Fast flexible space‐filling designs with nominal factors for nonrectangular regions

Abstract

AbstractSpace‐filling designs allow for exploration of responses when each continuous input factor is set to many different values over its range. While typical space‐filling designs treat all the input factors as continuous, some problems necessitate the use of nominal input factors. In such cases, it is desirable that the design for the continuous inputs only be space‐filling, as well as the subdesign of the continuous factors for each level of a nominal input. In this article, we present a solution that takes both aspects into account and allows the experimenter to balance between the space‐filling properties of the design ignoring the nominal inputs versus subdesigns on each level of nominal inputs. Space‐filling designs commonly employ rectangular design spaces. However, it is sometimes necessary to place constraints on the design region where some regions of the design space are impossible or undesirable to run. In addition to incorporating nominal factors, the methods presented in this article generate space‐filling designs that have the flexibility to accommodate nonrectangular design regions.