Application of Box–Behnken Design for Multivariable Optimization of Analytical Absorbance Response

Abstract

Response Surface Methodology (RSM) based on the Box–Behnken Design (BBD) was applied to optimize the absorbance response by evaluating the effects of pH, reagent volume, and extraction time. A total of 15 experimental runs were conducted to investigate the interaction and quadratic effects of the variables. The experimental data were fitted to a second-order polynomial model and analyzed using analysis of variance (ANOVA). The results demonstrated that all linear and quadratic terms significantly affected the absorbance response, while the interaction terms showed insignificant effects. Three-dimensional response surface and contour plots successfully described the interaction patterns among variables and identified the optimum experimental region. The optimum conditions were predicted at pH 5.25, reagent volume 2.27 mL, and extraction time 11.6 min, resulting in a maximum predicted absorbance response of 0.8070. Overall, the developed RSM model showed excellent predictive capability and proved effective for optimizing analytical conditions and improving response performance.