A note on selection of basis quantities for dimensional analysis

Dimensional analysis transforms a dimensionally homogeneous model into its simplest form; the number of input variables can be reduced. Such a reduction is very helpful in statistical design and analysis. Although the Buckingham π theorem provides a method of transforming the model based on the basis quantities (BQ’s), the choice of the BQ’s in general is not unique. In practice, a different choice of the BQ’s may lead to a different performance in statistical analysis. A new criterion, based on the BQ’s with a small coefficient of variation, is proposed to choose the optimal BQ’s. It is anticipated that such a criterion will be popularly used in practice. The distribution of the newly proposed criterion is derived to statistically differentiate the performance via different choices of the BQ’s. Three case studies are provided for illustration.