Selecting relevant effects in factorial designs

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...

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...

Equivalence of Fractional Factorial Designs

Two designs for a fractional factorial experiment are equivalent if one can be obtained from the other by reordering the treatment combinations, relabeling the factors and relabeling the factor levels. Designs can be viewed as sets of points in pdimensional space, where p is the number of factors. It is shown that, in this setting, two designs are equivalent if the Hamming distances between the...