Series of asymmetrical second order partially rotatable designs

Abstract

Response Surface Methodology (RSM) is commonly employed to establish connections between factors and responses, aiming to identify the optimal variables for maximizing desired outcomes. The excessive use of nitrogen, particularly when compared to phosphate and potassium, poses agronomic and environmental challenges. Soil potassium and phosphorus levels are declining, and unbalanced fertilizer application may result from diverse response curves for individual optimal doses. Consequently, determining the balanced N, P, and K amounts for various crops is a significant challenge. RSM offers a solution by allowing the adjustment and optimization of fertilizer dosage. While RSM typically addresses quantitative factors, it can also be applied to qualitative factors like soil type, seed varieties, and irrigation methods. In such cases, research has demonstrated the effectiveness of RSM. A rotatable design is crucial as it guarantees equal in formativeness in all directions. This article introduces a series of cost-effective asymmetrical second-order partially rotatable designs, achieved through a reduced number of runs utilizing main effect plans.