Central Composite Design — Response Surface Experimental Design
Central Composite Design for Response Surface Methodology · Also known as: CCD, Box-Wilson design, central composite response surface design, rotatable central composite design
Central Composite Design (CCD) is a second-order response surface design that allows researchers to efficiently fit a full quadratic model relating multiple continuous input factors to one or more response variables. Introduced by Box and Wilson in 1951, it combines a factorial (or fractional factorial) core, axial (star) points, and center-point replicates into a single unified design, making it the most widely used design for process optimization in engineering, chemistry, and manufacturing.
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When to use it
Use CCD when you need to fit a second-order (quadratic) model to map and optimize a continuous response over a region of k quantitative factors (typically k = 2–6). It is the standard choice in process optimization studies in chemical engineering, pharmaceutical development, food science, and manufacturing when you expect curvature in the factor–response relationship or when a first-order model has already shown significant lack of fit. CCD is preferred over Box-Behnken design when you can afford (or need) factor settings at the extreme axial points beyond the factorial range, and over a 3^k full factorial when run economy matters. Do NOT use CCD with categorical factors, binary or count response variables, or when the experimental region is geometrically constrained such that the axial points fall outside feasible operating ranges (in which case a Box-Behnken or D-optimal design is more appropriate). Also avoid CCD if a first-order model with a steepest-ascent strategy has not yet been used to move the design to the vicinity of the optimum — fitting a quadratic far from the optimum wastes runs.
Strengths & limitations
- Efficiently estimates all coefficients of a full second-order polynomial with fewer runs than a 3^k factorial design.
- Rotatability: the face-centered or rotatable CCD provides equal prediction variance at all points equidistant from the design center, giving uniform predictive precision.
- Center-point replicates provide an independent estimate of pure error, enabling a valid lack-of-fit test.
- Flexible: can be built sequentially — run the factorial core first (as a screening design), then augment with axial and center points if curvature is detected.
- Well supported in standard statistical software (JMP, Minitab, R rsm package, SAS PROC RSREG).
- Requires all factors to be continuous and quantitative; cannot handle categorical factors without modification.
- Axial points at distance alpha > 1 extend beyond the factorial cube, which may be infeasible when factor levels are physically constrained.
- As k grows (k > 5), the total run count increases rapidly and resource demands become substantial.
- The quadratic model is a local approximation; if the true response surface has higher-order nonlinearity, the CCD model may still show lack of fit near the optimum.
Frequently asked
What is the difference between a face-centered CCD and a rotatable CCD?
In a face-centered CCD (alpha = 1) the axial points lie on the faces of the factorial cube, so all factor settings stay within the [-1, +1] range — useful when axial excursions are not feasible. In a rotatable CCD alpha = (2^k)^(1/4), placing axial points farther out; this gives equal prediction variance at all points the same distance from the center (rotatability) but requires factor levels beyond the factorial range. Choose face-centered when physical constraints prevent extreme settings; choose rotatable when uniform predictive precision across the design sphere is the priority.
How many center-point replicates should I use?
The standard recommendation is 3–6 center-point replicates. Three is the practical minimum to get a meaningful lack-of-fit test and a stable pure-error estimate. Using 5–6 center points improves the stability of the variance estimate and is advisable when experimental noise is expected to be high. More than six center points rarely add proportionate value and increase total run count.
Can I use CCD when I have more than six factors?
Yes, but run economy deteriorates. For k > 5 the full 2^k factorial core becomes expensive, so practitioners typically substitute a resolution V fractional factorial, creating a fractional central composite design. Software such as JMP or Minitab automates this construction. For k > 6 a D-optimal or I-optimal computer-generated design often provides a more run-efficient alternative to any classical CCD.
How does CCD compare to Box-Behnken design?
Both are second-order response surface designs for k >= 3 factors. CCD includes corner (factorial) points plus axial points plus center points; Box-Behnken uses only edge midpoints and center points, so it never requires factor combinations at the extreme corners of the design space. Box-Behnken is preferred when corner settings are physically dangerous or infeasible and when alpha > 1 axial points cannot be achieved. CCD is preferred when corner settings are feasible and when the sequential (augmentation) strategy is desired, because the factorial block can serve double duty as an earlier screening experiment.
What software can I use to set up and analyze a CCD?
All major statistical packages support CCD: Minitab (Response Surface > Central Composite), JMP (Custom Design or Response Surface platform), SAS PROC RSREG, and R with the rsm package (ccd() function). The rsm package is freely available and provides full design generation, model fitting, and surface plotting in one workflow.
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. DOI: 10.1111/j.2517-6161.1951.tb00067.x ↗
- Montgomery, D. C. (2017). Design and Analysis of Experiments (9th ed.). Wiley. ISBN: 978-1119492443
How to cite this page
ScholarGate. (2026, June 3). Central Composite Design for Response Surface Methodology. ScholarGate. https://scholargate.app/en/experimental-design/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
- Design of experimentsExperimental design↔ compare
- Response Surface MethodologyExperimental design↔ compare