We consider the design of dimensional analysis experiments when there is more than a single response. We first give a brief overview of dimensional analysis experiments and the dimensional analysis (DA) procedure. The validity of the DA method for univariate responses was established by the Buckingham Π-Theorem in the early 20th century. We extend the theorem to the multivariate case, develop basic criteria for multivariate design of DA and give guidelines for design construction. Finally, we illustrate the construction of designs for DA experiments for an example involving the design of a heat exchanger.
Bibliographical noteFunding Information:
We are grateful to the editor, associate editor, and two anonymous referees whose comments led to a much improved version of this manuscript. This work was partially supported by NIH grant NICHD 1DP2HD091799-01.
© 2019, © 2019 American Statistical Association and the American Society for Quality.
- Buckingham Π-theorem
- Coordinate exchange algorithm
- Optimal design
- Robust-DA design