Selecting significant effects in factorial designs: Lenth’s method versus the Box-Meyer approach

Box-Hunter resolution extends to arbitrary fractional factorial designs

In a 1961 paper, Box and Hunter defined the resolution of a regular fractional factorial design as a measure of the amount of aliasing in the fraction. They indicated that the maximum resolution is equal to the minimum length of a defining word. Since then, various approaches have been offered to generalize the concept of resolution to arbitrary (possibly mixed-level) fractions. These have gene...

On the definition of effects in fractional factorial designs

This paper simplifies a previous exposition of Rao’s 1947 proof of his inequalities for orthogonal arrays. A key issue in the proof is the way in which one defines effects in a fractional factorial design. Here we replace the definition used in the earlier exposition with a simpler one, based on a more obvious interpretation of what Rao wrote and more in line with common practice, and show that...

Testing Multiple Dispersion Effects in Unreplicated Fractional Factorial Designs

In unreplicated 2kp designs, the assumption of constant variance is commonly made. When the variance of the response differs between the two levels of a column in the effect matrix, that column produces a dispersion effect. In this article we show that two active dispersion effects may create a spurious dispersion effect in their interaction column. Most existing methods for dispersion-effect t...

Model-Robust Factorial Designs

Multistratum Fractional Factorial Designs

Recent work on multistratum fractional factorial designs is set in a general and unified framework, and a criterion for selecting multistratum fractional factorial designs that takes stratum variances into account is proposed. Application of the general theory is illustrated on designs of experiments with multiple processing stages, including split-lot designs, blocked strip-plot designs, and p...