Modeling the Yield of Glycine max (L.) Merrill Using Mixture Process Variable Model within an Optimal Split-Plot Design

Abstract

A mixture design has become famous in statistical modeling in a mixture process variable experiment owing to its usefulness in modeling the blending surface that predicts the response of any mixture empirical. The mixture blends included manure from cows, chickens, goats, and sheep while the process variable was seeding rate of Glycine max seeds and the pH of the soil. The effect of variety of the seed used was established through variation of seeds per acre with uniform application of organic and inorganic fertilizer. This study's main aim was to determine the best desirable split-plot design for performing the Glycine max experiment with the settings mixture-process variables. The split-plot design (SPD) was used to solve the problem of restricted randomization. It constituted a simplex centroid design (SCD) of four design points of mixture components and  factorial design with a central composite design (CCD) of the process variable. We formulated a new Scheffe model and the proposed design for SPD for the combined second-order mixture process variable model with CCD.  We used the restricted maximum likelihood method to approximate values for  parameter models within the SPD. We also found the effect of mixture component at vertices of components of the mixture plus with interaction effect between mixture and process variable to have the highest impact on the growth and pod development of Glycine max. The optimum total yield of Glycine max for variety R184 and Blyvoor used in Bushel per acre was 180.53 and 219. 217, respectively on the Whole Plot with a pH of soil being 5.4. The mean response maximum optimum yield for the total number of pods per plant and seeds per pod of Glycine max were found to be 32.30 and 2.331, respectively. We recommend using SPDs in experiments involving mixture settings formulations to measure the interaction effects of both the mixture components and the processing conditions like a pH of the soil and seeding rate.