Dimensional Analysis and Statistics

• Activity Number: 298
• Type: Contributed
• Date/Time: Tuesday, August 5, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): Weijie Shen*+ and Dennis K.J. Lin
• Companies: Penn State and Penn State
• Keywords: Buckingham's Pi-Theorem ; Design of Experiment ; Dimension Reduction ; Statistical Analysis ; Additive Index Model

Abstract

Dimensional Analysis (DA) is a well-developed widely-employed methodology in the physical and engineering sciences. The implementation of DA before physical experimentation results in reductions of variables and primary insights of their relationships. The application of DA in statistics leads to three advantages: (1) the reduction of the number of potential causal factors that we need to consider, (2) the analytical insights into the relations among variables that it generates, and (3) the scalability of results. The formalization of the DA method in statistical design and analysis would give a clear view on its generality and overlooked significance. In this talk, we first provide general procedures for DA prior to statistical design and analysis. We then derive the sufficiency and completeness of DA variables and propose a proper analysis model tailored to the DA structure. Several numerical examples are provided to assess the significance and generality of DA. We compare results obtained via the DA approach to those via conventional approaches. From that, we recommend the DA approach based on its favorable performance.