Space-filling designs and robust orthogonal arrays

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Experimental design is an area of study in statistics that deal with efficient methods for collecting data for scientific and technological investigations. Factorial designs are a broad class of experimental plans for studying the relationship between a response variable and several explanatory variables. The proposed research centers on the study of two classes of designs: orthogonal arrays for physical experiments and space-filling designs for computer experiments. All these designs can be regarded as factorial designs. The usefulness of factorial designs is well documented in the literature. One major field where they have found and are continuing to find huge success is the manufacturing industries. Improving the quality of the exsiting products or designing new products all require the use of factorial designs. Today, we are seeing more and more fields in which factorial designs are successfully used. Examples are management, marketing, financial services, drug discovery, and computer software testing, to mention a few. In addition to being directly useful as discussed above, factorial designs form a basis on which other useful designs, such as those in response surface methodology, can be built. At an even more theoretical level, the study of factorial designs is very important because of their intimate relationship with combinatorics and graph theory.