are listed in tables and compared with the rankings under other criteria. A real example is provided to illustrate the proposed methods.