Guide8 min readJuly 15, 2026

Augment a Screening DoE into a Response Surface

Q: How many runs do I need to augment a screening design to an RSM?

For three factors, `covadoe_augment_design` returned 8 new runs: 6 axial points plus 2 new centre points, with one existing all-centre screening run reused as the third centre point. Combined with the 13-run definitive screening design, that gives 21 runs for a 10-term quadratic model. A fresh central composite design over the same three factors needs 17 new runs.

Q: What do I check before trusting the augmented model?

Run `covadoe_residual_diagnostics` on the fitted model. It reports normality tests, Cook's distance and leverage per run, which is where a bad screening run or a batch shift between the screening and augmentation campaigns will show up. Then check whether the optimum sits inside the cube. An optimum on a boundary means you have not bracketed it.

Q: Does augmentation work for Box-Behnken or fold-over designs too?

`covadoe_augment_design` takes a `target_type` argument and supports axial, fold-over and Box-Behnken augmentation in addition to central composite. Fold-over is the right choice when your screen was a Resolution III fractional factorial and you need to break the alias between main effects and two-factor interactions before you go anywhere near a response surface.

How to augment a DoE design to an RSM: turn a 13-run screening design into a 21-run CCD with 8 new runs instead of starting over with 17.

Oliver Kraft

CovaSyn

Augment a Screening DoE into a Response Surface

You ran a screening design, found the three factors that matter, and now someone wants a response surface and a design space. The default move is to build a fresh central composite design and run it. That throws away every screening run you already paid for. It also, in most real processes, asks you to run experiments outside your equipment limits.

Augmentation is the alternative: keep the screening runs, add only the runs the quadratic model is actually missing, and fit one model on the combined set.

The worked example

Suzuki-type aryl halide coupling, six factors screened: temperature (60-120 C), catalyst loading (0.5-5 mol%), base equivalents (1-3), water fraction (0-20%), time (2-16 h), boronic acid equivalents (1-1.5).

Screening design: a 13-run definitive screening design from covadoe_create_design (design_type="definitive_screening"). Thirteen runs, six factors, main effects clear of two-factor interactions, and curvature detectable because the DSD carries three levels per factor. Run 13 is the all-centre run.

Screening flags temperature, catalyst loading and time as active. Base equivalents, water fraction and boronic acid equivalents come back inactive.

Now the question: what does it cost to get a quadratic model on the three survivors?

Option A: augment - 8 new runs

One call to covadoe_augment_design with selected_factors=["Temperature","Catalyst","Time"], target_type="central_composite", n_center_points=3, reuse_center_points=true.

Verbatim return:

"axial_runs": 6,
"new_center_runs": 2,
"reused_center_indices": [12],
"total_new_runs": 8,
"total_with_existing": 21,
"alpha": 1.0,
"augmentation_type": "factorial_to_ccd"

Six axial runs, two new centre runs, and index 12 (run 13, the all-centre run from the screen) reused as the third centre point. Eight new experiments. Twenty-one runs in the combined model.

Augmenting reuses the screening runs, so a quadratic response surface costs 8 new experiments instead of the 17 a fresh central composite design would need. Source: Run counts returned verbatim by covadoe_augment_design (target_type=central_composite, n_center_points=3, reuse_center_points=true) on the 13-run definitive screening design in this article.

The eight new runs, in real units:

Run	Temperature (C)	Catalyst (mol%)	Time (h)	Role
14	60.0	2.75	9.0	axial, low T
15	120.0	2.75	9.0	axial, high T
16	90.0	0.5	9.0	axial, low cat
17	90.0	5.0	9.0	axial, high cat
18	90.0	2.75	2.0	axial, short
19	90.0	2.75	16.0	axial, long
20	90.0	2.75	9.0	centre
21	90.0	2.75	9.0	centre

Option B: start over - 17 new runs

For comparison I built a fresh three-factor CCD over the same ranges with covadoe_create_design (design_type="central_composite", n_center_points=3). It returns 17 runs: 8 factorial, 6 axial, 3 centre, with coded alpha = 2.1213 (rotatable).

That design is statistically prettier. It is also not runnable. The axial points it asks for, in real units:

Temperature 26.36 C and 153.64 C
Catalyst -2.02 mol% and 7.52 mol%
Time -5.85 h and 23.85 h

Negative catalyst loading and negative reaction time. That is what a rotatable CCD does when you hand it your operating range as the factorial range: it extrapolates the star points by a factor of 2.12 beyond the cube. In practice you either shrink the factorial box (and lose signal) or clamp alpha to 1.0 and end up with the face-centred design augmentation gives you anyway.

Side by side

	Augment (Option A)	Start over (Option B)
New experiments	8	17
Runs in the fitted model	21	17
Residual df (10-term quadratic)	10	6
Axial style	alpha = 1.0, face-centred	alpha = 2.12, rotatable
Axial points inside equipment limits	yes	no (negative time and catalyst)
Power, 1.0 sigma effect	0.984	0.927
Power, 0.5 sigma effect	0.544	0.411

Run counts and alpha from covadoe_create_design and covadoe_augment_design. Power figures from covadoe_power_analysis at alpha = 0.05, n_terms = 10 (intercept, 3 linear, 3 quadratic, 3 two-factor interaction), residual_variance = 1.

Augmenting costs 9 fewer experiments and buys 4 more residual degrees of freedom, because the 13 screening runs come along for free.

More runs in the model means more power: the augmented design leads at a 1 sigma effect (0.984 vs 0.927) and at 0.5 sigma (0.544 vs 0.411). These are run-count based planning figures, not per-coefficient guarantees. Source: Computed with covadoe_power_analysis at alpha = 0.05, n_terms = 10 and residual_variance = 1 for the two design sizes in this article.

Why the reuse is legitimate

This only works if the factors you dropped were genuinely inactive. The 13 screening runs vary base equivalents, water fraction and boronic acid equivalents across their full ranges. The 8 augmentation runs specify only temperature, catalyst and time - you run those at your fixed setpoints for everything else.

So the combined data set is not clean unless one of these is true:

1. Screening showed the dropped factors have effects small relative to noise, and you accept their residual contribution as part of experimental error. This is the normal case and the reason you ran a screen first. 2. You keep the dropped factors in the model as linear covariates, spending 3 more degrees of freedom.

If screening did not clearly rule those factors out, do not pool. Fix them, and run a design in the three factors you care about. Augmentation is a reward for a screen that gave a clean answer, not a way around an ambiguous one.

What you do with the 21 runs

Fit a quadratic model with covadoe_fit_rsm, then covadoe_find_optimum for the setpoint and covadoe_design_space for the proven acceptable range. In a separate documented CovaDOE example (an 18-run CCD with simulated yield values, so treat the fit quality as illustrative and the tool behaviour as real), that chain returned R2 = 0.9988 (adjusted 0.9974), an optimum at 91.2 C / 3.76 mol% / 9.7 h predicting 93.5% yield with a 95% confidence interval of 93.16-93.76 and a prediction interval of 92.73-94.20, and a design space over 10,000 Monte Carlo samples where only 10.6% of the range passed a 90% yield spec. Run covadoe_residual_diagnostics before you believe any of it - on that data set it flagged Shapiro-Wilk p = 0.036 and Cook's D = 0.277 at run 9.

Honest limits

Face-centred is not rotatable. With alpha = 1.0 the prediction variance is not uniform at equal distance from the centre, and the pure quadratic terms are estimated less precisely than in a rotatable design. You are trading statistical elegance for runs you can actually perform.
The power numbers are run-count based. covadoe_power_analysis computes power from n_runs, n_terms and effect size, not from your specific model matrix. Treat 0.984 and 0.927 as planning figures for comparing design sizes, not as guarantees for a particular coefficient.
Augmentation adds a time block. The 13 screening runs and the 8 augmentation runs were made on different days, possibly different reagent lots. If you suspect a shift, add a block term and test it. Nothing in the augmentation output does this for you.
Extrapolation stays extrapolation. The face-centred design covers the cube you screened. Any optimum the RSM puts at a corner is a signal to run another campaign, not a setpoint.
This is decision support. A response surface built from 21 runs guides your next experiments and your control strategy discussion. It is not a validated method and it is not a filing.

Frequently asked questions

How many runs do I need to augment a screening design to an RSM?

For three factors, covadoe_augment_design returned 8 new runs: 6 axial points plus 2 new centre points, with one existing all-centre screening run reused as the third centre point. Combined with the 13-run definitive screening design, that gives 21 runs for a 10-term quadratic model. A fresh central composite design over the same three factors needs 17 new runs.

Can I reuse screening runs in a response surface model?

Yes, if the factors you dropped were shown to be inactive during screening. The screening runs vary those dropped factors, so their effect ends up in the residual. That is acceptable when screening showed the effects are small relative to noise. If the screen was ambiguous, either keep the dropped factors in the model as covariates or run a clean design in the surviving factors instead.

Why does the augmented CCD use alpha = 1.0 instead of a rotatable alpha?

Because a rotatable alpha extrapolates outside your operating range. For temperature 60-120 C, catalyst 0.5-5 mol% and time 2-16 h, a rotatable CCD with alpha = 2.12 asks for -2.02 mol% catalyst and -5.85 h reaction time. Alpha = 1.0 puts the axial points on the faces of the cube you already screened, so every run is physically executable.

Is augmenting statistically worse than running a fresh CCD?

Not in this case. The 21-run augmented design leaves 10 residual degrees of freedom against 6 for the 17-run fresh CCD, and covadoe_power_analysis gives it higher power at both effect sizes tested (0.984 vs 0.927 at 1 sigma). The trade-off is geometry: the augmented design is face-centred, so prediction variance is less uniform than a rotatable design.

What do I check before trusting the augmented model?

Run covadoe_residual_diagnostics on the fitted model. It reports normality tests, Cook's distance and leverage per run, which is where a bad screening run or a batch shift between the screening and augmentation campaigns will show up. Then check whether the optimum sits inside the cube. An optimum on a boundary means you have not bracketed it.

Does augmentation work for Box-Behnken or fold-over designs too?

covadoe_augment_design takes a target_type argument and supports axial, fold-over and Box-Behnken augmentation in addition to central composite. Fold-over is the right choice when your screen was a Resolution III fractional factorial and you need to break the alias between main effects and two-factor interactions before you go anywhere near a response surface.