Trend-Free Run Orders of Mixed-Level Fractional Factorial Designs

Construction of Efficient Fractional Factorial Mixed-Level 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...

Indicator function and complex coding for mixed fractional factorial designs

In a general fractional factorial design the n levels of each factor are coded by the n-th roots of the unity. This device allows a full generalization to mixed designs of the theory of polynomial indicator function already introduced for binary designs by Fontana and the Authors (2000). Properties of orthogonal arrays and regular fractions are discussed.

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...