Novel univariate and chemometrics-aided UV spectrophotometric methods were tailored to undergo the fundamentals of green and white analytical chemistry for the simultaneous estimation of a ternary mixture of olanzapine (OLA), fluoxetine HCL (FLU), and its toxic impurity 4-(Trifluoromethyl) phenol (FMP) without any prior separation. The dual-wavelength ratio spectrum univariate method was used to determine OLA and FLU in the presence of FMP in the range of (4–20) and (5–50) μg/ml, respectively. In compliance with the International Conference on Harmonization (ICH) standards, the technique was validated and established Remarkable accuracy (98–102%) and precision (< 2%) with limits of quantification (LOQs) of 0.432 and 2.002 μg/ml, respectively. Partial least squares (PLS) and artificial neural networks (ANNs) are chemometric methodologies that have advantages over the univariate method and use significant innovations employing Latin hypercube sampling (LHS), allowing the generation of a reliable validation set to guarantee the effectiveness and sustainability of these models. The concentration ranges used were (2–20), (2–20), and (5–50) μg/ml; for PLS, the LOQs were 0.602, 0.508, and 1.429 μg/ml, and the root mean square errors of prediction (RMSEPs) were 0.087, 0.048, and 0.159 for OLA, FMP, and FLU, respectively; and for ANNs, the LOQs were 0.551, 0.465, and 0.965 μg/ml, with RMSEPs of 0.056, 0.047, and 0.087 for OLA, FMP, and FLU, respectively. The developed methods yield a greener National Environmental Methods Index (NEMI) with an eco-scale assessment (ESA) score of 90 and a complementary Green Analytical Procedure Index (complex GAPI) in quadrants with an analytical greenness metric (AGREE) score of 0.8. The Red‒Green–Blue 12 algorithm (RGB 12) scored 88.9, outperforming on reported methods and demonstrating widespread practical and environmental approval. Statistical analysis revealed no noteworthy differences (P > 0.05) among the proposed and published techniques. Both pure powders and pharmaceutical capsules were analyzed via these methods.
