A note on selection of basis quantities for dimensional analysis

Abstract

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.

Keywords:

• Classification
• dimension reduction
• linear regression
• variable selection

Additional information

Notes on contributors

Ching-Chi Yang

Ching-Chi Yang is an Assistant Professor of Mathematical Sciences at the University of Memphis. He received a doctoral degree in Statistics from The Pennsylvania State University in 2019. His primary interests focus on industrial and engineering statistics, statistical learning, dimensional analysis, response surface methodology, and data mining. His related research projects vary from response surface methodology, tropical cyclone predictions, to stock price predictions. He has received awards including the American Society for Quality 2018 Fall Technical Conference Student Scholarship, and Jack and Eleanor Pettit Scholarship in Science from Penn State University.

Dennis K. J. Lin

Dennis K.J. Lin is the Department Chair of Purdue University. His research interests are quality assurance, industrial statistics, data mining, and response surface. He has published near 250 SCI/SSCI papers in a wide variety of journals. He currently serves or has served as associate editor for more than 10 professional journals and was co-editor for Applied Stochastic Models for Business and Industry. Dr. Lin is an elected fellow of ASA, IMS, and ASQ, an elected member of ISI, and a lifetime member of ICSA, and a fellow of RSS. He is an honorary chair professor for various universities, including a Chang-Jiang Scholar at Renmin University of China, Fudan University, and National Chengchi University (Taiwan). His recent awards include the 2004 Faculty Scholar Medal Award (Penn State), the Youden Address (ASQ, 2010), the Shewell Award (ASQ, 2010), the Don Owen Award (ASA, 2011), the Loutit Address (SSC, 2011), the Hunter Award (ASQ, 2014), the Shewhart Medal (2015), and the SPES Award at the Joint Statistical Meeting (2016). Dr. Lin has just been selected as the 2020 Deming Lecturer at the Joint Statistical Meetings.