Abstract: Factorial and fractional factorial designs are widely used for assessing the impact of several factors on a process. Frequently, restrictions are placed on the randomization of the experimental trials. The randomization structure of such a factorial design can be characterized by its set of randomization defining contrast subspaces. It turns out that in many practical situations, these subspaces will overlap, thereby making it impossible to assess the significance of some of the factorial effects. In this article, we propose new designs that minimize the number of effects that have to be sacrificed. We also propose new designs, called stars, that are easy to construct and allow the assessment of a large number of factorial effects under an appropriately chosen overlapping strategy.
Key words and phrases: Block design, finite projective geometry, minimal -cover, split-lot design, split-plot design, -spread.