Abstract: The baseline parametrization for two-level factorial designs has been receiving increasing attention recently. While the orthogonal parametrization is appropriate for experiments where the two levels of each factor are symmetrical, the baseline parametrization is well suited for experiments where the two levels of each factor are asymmetrical and one level, called a baseline level, is the default level. This paper considers a general situation where some factors have a baseline level while others do not. A mixed parametrization of factorial effects is proposed and its connection with the existing parametrizations is established. Under this new parametrization, we show that orthogonal arrays continue to be optimal for estimating main effects, and then put forward two minimum aberration criteria for further design selection. Both theoretical and algorithmic constructions of minimum aberration designs are examined and useful designs are obtained.

Key words and phrases: Baseline parametrization, contamination, orthogonal array.