Row‐column factorial designs with multiple levels

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...

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...

Generation of Fractional Factorial Designs

The joint use of counting functions, Hilbert basis and Markov basis allows to define a procedure to generate all the fractions that satisfy a given set of constraints in terms of orthogonality. The general case of mixed level designs, without restrictions on the number of levels of each factor (like primes or power of primes) is studied. This new methodology has been experimented on some signif...