Sensitivity Analysis with Central Composite Design
Also known as: SA-CCD, CCD sensitivity analysis, RSM sensitivity analysis, response surface sensitivity study
Sensitivity analysis with Central Composite Design (CCD) combines a structured, space-filling experimental layout with a systematic examination of how much each input factor drives changes in the response. CCD supports estimation of a full quadratic response surface model; sensitivity analysis then interrogates that model to rank factors by influence, identify interactions, and map the performance landscape — guiding engineers and researchers toward robust operating conditions and efficient optimisation.
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When to use it
Use this approach when you need to understand and optimise a continuous response that depends on multiple quantitative factors, particularly in engineering, chemical process development, pharmaceutical formulation, or manufacturing contexts where you can control experimental conditions precisely. CCD is ideal when you suspect curvature in the response — if you expect a purely linear surface, a two-level factorial is sufficient and CCD is overkill. Avoid this combination when factors are categorical only, when the number of factors exceeds roughly 7 (the run count becomes large; consider Definitive Screening Designs instead), when experimental units are expensive and few replicates are feasible without a centre block, or when the system is so stochastic that the quadratic model cannot be fitted reliably.
Strengths & limitations
- Estimates a full quadratic response surface model in fewer runs than a full 3^k factorial, making it highly efficient for 2–5 factors.
- Rotatability ensures equal prediction variance at equal distances from the design centre, giving balanced sensitivity information across the factor space.
- Sensitivity analysis on the fitted model can rank all factors and interactions without additional experiments, focusing resources on truly important variables.
- Centre-point replicates simultaneously provide an estimate of pure experimental error and allow a formal lack-of-fit test.
- Directly supports multi-response optimisation via desirability functions once sensitivities are understood.
- Run count grows quickly with the number of factors: a CCD for k=5 requires at least 50 runs including replicates, which may be prohibitive in expensive or slow experiments.
- The quadratic model may not capture highly non-linear or discontinuous responses; sensitivity indices derived from a mis-specified model are unreliable.
- Local sensitivity indices (partial derivatives at a point) may not represent global behaviour when factor ranges are wide or the surface is complex.
- Assumes that the experimental region is continuous and that factors can be set precisely; measurement error in factor settings inflates residual variance and biases sensitivity estimates.
Frequently asked
How is this different from simply running a factorial design and then doing sensitivity analysis?
A two-level factorial can only fit a linear model with interactions; it cannot detect or model curvature. CCD adds axial points specifically to enable estimation of quadratic (curved) terms, which are essential when the response has a maximum or minimum within the factor space. Sensitivity analysis on a linear model misses the curvature-driven behaviour that CCD is designed to capture.
What is the difference between local and global sensitivity analysis in this context?
Local sensitivity is the partial derivative of the fitted response surface at a specific point (usually the centre or optimum) — it tells you how the response changes per unit change in a factor at that exact location. Global sensitivity (e.g., Sobol indices) integrates over the entire factor space and accounts for both factor range and interactions. For wide factor ranges or strongly non-linear surfaces, global indices can reverse the ranking produced by local derivatives.
How many centre-point replicates should I include?
Three to five centre-point replicates are the standard recommendation. Fewer than three provide an unreliable estimate of pure error and weaken the lack-of-fit test. More than five typically yield diminishing returns in precision, though additional replicates may be warranted when experimental variability is known to be high.
Can I use this approach with a computer simulation instead of physical experiments?
Yes, but with important adjustments. Computer experiments are typically deterministic (no random error), so pure-error estimation is meaningless and centre-point replicates serve only to check numerical reproducibility. In deterministic settings, Gaussian process (kriging) surrogates often outperform polynomial response surfaces, and variance-based Sobol indices are the preferred global sensitivity measure.
What should I do if my quadratic model shows significant lack-of-fit?
First, inspect residual plots for outliers or non-constant variance that might be corrected with a response transformation (log, square-root). If the surface is genuinely non-quadratic, consider augmenting the design with additional points to support a higher-order model or a cubic spline surface, or switch to a non-parametric surrogate such as kriging before recomputing sensitivity indices.
Sources
- Box, G. E. P., & Wilson, K. B. (1951). On the Experimental Attainment of Optimum Conditions. Journal of the Royal Statistical Society: Series B, 13(1), 1–45. link ↗
- Montgomery, D. C. (2017). Design and Analysis of Experiments (9th ed.). Wiley. ISBN: 978-1119113478
How to cite this page
ScholarGate. (2026, June 3). Sensitivity Analysis with Central Composite Design. ScholarGate. https://scholargate.app/en/experimental-design/sensitivity-analysis-with-central-composite-design
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
- Box-Behnken DesignExperimental design↔ compare
- Central Composite DesignExperimental design↔ compare
- Full Factorial DesignExperimental design↔ compare
- Response Surface MethodologyExperimental design↔ compare