Efficient asymmetric response surface designs for mixed quantitative and qualitative factors

Verma, Ankita and Jaggi, Seema and Varghese, Eldho and Varghese, Cini and Bhowmik, Arpan and Datta, Anindita and Dalal, Ashutosh (2025) Efficient asymmetric response surface designs for mixed quantitative and qualitative factors. International Journal of Advances in Engineering Sciences and Applied Mathematics, 17. pp. 266-278. ISSN 0975-5616

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Abstract

Response Surface Methodology (RSM) is most effectively applied in scenarios involving multiple input factors that influence a specific performance measure or quality characteristic of a product or process. Agricultural experiments often present cases where both qualitative and quantitative factors are critical. For instance, in fertilizer studies, crop yield is affected not only by the amount of fertilizer applied (a quantitative factor) but also by the method of application, such as broadcasting, placement behind the plough, or foliar spraying (a qualitative factor). This paper presents a systematic approach to developing response surface designs (RSDs) that integrate both symmetric and asymmetric levels in quantitative factors. We provide a list of designs for 3–10 factors, along with evaluations of G- and D-efficiency, highlighting the high efficiency of the proposed designs. Additionally, the methodology for constructing a third-order design with v-1 quantitative factors and one qualitative factor is outlined. Using SAS IML, macro was developed to facilitate generation of moment matrices, calculating unique variances of estimated responses, and determining D- and G-efficiency for the proposed designs. Furthermore, an R package, MixedLevelRSD, has been developed to generate efficient response surface designs accommodating mixed levels of qualitative and quantitative factors, along with other asymmetrical designs.

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