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Related Concept Videos

Design Example: Managing Concrete Workability01:14

Design Example: Managing Concrete Workability

This example deals with managing the workability of concrete for a raft foundation project under hot weather conditions. Workability is crucial for ensuring the concrete is easy to place, compact, and finish. In this scenario, a slump test — a common method to measure the workability of fresh concrete — initially indicated low workability. This was attributed to the rapid water loss from the concrete mix, exacerbated by the high temperatures causing the course aggregates to heat up.
To address...
Methods of Medium Optimization01:28

Methods of Medium Optimization

Optimizing growth media enhances microbial proliferation and maximizes product yield. Statistical experimental design methodologies provide structured and reproducible approaches, offering progressively higher levels of robustness and efficiency.The One-Factor-at-a-Time (OFAT) MethodThe One-Factor-at-a-Time (OFAT) method involves adjusting a single variable while keeping all others constant. However, it cannot detect interactions between variables, often leading to suboptimal outcomes when...
Stress Concentrations in Circular Shafts01:18

Stress Concentrations in Circular Shafts

Consider the elastic torsion formula, which applies to a circular shaft with a consistent cross-section. This formula assumes that the shaft's ends are loaded with rigid plates firmly attached. However, in many cases, torques are applied to the shaft through mechanisms like flange couplings or gears, which are connected by keys inserted into keyways. This application method modifies the stress distribution near the point of torque application, causing it to deviate from the distributions...
Transmission Shafts: Problem Solving01:09

Transmission Shafts: Problem Solving

Designing a solid shaft that transmits power from a motor to a machine tool involves a series of calculations to ensure the shaft can withstand the stresses applied by bending moments and torques. First, calculate the torque exerted on the gear, considering the power transmitted by the shaft and its rotational speed. Following this, compute the tangential forces acting on the gears, which directly relate to the torque and the gear radius.
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Thin-Walled Hollow Shafts01:15

Thin-Walled Hollow Shafts

In analyzing a thin-walled hollow shaft subjected to torsional loading, a segment with width dx is isolated for examination. Despite its equilibrium state, this segment faces torsional shearing forces at its ends. These forces are quantitatively described by the product of the longitudinal shearing stress on the segment's minor surface and the area of this surface, leading to the concept of shear flow. This shear flow is consistent throughout the structure, indicating a uniform distribution of...
Weighted Mean00:57

Weighted Mean

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Surrogate Model Development for Digital Experiments in Welding
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A mathematical framework for predicting tablet weight variability from blend particle size distribution and tooling

Rajarshi Sengupta1, Y-H Kiang1, Behzad Changalvaie1

  • 1Drug Product Technologies, Process Development, Amgen Inc., One Amgen Center Drive, Thousand Oaks, CA, 91320, USA.

Journal of Pharmaceutical Sciences
|June 19, 2026
PubMed
Summary

This study introduces a physics-based statistical model to predict tablet weight variability in pharmaceutical manufacturing. The model accurately forecasts weight variations based on tablet properties, punch size, and particle distribution, improving quality control.

Keywords:
CompressionMathematical model(s)Particle sizePediatricSolid dosage formsTablet(s)

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Area of Science:

  • Pharmaceutical Manufacturing
  • Materials Science
  • Statistical Modeling

Background:

  • Tablet weight variability is a critical quality attribute in pharmaceutical manufacturing.
  • Current methods for predicting weight variability are primarily empirical.
  • A need exists for a predictive framework grounded in first principles.

Purpose of the Study:

  • To develop a first-principles statistical model for predicting tablet weight variability.
  • To incorporate formulation and tooling parameters into the model.
  • To provide a quantitative understanding of factors influencing weight variation.

Main Methods:

  • Developed a statistical model based on particle-sampling theory.
  • Integrated tablet weight, punch diameter, and blend particle size distribution into the model.
  • Validated the model using experimental data from Suglets® spheres across various parameters.

Main Results:

  • The model accurately predicts tablet weight variability (R² ≈ 0.93, normalized RMSE ≈ 0.05).
  • Confirmed predicted scaling relationships with tablet mass, punch diameter, and particle size.
  • Demonstrated model robustness through resampling and cross-validation techniques.

Conclusions:

  • The developed framework provides a predictive tool for understanding and controlling tablet weight variability.
  • Enables quantitative assessment of empirical relationships and construction of design maps.
  • Offers a pathway to optimize formulation and tooling for consistent tablet quality.