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B0981
**Title: **Enumeration and evaluation of orthogonal three-level designs with small number of runs for definitive screening
**Authors: **Haralambos Evangelaras - University of Piraeus / University of Piraeus Research Center (Greece) **[presenting]**

Viktor Trapouzanlis - University of Piraeus (Greece)

**Abstract: **A class of three-level designs for definitive screening in the presence of second-order effects has been previously introduced. These designs are called Definitive Screening Designs (DSD), they possess a foldover structure and guarantee that (i) the estimates of main effects are not biased by two-factor interactions, (ii) the two-factor interactions are not completely confounded with each other, and (iii) the quadratic effects are orthogonal to main effects and not completely confounded with two-factor interactions. With respect to the number of runs, these designs require (2k+1) runs to study k quantitative factors since their construction uses a suitable k x k matrix C, its foldover and a center point. Therefore, each column of the DSD has (k-1) elements equal to +1, (k-1) elements equal to -1 and three zeros so, is mean orthogonal. It must be noted, however, that not all (2k+1) x k such matrices have orthogonal columns. We search for small n x k orthogonal three-level designs that possess the attractive properties of a DSD. Complete lists of non-isomorphic designs are given for n <= 33 runs (n odd) and 2 <= k <= (n-1)/2 columns. We further evaluate the constructed designs for their efficiency to estimate the parameters of second-order models, using the popular D-efficiency criterion. This work has been partly supported by the University of Piraeus Research Center.

Viktor Trapouzanlis - University of Piraeus (Greece)