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 column-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 a strength of 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. 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.

In 2014, I had a sabbatical, which I spent mainly by creating an course on orthogonal array featuring computational exercises with Matlab. I taught the course a lot of times. Recently, I reformulated the exercises to take advantage of the open source Python OApackage, written by Pieter Eendebak and Alan Vazquez. Alan and I are currently involved in writing the book Orthogonal Arrays for Practical Experimentation to be published by Springer.