Statistical Design of Experiments: An introductory case study for polymer composites manufacturing applications

¹ Operational Intelligence, Next Generation Enterprises and Institutions, Council for Scientific and Industrial Research, South Africa
² Department of Mechanical and Aeronautical Engineering, University of Pretoria, South Africa
³ Department of Statistics, North-West University, South Africa
⁴ Department of Chemical Engineering, University of Pretoria, South Africa

^* e-mail: nbotha1@csir.co.za
^** e-mail: helen.inglis@up.ac.za
^*** e-mail: roelof.coetzer@nwu.ac.za
^**** e-mail: johan.labuschagne@up.ac.za

Abstract

Statistical design of experiments (DoE) aims to develop a near efficient design while minimising the number of experiments required. This is an optimal approach especially when there is a need to investigate multiple variables. DoE is a powerful methodology for a wide range of applications, from the efficient design of manufacturing processes to the accurate evaluation of global optima in numerical studies. The contribution of this paper is to provide a general introduction to statistical design of experiments for a non-expert audience, with the aim of broadening exposure in the applied mechanics community. We focus on response surface methodology (RSM) designs — Taguchi Design, Central Composite Design, Box-Behnken Design and D-optimal Design. These different RSM designs are compared in the context of a case study from the field of polymer composites. The results demonstrate that an exact D-optimal design is generally considered to be a good design when compared to the global D-optimal design. That is, it requires fewer experiments while retaining acceptable efficiency measures for all three response surface models considered. This paper illustrates the benefits of DoE, demonstrates the importance of evaluating different designs, and provides an approach to choose the design best suited for the problem of interest.