My research activities are focused on orthogonal arrays that could be useful for statistical designs of experiments.

The columns correspond with experimental factors, which can be varied at will in experimentation. Examples are temperature of a liquid, coarseness of material, and variety of wheat. Each coumn-entry is a factor-setting. So the first factor has four settings and the remaining three factors have two settings each. For example, one may wish to include four formulations of detergents and two washing temperatures in an experiment on cleaning towels.

The 16 rows of the orthogonal array shown here correspond with different experiments, or runs. When carried out in practice, each experiment will result in the measurement of one or more output variables that characterize the product or process one is interested in. The purpose of the series of experiments is to establish a relation between the outputs and the factor settings.

The array in the example has strength t=3, because each triple of columns is a full factorial design in three factors (repeated if the triple consists of two-level factors only). This property is convenient when you look at observations averaged over the runs with a common level of one of the factors. For example, there are four such averages for the four-level factor. We can study the main effect of this factor by comparing the four averages. Because of the strength-3 property, the difference in averages of a factor is not affected by the joint effect of any pair of other factors.

Strength, run size, and level numbers of the factors are collectively called the parameters of an orthogonal array. In 2008, Pieter Eendebak and I started a collaboration which resulted in a tremendous collection of arrays with a wide variety of parameters.