Abstract: Minimum aberration is a popular method of selecting fractional factorial designs. Numerous extensions to the original methods have benefited fields of experimental design such as multi-stratum designs, multi-group designs, and multi-platform designs. However, most of these extensions are ad hoc, developed on case-by-case bases without strong statistical justifications or a unified rationale. As such, we provide a new perspective on minimum aberration using a Bayesian approach. Our theory includes a unified framework for minimum aberration and is easily applied to many situations. Furthermore, it enables experimenters to derive their own aberration criteria. Several theoretical results and three numerical illustrations are provided.

Key words and phrases: Bayesian, blocking, fractional factorial, mixed-level, multigroup, multi-platform, multi-stratum, split-plot, strip-plot.