Blocking OMARS designs and definitive screening designs

Abstract

The family of orthogonal minimally aliased response surface or OMARS designs comprises traditional response surface designs, such as central composite designs and Box-Behnken designs, as well as definitive screening designs. Key features of OMARS designs are the facts that they are orthogonal for the main effects and that the main effects are not at all aliased with any two-factor interaction effect or with any quadratic effect. In this article, we present a method to arrange the runs of an OMARS design in blocks of equal size, so that the main effects can be estimated independently from the blocks, and the interaction effects and the quadratic effects are confounded as little as possible with the blocks. We show that our new method for blocking OMARS designs offers much flexibility when it comes to choosing the number of runs, the number of blocks and the block sizes, and that it often outperforms the blocking arrangements of definitive screening designs available in the literature and in commercial software.

Keywords:

• foldover design
• mixed integer linear programming
• mixed-level OMARS design
• orthogonal blocking
• response surface design

Disclosure statement

The authors attempt to valorize their research on blocked and unblocked OMARS designs, through the creation of a web-based commercial software named EFFEX®.

Data availability statement

The data supporting the findings reported in this article are available within the article and its supplementary materials.

Additional information

Notes on contributors

José Núñez Ares

José Núñez Ares is a postdoctoral researcher within the group of Prof. Peter Goos at KU Leuven in Belgium. His research interests lie in design of experiments, data analysis and optimization. Together with Prof. Goos, he received the 2019 Shewell Award for the presentation “OMARSDesigns: Bridging the Gap between Definitive Screening Designs and Standard Response Surface Designs”. Besides his academic work, José is active in research valorization, allowing experimenters in business and industry to access state-of-the art results in design of experiments in an intuitive way.

Peter Goos

Peter Goos is a full professor at the Faculty of Bio-Science Engineering of KU Leuven, and at the Faculty of Business and Economics of the University of Antwerp, where he teaches various introductory and advanced courses on statistics and probability. His main research area is the statistical design and analysis of experiments. Besides numerous influential articles in various kinds of scientific journals, he published the books The Optimal Design of Blocked and Split-Plot Experiments, Optimal Experimental Design: A Case Study Approach, Statistics with JMP: Graphs, Descriptive Statistics and Probability and Statistics with JMP: Hypothesis Tests, ANOVA and Regression. For his work, Peter Goos has received three Shewell Awards, two Lloyd S. Nelson Awards and a Brumbaugh Award from the American Society for Quality, the Ziegel Award and the Statistics in Chemistry Award from the American Statistical Association, and the Young Statistician Award of the European Network for Business and Industrial Statistics (ENBIS).