Separating Location and Dispersion Effects in Unreplicated Fractional Factorial Designs

Abstract

Fractional factorial designs are often used in industry to screen potentially important factors in terms of their impact on the mean response, that is, their location effect. To save resources, these experiments are often unreplicated, in that only one observation is made at each design point. In addition to studying location effects, these designs may also be used to study dispersion effects. One of the difficulties in studying dispersion in these unreplicated designs is that dispersion effects are confounded with pairs of location effects. In this paper, we investigate the situation where a single dispersion effect is identified. We develop a procedure to determine the minimum number of additional runs needed to totally remove the confounding between this dispersion effect and two location effects. For situations where replication is not feasible, we develop a test for a pair of unidentified location effects conditioned on a single dispersion effect being detected. An example from the literature is used to demonstrate these two procedures.