Constructing Large Orthogonal Minimally Aliased Response Surface Designs by Concatenating Two Definitive Screening Designs

TL;DR

This paper introduces a new construction method for large orthogonal minimally aliased response surface designs by concatenating two definitive screening designs, enhancing design properties while reducing computational complexity.

Contribution

The paper proposes a novel concatenation approach for constructing large OMARS designs that improves statistical features and reduces computational demands compared to existing methods.

Findings

The new designs exhibit reduced aliasing among second-order effects.

The concatenation method enhances the statistical efficiency of the designs.

Compared to existing designs, the proposed method is more computationally feasible for larger problems.

Abstract

Orthogonal minimally aliased response surface (OMARS) designs permit the study of quantitative factors at three levels using an economical number of runs. In these designs, the linear effects of the factors are neither aliased with each other nor with the quadratic effects and the two-factor interactions. Complete catalogs of OMARS designs with up to five factors have been obtained using an enumeration algorithm. However, the algorithm is computationally demanding for designs with many factors and runs. To overcome this issue, we propose a construction method for large OMARS designs that concatenates two definitive screening designs and improves the statistical features of its parent designs. The concatenation employs an algorithm that minimizes the aliasing among the second-order effects using foldover techniques and column permutations for one of the parent designs. We study the properties of the new OMARS designs and compare them with alternative designs in the literature.