On construction of optimal mixed-level supersaturated designs

TL;DR

This paper develops methods for constructing optimal mixed-level supersaturated designs that avoid full aliasing and control nonorthogonality, enhancing factor screening efficiency in experimental design.

Contribution

It introduces new construction techniques for mixed-level SSDs using equidistant designs and difference matrices, providing many new optimal designs with controlled nonorthogonality.

Findings

New optimal mixed-level SSDs are constructed and tabulated.

Methods effectively prevent fully aliased columns.

Nonorthogonality is well controlled by source designs.

Abstract

Supersaturated design (SSD) has received much recent interest because of its potential in factor screening experiments. In this paper, we provide equivalent conditions for two columns to be fully aliased and consequently propose methods for constructing $E(f_{\mathrm{NOD}})$- and $\chi^2$-optimal mixed-level SSDs without fully aliased columns, via equidistant designs and difference matrices. The methods can be easily performed and many new optimal mixed-level SSDs have been obtained. Furthermore, it is proved that the nonorthogonality between columns of the resulting design is well controlled by the source designs. A rather complete list of newly generated optimal mixed-level SSDs are tabulated for practical use.