Modifying 22 Factorial Designs to Accommodate a Restricted Design Space

Abstract

With standard designs we typically assume that the factor space is a p-dimensional hypercube or hypersphere, with any point inside or on the boundary of the shape being a candidate design point. However, some economical, practical, or physical constraints may occur on the factor settings resulting in an irregular experimental region. One often encounters situations in which it is necessary to eliminate some portion of the design space where it is infeasible or impractical to collect experimental data. Hence, standard designs are not always feasible, and the need arises for best possible designs under these restrictions. For the two-factor case with one corner of the square design space excluded, we propose a strategy for defining the new design space and three designs. These involve either reducing the factor levels to make a smaller but standard factorial design fit or modifying the levels of the variables at the excluded corner to locate the runs in the feasible design region. We discuss properties of these designs and relative tradeoffs.