Strongly Coupled Designs for Computer Experiments with Both Qualitative and Quantitative Factors - Meng-Meng Liu; Min-Qian Liu; Jin-Yu Yang (Mathematics)
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 <semantics>s⩾2</semantics> is a prime or a prime power, the constructed SCDs of <semantics>λs3</semantics> runs can accommodate <semantics>2s−1</semantics> qualitative factors and a substantial number of quantitative factors. Furthermore, a series of SCDs with <semantics>su</semantics> rows and <semantics>(u−3)s3</semantics> columns of quantitative factors are constructed, where <semantics>u⩾4</semantics>, 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 <semantics>s2</semantics>, DCDs have <semantics>λs4</semantics> rows, while SCDs have only <semantics>λs3</semantics> 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.