Abstract

Fractional factorial designs under the baseline parameterization have

received significant attention, with two-level designs being the most popular due

to their simplicity. However, extending them to s-level designs for s ≥3 introduces additional challenges.

This paper explores the general theory of s-level

baseline designs for any s ≥3. Under the baseline parameterization, we demonstrate that orthogonal arrays maintain Ds- and G-optimality across all designs,

while also achieving As-optimality among balanced designs. We also establish

the connection between the wordlength pattern in orthogonal parameterization

and the K-value sequence of the designs under the baseline parameterization.

Finally, we propose a general method for minimum aberration baseline designs.

Information

Preprint No.SS-2025-0061
Manuscript IDSS-2025-0061
Complete AuthorsXinxin Xia, Fasheng Sun, Chunyan Wang
Corresponding AuthorsChunyan Wang
Emailschunyanwang@ruc.edu.cn

References

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Acknowledgments

The authors thank Editor Yi-Hau Chen, an associate editor, and two referees for their valuable comments and suggestions. This work was supported

by the National Natural Science Foundation of China (Grant Nos. 12301323

and 12371259), the Fundamental Research Funds for the Central Universities, China (2412023YQ003), and MOE Project of Key Research Institute

of Humanities and Social Sciences (22JJD110001).

Chunyan Wang and

Fasheng Sun are the corresponding authors.

Supplementary Materials

presents the proofs of theoretical results and lists

5-level approximate BP-MA designs and their K2 and K3 values for runs of

25, 50, 75, 100, and 125.

Supplementary materials are available for download.