LAUSR

The conditional main effect (CME) parameterization system resolves the long-standing aliasing dilemma of the traditional orthogonal components system for two-level regular fractional factorial designs. However, the algebra of the CME system is not yet fully understood, which impedes the development of general results on this system that possess a broad scope of application across designs. We establish a comprehensive algebra for the CME system based on indicator functions. Our algebra facilitates the derivations of general partial aliasing relations for a wide variety of two-level designs. By means of our algebra, we illuminate the implications of traditional design criteria under the CME system for resolution IV designs. A novel feature of our algebra is that it enables immediate and simple D-efficiency calculations for two-level regular designs and models consisting of multiple conditional and traditional effects.