Quick Input‐Response Space‐Filling (QIRSF) Designs

ABSTRACT Standard space‐filling designs are robust choices when little is assumed about the underlying relationship and the focus is on good spread or coverage throughout the input space. In some applications, historical or subject matter expertise can provide knowledge about an assumed plausible model(s) connecting inputs and response(s). By incorporating this information, it is possible to think about good space‐filling in both the input space and across the range of anticipated response values. In this paper, we propose an efficient scalable algorithm, QIRSF, that allows for quick construction of Pareto front solutions for flexibly balancing different emphases on input and response space‐filling criteria from which the experimenter can select the best option for their experiment. The proposed method has the following advantages: (1) It is dramatically faster than construction of the original IRSF designs; (2) It can handle both discrete and continuous design spaces; (3) It allows easy adaptation for considering different space‐filling characteristics; and (4) It offers a close approximation of the Pareto front of IRSF designs for maximizing spread of design points across the input and response spaces. As a result of these advantages, it allows convenient and computationally affordable solutions for higher‐dimensional experiments with a flexible number of input and response variables than the IRSF designs. The new algorithm is illustrated with several examples. A new graphical tool, named the Distance Fractional Design Space (DFDS) plot, is introduced to summarize the coverage of design points in each of the input and response spaces.