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...

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...

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.

Factor screening with statistical control makes sense in the context of simulation experiments that have random error, but can be run automatically on a computer and thus can accommodate a large number of replications. The discrete-event simulations common in the operations research field are well suited to controlled screening. In this paper two methods of factor screening with control of Type...

Random Forests are a powerful classification technique, consisting of a collection of decision trees. One useful feature of Random Forests is the ability to determine the importance of each variable in predicting the outcome. This is done by permuting each variable and computing the change in prediction accuracy before and after the permutation. This variable importance calculation is similar t...

Fractional factorial split-plot design has been widely used in many fields due to its advantage of saving experimental cost. The general minimum lower order confounding criterion is usually as one the attractive for selecting fractional design. In this paper, we are interested theoretical construction methods optimal designs under criterion. We present several conditions.