Selecting baseline designs using a minimum aberration criterion when some two-factor interactions are important

ABSTRACT

This article considers the problem of selecting two-level designs under the baseline parameterisation when some two-factor interactions are important. We propose a minimum aberration criterion, which minimises the bias caused by the non-negligible effects. Using this criterion, a class of optimal designs can be further distinguished from one another, and we present an algorithm to find the minimum aberration designs among the D-optimal designs. Sixteen-run and twenty-run designs are summarised for practical use.

Keywords:

• Efficiency criterion
• fractional factorial design
• isomorphic design
• isomorphic model
• orthogonal array
• robust parameter design

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by Natural Sciences and Engineering Research Council of Canada [Discovery Grant].

Notes on contributors

Anqi Chen

Anqi Chen, is currently studying biostatistics, working towards her PhD at Simon Fraser University. She obtained her BSc and MSc in 2017 and 2019, respectively, from the same institution.

Cheng-Yu Sun

Cheng-Yu, a PhD student in statistics, is working towards his PhD at Simon Fraser University. His research interest is in experimental design, and has published one paper prior to this one.

Boxin Tang

Boxin Tang, a professor of statistics at Simon Fraser University, conducts research in the area of experimental design. He is an elected Fellow of ASA and IMS, and has published more than 60 papers in refereed journals.