What are the advantages and disadvantages of using central composite design?

A Central Composite Design is a response surface design aimed at understanding and optimizing one or multiple responses. This design supports sequential experimentation, encompassing three key phases: 🔎 Screening: Identifying significant main effects and important interactions through a factorial design. 📈 Improvement: Detecting curvature or nonlinear responses using centre points. 🎯 Optimization: Estimating quadratic effects and seeking an optimum response using star/axial points. It provides cost-effective efficiency by fitting a complete quadratic model without the need to realize a three-level full factorial design.

A central composite design (CCD) is a statistical experimental design used to model and optimize responses by varying multiple factors. It consists of a combination of factorial, axial, and center points, allowing for the estimation of main effects, interactions, and quadratic effects. The design is typically used to identify the optimal levels of factors that maximize or minimize a response variable, and is particularly useful in response surface methodology (RSM) and design of experiments (DOE). By using CCD, researchers can efficiently explore the relationship between factors and responses, and identify the optimal conditions for a process or system.

Central Composite design is widely used for response surface modeling because of its properties : ➡️ Sequential construction possible from a screening/factorial design ➡️ Minimum number of treatment combinations to estimate main effects, 2-factors interactions and quadratic effects ➡️ Estimation of the responses nonlinearity through quadratic effects ➡️ Suitable for blocking: A central composite design can always be separated into a factorial block and an axial point block ➡️ Constant prediction variance for all points equidistant from the design center (Rotability property) ➡️ Good lack of fit detection ➡️ Graphical analysis possible through simple tools (scatterplots, contour plot, 3D surface plot...)

The central composite design is used for optimisation purposes, that is when the influential factors are identified. The primary feature of the CCD is its sequential nature. The structure is the following: - Base design: Based on complete or fractional factorial - Centre points: to estimate the experimental error - Axial points: to account for curvature (non-linear effects) Efficiency: Best among symmetric and balanced designs Assumption: The experimental error is the same everywhere within the experimental domain.

A central composite design (CCD) is used in various fields, including food science, pharmaceuticals, and engineering, to optimize processes and products by modeling complex relationships between multiple variables. It is particularly useful in situations where interactions and curvature are expected, such as in product formulation, process optimization, and quality improvement. CCD is commonly applied in response surface methodology (RSM) to identify optimal conditions, predict responses, and reduce variability in systems, making it an essential tool in research, development, and quality control.

✳️ The position of star points (on face, rotatable, orthogonal) has an influence on the design performances. The farthest the star points are from the centre of the experimental space : ➡️ The higher the power for main effects and quadratic effects, but the lower the power for the intercept, ➡️ The higher the variance in the centre of the experimental space, but the lower the variances at the border of the experimental space. Choosing the right position of the star points in this design depends on the objectives and knowledge about the system. If the centre point is very close to the optimal point, then it's appropriate to choose an inscribed design type, so that variance in the centre of the experimental space is the lowest possible.

To create a central composite design (CCD), define the number of factors (variables) and levels, then construct the design using a combination of factorial, axial, and center points. Start with a full or fractional factorial design, add axial points (±α) to estimate curvature, and include multiple center points to assess variability. The design can be rotated or scaled to improve its properties. Use design software or statistical tools, such as Design-Expert or R, to generate the CCD, specifying the number of factors, levels, and points, and ensuring the design is orthogonal and has adequate resolution.

🎯 Response Surface Methodology (RSM) involves a series of designed experiments (through designs like CCD), to fit a second-degree polynomial model. This model serves as an approximation of the response, enabling the identification of significant variables and optimization of the response. 📈 As a polynomial regression, RSM adheres to traditional regression assumptions, including a linear relationship between factors and response, normal distribution of the response (verified through residual normality checks), independence between factors, and homoscedasticity. 🎨 Graphical visualizations like scatterplots, contour plots, and 3D surface plots play a crucial role in results interpretation and the visualization of optimal conditions.

BI tools such as PowerBI or Tableau can integrate analysis features to derive summary statistics or graph illustrations. This analysis can be further enhanced with R or Python as a data input feature into the 2 platforms.

To analyze a central composite design (CCD), use statistical software to fit a response surface model, typically a quadratic polynomial, to the data. Perform analysis of variance (ANOVA) to assess model significance, and evaluate coefficients to identify significant factors and interactions. Use diagnostic plots, such as residual plots and normal probability plots, to check model assumptions. Generate response surface and contour plots to visualize relationships and identify optimal conditions. Perform optimization techniques, such as desirability functions or numerical optimization, to find the best combination of factors. Validate the model with confirmation experiments to ensure its accuracy and reliability.

The limitations of a central composite design (CCD) include: assumption of quadratic relationships, which may not always hold true; sensitivity to outliers and missing values; requirement of a large number of experiments for multiple factors; assumption of continuous variables, which may not apply to categorical factors; and potential for aliasing and confounding effects. Additionally, CCD can be computationally intensive, and the design may not be optimal for non-standard regions of interest. Furthermore, CCD assumes a fixed and known number of factors, and adding or removing factors can be challenging. Finally, CCD may not account for complex interactions or nonlinear effects beyond quadratic relationships.

Central Composite Design (CCD) presents a structured approach to experimental design, yet it comes with certain limitations : ➡️ As for any model-based design, it can be sensitive to model misspecifications, and may be hard to analyze in case of missing or failing experiments. ➡️ It requires a rigid pattern of symmetrically spaced data points which do not always fit the needs of engineering studies. ➡️ It is originally limited to continuous factors. ➡️ Circumscribed CCD may encounter impracticalities with axial points positioned beyond the region of interest, impacting feasibility and safety. ➡️ Additionally, CCD has lower power and precision for quadratic effects compared to alternative response surface designs like the Box Behnken design.

Most of the things are already written. I love CCD and in most of the situations you can adapt the design to the different limitations ... But there is a IMPORTANT limitation that is related to the nature of the system where you are doing experiments The main thing that makes ME hesitate between CCD or Box-Behken design is that CCC contain "corners" of the design, specially the conditions "all factors at low level" and "all factor at high level" and in same cases those conditions are to extremes. Box-Behken design however gives more smooth conditions...but is is a little more complicated the other aspects....