Geometric Aliasing, Generalized Deening Relations, and Grr Obner Basis: a New Look at Multi-level Factorial Designs

Multi-level factorial designs are useful in experiments but their aliasing structure are complex compare to two-level fractional factorial designs. A new framework is proposed to study the complex aliasing of those designs. Geometric aliasing is deened for factorial designs. It generalize of the aliasing relation of regular two level fractional fac-torial designs to all factorial designs. Based on geometric aliasing, generalized deening relations are deened for a large group of factorial designs. They determine the complete geometric aliasing structure of a design. The mathematical tools for studying geometric aliasing are available in computational algebraic geometry. Two examples are pre-1 sented to show how this methodology can be used to reveals structure of factorial designs.