Strongly Coupled Designs for Computer Experiments with Both Qualitative and Quantitative Factors

Computer experiments often involve both qualitative and quantitative factors, posing challenges for efficient experimental designs. Strongly coupled designs (SCDs) are proposed in this paper to balance flexibility in run size and stratification properties between qualitative and quantitative factor columns. The existence and construction of SCDs are investigated. When s⩾2 is a prime or a prime power, the constructed SCDs of λs3 runs can accommodate 2s−1 qualitative factors and a substantial number of quantitative factors. Furthermore, a series of SCDs with su rows and (u−3)s3 columns of quantitative factors are constructed, where u⩾4, with certain columns of quantitative factors achieving stratification in two or higher dimensions. The proposed SCDs achieve stratification between any two qualitative factors and all quantitative factors, which is superior to MCDs. With the number of levels of the qualitative factors given as s2, DCDs have λs4 rows, while SCDs have only λs3 rows, offering more flexibility. Furthermore, in the designs constructed in this paper with fewer than 100 rows, in 11 out of 17 cases, SCDs have a larger number and higher levels of qualitative factors than DCDs.