Grouped Orthogonal Arrays and Their Applications

TL;DR

This paper introduces grouped orthogonal arrays as a new class of experimental designs tailored for additive models with disjoint variable groups, offering flexible construction methods and improved properties over existing designs.

Contribution

It proposes the concept of grouped orthogonal arrays for additive models, providing novel construction methods and practical design tables that outperform existing techniques.

Findings

More designs with flexible run sizes are generated.

Designs exhibit better within-group projection properties.

Construction methods are applicable for any prime power levels.

Abstract

In computer experiments, it has become a standard practice to select the inputs that spread out as uniformly as possible over the design space. The resulting designs are called space-filling designs and they are undoubtedly desirable choices when there is no prior knowledge on how the input variables affect the response and the objective of experiments is global fitting. When there is some prior knowledge on the underlying true function of the system or what statistical models are more appropriate, a natural question is, are there more suitable designs than vanilla space-filling designs? In this article, we provide an answer for the cases where there are no interactions between the factors from disjoint groups of variables. In other words, we consider the design issue when the underlying functional form of the system or the statistical model to be used is additive where each component depends on one group of variables from a set of disjoint groups. For such cases, we recommend using {\em grouped orthogonal arrays.} Several construction methods are provided and many designs are tabulated for practical use. Compared with existing techniques in the literature, our construction methods can generate many more designs with flexible run sizes and better within-group projection properties for any prime power number of levels.