Comparison8 min readJuly 15, 2026

Central Composite vs Box-Behnken: Which Design, When

Q: Which design has more statistical power, CCD or Box-Behnken?

For our 3-factor case, `covadoe_power_analysis` gave the 18-run CCD power 0.951 and the 16-run Box-Behnken power 0.887, both against a 10-term quadratic model at a 1.0 sigma effect and alpha 0.05. The CCD gains roughly 6 percentage points from its 2 extra runs. That gain only counts if the extra axial runs are actually feasible.

Central composite vs Box-Behnken on the same 3 factors: real CovaDOE run counts, axial points, power and the corners each design does not visit.

Oliver Kraft

CovaSyn

Central Composite vs Box-Behnken: Which Design, When

You have three factors, a screening study behind you, and you need a quadratic model to find an optimum and defend a design space. The textbook gives you two choices: central composite (CCD) or Box-Behnken (BBD). The choice is usually made on run count alone, which is the wrong reason - the real difference is which corners of your factor space each design asks you to actually run.

This article builds both designs on the same three factors using covadoe_create_design, then compares them with covadoe_compare_designs and covadoe_power_analysis. Every number below is verbatim tool output.

The short answer

Use Box-Behnken when the extreme corners of your factor space are chemically or operationally implausible, or when the axial points of a CCD would fall outside a feasible range. Use central composite when you can run the corners, want a wider explored region, and expect to augment an existing two-level factorial rather than start fresh.

The setup

Three factors, realistic ranges for a coupling reaction:

Temperature: 70 to 110 C
Catalyst loading: 1 to 6 mol%
Time: 4 to 14 h

Both designs were requested with n_center_points=4 so the centre replication is identical and the comparison is fair.

What the tool actually returned

covadoe_create_design with design_type="central_composite" returned 18 runs: 8 factorial corners, 6 axial (star) points, 4 centre points.

covadoe_create_design with design_type="box_behnken" returned 16 runs: 12 edge midpoints, 4 centre points. No corners, no axials.

	Central composite	Box-Behnken
Total runs (4 centre points)	18	16
Factorial corner runs	8	0
Edge midpoint runs	0	12
Axial / star runs	6	0
Distinct levels per factor	5	3
Max coded distance from centre	2.236 (axial)	1.414 (edge)
Visits extreme corner (+1,+1,+1)?	Yes	No
Runs outside the stated factor range?	Yes, 6	No

Source: two covadoe_create_design calls, same factor definitions, same n_center_points.

The finding that decides it: the CCD axials leave your range

This is the part that a run count comparison hides. The CCD axial points came back at a coded distance of plus/minus 2.236, which in real units means:

Axial run	Temperature (C)	Catalyst (mol%)	Time (h)
9	45.28	3.5	9.0
10	134.72	3.5	9.0
11	90.0	-2.09	9.0
12	90.0	9.09	9.0
13	90.0	3.5	-2.18
14	90.0	3.5	20.18

Two of those runs are not experiments. You cannot charge -2.09 mol% of catalyst, and you cannot run a reaction for -2.18 hours. A third, 134.72 C, is above the boiling point of a lot of common solvent systems.

That is the practical case for Box-Behnken in one table. The BBD never goes past the stated low/high on any factor - its most extreme run is an edge midpoint at coded radius 1.414, e.g. 110 C at 6 mol% and 9 h (mid time). Every one of the 16 runs is inside the box you told it about.

Two honest caveats on the CCD number. First, the coded axial distance of 2.236 is larger than the classic rotatable value for three factors, which is 2^(3/4) = 1.682. If rotatability matters to you, check the axial column of the returned design before you book instrument time rather than assuming a default. Second, if you cannot run the axials as returned, do not silently clip them to the range - a "face-centred" CCD (axials at plus/minus 1) is a different design with different variance properties, and you should request it deliberately.

Efficiency and power on the same problem

covadoe_compare_designs (goal optimization, same three factors, tool default centre points) ranked five candidates. Note the run counts differ slightly from the section above because this tool applies its own default centre replication (3, not 4):

Design	n_runs	D-efficiency	G-efficiency	Estimated power	Score
Box-Behnken	15	0.3664	0.8889	0.868	0.679
Central composite	17	0.0971	0.8257	0.940	0.598
Full factorial 2k	11	0.0	0.0	0.205	0.271
Definitive screening	9	0.0003	1.0256	0.0	0.191
D-optimal	10	0.0	0.0	0.0	0.190

Recommended: box_behnken. The bottom three rows nominally estimate the same terms, but with 9 to 11 runs against 10 model parameters they have essentially no residual degrees of freedom, which is what the zero power figures are telling you. The D-efficiency values are the tool's internal normalisation: treat them as a within-call ranking, not as a number to quote against another package.

Separately, covadoe_power_analysis on the 18-run CCD and 16-run BBD from the first section, both against a 10-term quadratic model at a 1.0 sigma effect and alpha 0.05:

CCD, n=18, 10 terms: power 0.951, error df 7
BBD, n=16, 10 terms: power 0.887, error df 5

So the CCD buys about 6 percentage points of power for 2 extra runs. Whether that is worth it depends entirely on whether those extra runs are the infeasible axials.

covadoe_suggest_design for 3 factors, goal optimization, returns central_composite as the default ("CCD provides full quadratic model for 3 factors") and lists Box-Behnken as the alternative that "avoids extreme corners". The two tools agree on the trade-off and weight it differently. That is the point: the call is a domain judgement, not a statistics one.

How to choose, in order

1. List the corners. Write down the 8 combinations of low/high on all three factors. If any of them would decompose the product, exceed a pressure rating, or produce an unmeasurable sample, drop the CCD. 2. Compute the axials. Take your centre plus/minus the returned alpha in real units. If any land below zero or outside equipment limits, either widen the factor range so the axials land inside it, or take the BBD. 3. Check whether you already have a factorial. If you ran a 2^3 screen, a CCD is cheap to reach - you add axials and centre points to what you already have (covadoe_augment_design). A BBD would mean starting over. 4. Then look at run count. Here the difference was 18 vs 16, rarely the deciding factor at 3 factors. It widens in BBD's favour at 4 and 5 factors.

One more physical constraint: BBD needs 3 levels per factor, CCD needs 5. If a factor is a discrete setting (a fixed rpm step, an available sieve cut), 3 levels may be all you can set.

What this comparison does not tell you

Nothing about your chemistry. These are geometry and variance properties of a design matrix. They cannot tell you whether a quadratic model is the right model, or whether your response is monotone across the range.
No lack-of-fit guarantee. Both designs support a lack-of-fit test only because of the replicated centre points. With 4 centre points you have 3 pure-error degrees of freedom. That is thin. If the model fails, you will know it failed but not much about why.
BBD extrapolates at the corners. The BBD never observes the corners, so any prediction there is extrapolation from a fitted quadratic. If your optimum drifts toward a corner, the BBD prediction is less trustworthy exactly where you care.
Power figures assume a model and a noise level. The 0.951 and 0.887 above are for a 1.0 sigma effect against a 10-term model. Halve the effect size and both collapse. Run covadoe_power_analysis with your own assay repeatability before you commit.
This is design support, not a filing. A design matrix from CovaDOE is a starting point for a study you still have to run, analyse and defend. It does not replace wet-lab confirmation runs or a validated statistical package in a regulatory submission.

Frequently asked questions

How many runs is a Box-Behnken design for 3 factors?

A Box-Behnken design for 3 factors has 12 edge-midpoint runs plus centre point replicates. With 4 centre points, covadoe_create_design returned 16 total runs; with 3 centre points it returns 15. There are no corner runs and no axial runs, so every run sits inside the low/high range you specify for each factor.

How many runs is a central composite design for 3 factors?

A full central composite design for 3 factors has 8 factorial corner runs, 6 axial (star) runs and centre replicates. With 4 centre points, covadoe_create_design returned 18 total runs. The axial runs sit outside the stated factor range, so the design uses 5 distinct levels per factor rather than 3.

Why do central composite axial points fall outside my factor range?

Axial points sit at a coded distance alpha from the centre, and alpha is greater than 1 in a standard (circumscribed) CCD. In our 3-factor example the tool returned alpha = 2.236, which put catalyst loading at -2.09 mol% and time at -2.18 h. Both are physically impossible, so you must either widen the range, use a face-centred CCD, or switch to Box-Behnken.

Which design has more statistical power, CCD or Box-Behnken?

For our 3-factor case, covadoe_power_analysis gave the 18-run CCD power 0.951 and the 16-run Box-Behnken power 0.887, both against a 10-term quadratic model at a 1.0 sigma effect and alpha 0.05. The CCD gains roughly 6 percentage points from its 2 extra runs. That gain only counts if the extra axial runs are actually feasible.

When should I prefer Box-Behnken over central composite?

Prefer Box-Behnken when the extreme factor combinations are implausible, when a factor has a hard floor at zero (concentration, time, pressure), or when you can only set three levels of a factor. Prefer CCD when you can run the corners, when you want to explore a wider region, or when you are augmenting an existing two-level factorial rather than starting a new study.

Can I turn a factorial screening design into a CCD?

Yes. A circumscribed CCD is a two-level factorial plus axial and centre points, so an existing 2^k screen can be augmented rather than repeated. covadoe_augment_design does this: in a previously documented CovaDOE run, a 13-run definitive screening design was augmented with 8 new runs (6 axial, 2 centre) into a 21-run CCD on three factors. Box-Behnken cannot be reached this way.