A mathematical framework for predicting tablet weight variability from blend particle size distribution and tooling...

Tablet weight variability is a critical quality attribute in solid oral dosage manufacturing. Despite its practical importance, existing approaches for relating tablet weight variability to formulation and tooling parameters remain largely empirical. In this work, we develop a first-principles statistical model that predicts tablet weight variability as a function of tablet weight, punch diameter, and blend particle size distribution. The model builds on particle-sampling theory used in content uniformity analysis and explicitly incorporates tooling geometry and particle size distribution to describe the statistical origins of weight variability. Experimental data spanning multiple punch diameters, tablet weights, and particle sizes were generated using Suglets® spheres to validate the model. The predicted scaling relationships with tablet mass, punch diameter, and particle size were independently confirmed, and a single scaling factor was sufficient to capture the full dataset with high accuracy (R² ≈ 0.93, normalized RMSE ≈ 0.05). Model robustness was demonstrated using bootstrap resampling and a leave-one-out cross-validation scheme. The framework was further applied to quantitatively assess commonly used empirical relationships between particle size and tooling dimensions and to construct design maps illustrating their combined effects on tablet weight variability. This work provides a predictive framework for understanding and controlling tablet weight variability.