A Class of Partially Replicated Two Level Fractional Factorial Designs

Abstract

Resolution III fractional factorial designs permit the uncorrelated estimation of all main effects under the assumption of no interactions among the factors and are often used in the initial phases of an experimental program to screen factors. Even in these experimental situations, it may be desirable to include partial replication of the design, thereby allowing for the unbiased estimation of the experimental error while maintaining the orthogonality of the main effects. It is often then possible to assess the no-interactions assumption by comparing the sample of confounded interactions with the pure error estimate. In this paper, a new class of partially replicated two-level fractional factorial designs based on Hadamard matrices is proposed. A method of constructing these designs is given and the relative performance of the designs is evaluated by comparing them with competing fractional factorial designs.