Practical choices for space‐filling designs

• Published in: Quality and reliability engineering international 2022-04, Vol.38 (3), p.1165-1188
• Main Authors: Lu, Lu, Anderson‐Cook, Christine M., Martin, Miranda, Ahmed, Towfiq
• Format: Article
• Language: English
• Subjects: Chemical engineering; comparable input ranges; constrained regions; Design of experiments; Experiments; maximin and minimax designs; non‐uniform space‐filling designs; ranked versus direct weights |non‐uniform weight comparison plot|proportional weight distribution plot
• ISSN: 0748-8017; 1099-1638
• DOI: 10.1002/qre.2884

Space‐filling designs are now commonly used as a flexible model‐free strategy for providing good coverage throughout an input space of interest for a variety of computer and physical experiment design scenarios. Some of the preliminary choices about how to frame the problem and which type of design to use can have a substantial impact on the success or failure of the experiment, and yet how to make these critical choices is often under‐emphasized in the literature. In this paper, we explore several of the practical choices required by the experimenter and describe a sequence of steps to help create an ideal design that matches the goals and constraints of the experiment. These choices include the specification of the input space, the scaling of the variables, the degree of uniformity of the design points across the input space, and the space‐filling characteristics. In addition, some new tools for defining the weights to implement non‐uniform space‐filling designs are provided. The methods are demonstrated with several illustrative examples and a real‐world chemical engineering experiment for carbon capture.