Common Terms in Design of Experiments (DoE)

Design of Experiments (DoE), is a statistical method used to prepare the plan, implement, analyze, and interpret experiments. By systematically changing the inputs (independent variables) and observing the changes in the outputs (dependent variables), we can better understand the relationships between these factors and optimize a process or product.

Key concepts in DoE:

• Design: Based on the objective and the number of factors to be studied, the type of experimental design is selected to construct the experiments efficiently. Common experimental designs include full factorial design, fractional factorial design, central composite design, and Box-Behnken design. Based on the type of experimental design selected, the level and number of runs are also determined.
• Factor: are input variables that are changed in the experimental design, related to raw material properties/process parameters to see their influence on the target product quality. For example: API particle size, compression force, blending time and speed, etc.
• Level: is the number of values ​​examined of a factor in an experimental design. For example, if the factor is blending time, the three possible levels are 5, 10, and 15 minutes.
• Response: is the output variable of the experiment that you want to optimize or study. For example: solubility, abrasion, blending uniformity (%RSD),…
• Experimental design model (Design model): based on regression equations to establish mathematical relationships between factors and results from experiments. These relationships are expressed through polynomial regression models: first-order linear models, often used to screen important factors, higher-order non-linear models (second-order, third-order, …) used for optimization purposes.

Evaluate an experimental design model.

• Analysis of Variance (ANOVA): performed to test the significance of the selected model with F-Value >>1 & p < 0.05, which helps to identify the significant factors.
• Model fit is assessed based on key parameters:
  • R² (R-squared): This index measures how much of the variation in the experimental design data can be predicted by the model. The closer the R² value is to 1, the better the experimental design model fits.
  • Adjusted R²: Similar to R² but adjusted for the number of factors in the model. Often used when there are many factors to avoid overcomplicating the model without actually improving accuracy.
  • Predicted R²: indicates how well the model can accurately predict the output values ​​(responses) for a different dataset, independent of the dataset used to build the model. A high Predicted R² (close to 1) indicates that the model has good predictive ability for new data. This value should be less than R-squared of about 0.2.
  • Residuals: Analyzes the deviations between the experimental data and the values ​​predicted by the experimental model. The smaller the residuals, the better the model fits.
  • Lack of fit:Shows the ability to match the actual value with the model. Lack of fit test is usually performed in a model with replicate points and is evaluated on the p-value of ANOVA.
  • Curvature effect and center point: The center point is defined as the point with the average value of the highest and lowest levels (-1;0;+1). The center point is included in the model to evaluate the linearity of the linear regression equation. In case the center point has a significant effect (p-value < alpha), the model is said to have a curvature effect and higher-order models such as RSM, CCD need to be performed.

Through these parameters, we can evaluate the DoE model comprehensively, ensuring that the model is accurate, reliable and useful in predicting and optimizing the process.

References:

1. “(PDF) Design of Experiment (DoE) Step Guide © by Shivang Chaudhary from QbD-ExpertTM.”
2. How to Select DESIGN for DoE © by Shivang Chaudhary QbD-ExpertTM
3. QbD Model of Generic IR ‘Solid Oral Uncoated Tablets’ FBP Process © by Shivang Chaudhary QbD-ExpertTM