Analytical Purity Determinations of Universal Food-Spice Curcuma longa through a QbD Validated HPLC Approach with Critical Parametric Predictors and Operable-Design’s Monte Carlo Simulations: Analysis of Extracts, Forced-Degradants, and Capsules and Tablets-Based Pharmaceutical Dosage Forms

Applications of analytical quality by design (QbD) approach for developing HPLC (High Performance Liquid Chromatography) methods for food components assays, and separations of complex natural product mixtures, are still limited. The current study developed and validated, for the first time, a stability-indicating HPLC method for simultaneous determinations of curcuminoids in Curcuma longa extracts, tablets, capsules, and curcuminoids’ forced degradants under different experimental conditions. Towards separation strategy, critical method parameters (CMPs) were defined as the mobile phase solvents’ percent-ratio, the pH of the mobile phase, and the stationary-phase column temperature, while the peaks resolution, retention time, and the number of theoretical plates were recognized as the critical method attributes (CMAs). Factorial experimental designs were used for method development, validation, and robustness evaluation of the procedure. The Monte Carlo simulation evaluated the developing method’s operability, and that ensured the concurrent detections of curcuminoids in natural extracts, commercial-grade pharmaceutical dosage-forms, and the forced degradants of the curcuminoids in a single mixture. The optimum separations were accomplished using the mobile phase, consisting of an acetonitrile–phosphate buffer (54:46 v/v, 0.1 mM) with 1.0 mL/min flow rate, 33 °C column temperature, and 385 nm wavelength for UV (Ultra Violet) spectral detections. The method is specific, linear (R2 ≥ 0.999), precise (% RSD < 1.67%), and accurate (% recovery 98.76–99.89%), with LOD (Limit of Detection) and LOQ (Limit of Quantitation) at 0.024 and 0.075 µg/mL for the curcumin, 0.0105 µg/mL and 0.319 µg/mL for demethoxycurcumin, and 0.335 µg/mL and 1.015 µg/mL for the bisdemethoxycurcumin, respectively. The method is compatible, robust, precise, reproducible, and accurately quantifies the composition of the analyte mixture. It exemplifies the use of the QbD approach in acquiring design details for developing an improved analytical detection and quantification method.