# A Class of Multilevel Nonregular Designs for Studying Quantitative Factors

## TL;DR

This paper introduces a new class of multilevel nonregular fractional factorial designs for quantitative factors, offering improved estimation accuracy and screening efficiency over traditional regular designs, with a theoretical construction method.

## Contribution

It presents a novel permutation-based construction of multilevel nonregular designs, avoiding computer search and enhancing design properties for quantitative factor experiments.

## Key findings

- Nonregular designs outperform regular designs in effect estimation.
- The proposed designs exhibit superior space-filling properties.
- The sequential construction method simplifies design generation.

## Abstract

Fractional factorial designs are widely used for designing screening experiments. Nonregular fractional factorial designs can have better properties than regular designs, but their construction is challenging. Current research on the construction of nonregular designs focuses on two-level designs. We provide a novel class of multilevel nonregular designs by permuting levels of regular designs. We develop a theory illustrating how levels can be permuted without computer search and accordingly propose a sequential method for constructing nonregular designs. Compared to regular designs, these nonregular designs can provide more accurate estimations on factorial effects and more efficient screening for experiments with quantitative factors. We further explore the space-filling property of the obtained designs and demonstrate their superiority.