Construction of Twenty-five Points Second Order Rotatable Design in Three Dimensions using Trigonometric Functions

This study focuses on the construction of (25SOR) in Three Dimensions (3D) engaging trigonometric functions. Designing experiments in multiple dimensions is crucial for efficiently exploring complex systems and optimizing various processes. The proposed methodology utilizes trigonometric functions to generate a set of experimental points that exhibit desirable properties, such as rotatability, orthogonality, and uniformity, in the three-dimensional space. By employing trigonometric transformations, a design with twenty-five equally spaced points is constructed, ensuring the ability to conduct thorough investigations across the entire experimental region. The advantages of utilizing trigonometric functions in the design construction process include the flexibility to achieve rotational symmetry and the capability to control the distribution of points systematically. The resulting 25SOR design facilitates comprehensive experimentation and enables researchers to efficiently evaluate response surfaces and identify optimal operating conditions in three-dimensional spaces. This approach holds promise for applications in various fields, including agriculture, where the exploration of multidimensional parameter spaces is essential for enhancing performance and efficiency.