Comparison8 min readJuly 15, 2026

Screening Designs Compared: Fractional, PB and DSD

Q: Can I turn a screening design into a response surface without starting over?

Yes. `covadoe_augment_design` extends an existing design rather than replacing it. In our documented CovaDOE example, the 13-run DSD was augmented with 8 further runs (6 axial, 2 centre) to give a 21-run central composite design on the three surviving factors. The screening runs are reused, so only the new runs cost lab time.

Screening design comparison for DoE: fractional factorial vs Plackett-Burman vs definitive screening, with real run counts, resolution and power from.

Oliver Kraft

CovaSyn

Screening Designs Compared: Fractional, PB and DSD

You have six factors, a limited amount of API and a manager who wants an answer this month. The full factorial is out. The question is which screen to run instead, and what you are giving up when you pick the cheapest one. This article compares fractional factorial, Plackett-Burman and definitive screening designs on the same six-factor problem, using real output from the CovaDOE tools.

The test case

A Suzuki-type aryl halide coupling with six factors: temperature (60-100 C), catalyst loading (0.5-5 mol%), base equivalents (1-3), water fraction (0-0.3), time (2-16 h) and ArB equivalents (1-2). Response: yield.

All numbers below come from covadoe_compare_designs, covadoe_create_design, covadoe_alias_structure and covadoe_power_analysis called on exactly those factor definitions. Nothing is illustrative.

The comparison, in one table

covadoe_compare_designs with goal="screening" ranked six candidates. The four that matter for a screening decision:

Design	Runs	Resolution	D-efficiency	G-efficiency	Estimated power	Score
D-optimal	19	VI	0.990	0.826	0.979	0.953
Definitive screening (DSD)	13	VI	0.799	0.933	0.850	0.868
Full factorial 2^6	67	Full	0.962	0.961	1.000	0.854
Fractional factorial	11	III	0.761	0.757	0.702	0.817
Plackett-Burman	8	III	1.000	1.000	0.176	0.737

Two things jump out. The full factorial at 67 runs (64 corners plus 3 centre points) buys power 1.0 and every two-factor interaction, and still ranks third, because cost is part of the score. And Plackett-Burman has a perfect D-efficiency of 1.000 and a power of 0.176. That is not a contradiction, and it is the most useful thing on the table.

D-efficiency measures how well a design spreads information; power measures whether an effect can be told from noise. The saturated 8-run Plackett-Burman wins the first and loses the second. Source: Computed with covadoe_compare_designs (goal=screening) on the six-factor Suzuki-type coupling described in this article.

What resolution actually means

Resolution describes which effects are indistinguishable from which. In a fractional design you are running a subset of the full factorial, and the price is that some effects share a column in the model matrix. Those effects are aliased: the data cannot separate them.

Resolution III: main effects are aliased with two-factor interactions.
Resolution IV: main effects are clear of two-factor interactions, but two-factor interactions are aliased with each other.
Resolution V and above: main effects and two-factor interactions are all estimable separately.

The 2^(6-3) fractional factorial built by covadoe_create_design (resolution=3) is 8 corner runs with defining relation I=ABD, I=ACE, I=BCF, I=DEF. Running covadoe_alias_structure on that coded matrix returns resolution III and 14 alias chains across 21 terms checked. The main-effect chains are explicit:

Temperature      = CatalystLoading*WaterFraction = BaseEquiv*Time
CatalystLoading  = Temperature*WaterFraction     = BaseEquiv*ArBEquiv
BaseEquiv        = Temperature*Time              = CatalystLoading*ArBEquiv
WaterFraction    = Temperature*CatalystLoading   = Time*ArBEquiv
Time             = Temperature*BaseEquiv         = WaterFraction*ArBEquiv
ArBEquiv         = CatalystLoading*BaseEquiv     = WaterFraction*Time

Read the first line as a warning. If this screen reports a large temperature effect, that number is temperature plus a catalyst x water interaction plus a base x time interaction. In a coupling reaction where catalyst and water genuinely interact, that is not hypothetical. You cannot untangle it from these 8 runs; you need a fold-over or a different design.

On run counts: covadoe_create_design returns 8 corner runs, covadoe_compare_designs reports 11 because it costs in 3 centre points for a pure-error estimate. Same design, different booking.

Why Plackett-Burman scores 1.000 on efficiency and 0.176 on power

D-efficiency and G-efficiency measure how well a design fills the space it can address. The 8-run Plackett-Burman that CovaDOE returned for 6 factors is a saturated orthogonal array: every column is balanced, every pair is orthogonal, and the information matrix is as good as it gets. Hence 1.000 and 1.000.

Power is a different question: given the residual noise, can you tell a real effect from zero? That depends on degrees of freedom left over after fitting.

Run covadoe_power_analysis at 8 runs with 7 terms (intercept plus 6 main effects) and effect size 1.0 sigma, and it returns:

power: 0.0
df_error: 0
warning: "Too few runs for the number of terms."

Zero residual degrees of freedom. The model fits the data exactly, and there is nothing left to estimate the error with. A saturated design gives you effect estimates and no way to test them.

Compare the same call at other run counts, all at 7 terms and 1.0 sigma:

Runs	Residual df	Power at 1.0 sigma
8 (saturated)	0	0.00 (tool warns)
11	3	0.61
12	4	0.74
13 (DSD)	5	0.82

The jump from 8 to 13 runs is five experiments. It takes you from "no test is possible" to "82% chance of catching a one-sigma effect". That is the cheapest statistical purchase in the whole table.

A saturated 8-run design has zero residual degrees of freedom, so nothing can be tested. Moving to 13 runs costs five experiments and buys 82% power. Source: Computed with covadoe_power_analysis at 7 terms, 1.0 sigma effect and alpha 0.05 for the six-factor screening problem in this article.

The DSD sweet spot

The definitive screening design for these six factors is 13 runs, resolution VI, estimated power 0.850, produced by covadoe_create_design with design_type="definitive_screening". covadoe_suggest_design(n_factors=6, goal="screening") picks it directly, with the rationale that it detects main and quadratic effects in 13 runs; its listed classical alternative is a fractional factorial at 32 runs.

Three levels per factor plus a centre run means DSDs do something the two-level screens cannot: they detect curvature. Main effects are not aliased with two-factor interactions at all, and two-factor interactions are not fully aliased with each other. If a factor has an optimum inside your range rather than at an edge, a two-level screen will report it as a weak linear effect and you will drop it. The DSD will flag it.

Power depends on the effect you are hunting. covadoe_power_analysis at 13 runs and 7 terms:

Effect size	Power
0.5 sigma	0.31
1.0 sigma	0.82
2.0 sigma	1.00

Be honest about this before you run it. A 13-run DSD is not built to find half-sigma effects. If your assay noise is 2% yield and you care about 1% differences, no 13-run design will help you. Reduce the noise or increase the runs.

How to choose

6 to 12 factors, want main effects plus curvature, want to move straight into a response surface: definitive screening design. 13 runs here, resolution VI, power 0.85, and it augments cleanly into a central composite design.
Many factors, you only need a rank order, effects are large and interactions are genuinely believed negligible: Plackett-Burman. Add centre points or replicates, or you have zero residual df and cannot test anything.
You need a specific defining relation, blocking, or a fold-over strategy your site already has SOPs for: fractional factorial. Choose resolution IV or higher if any interaction is plausible. Resolution III is for triage only.
Irregular factor ranges, hard constraints, categorical factors, or a fixed run budget: D-optimal. It topped this comparison at 19 runs with power 0.979, because it optimises against the model you specify rather than a catalogue design.
Fewer than 5 factors and runs are cheap: run the full factorial and stop reading comparison articles.

What this comparison does not tell you

Power figures are model-relative. They assume the 7-term main-effects model, alpha 0.05 and normally distributed residuals. Change the model and the numbers change.
Effect sizes are in sigma units. "Power 0.82 at 1.0 sigma" is only meaningful once you know your own run-to-run standard deviation. Estimate it from replicates before you trust any of these numbers.
Efficiency metrics say nothing about chemistry. A design can be D-optimal and still put every run in a region where your catalyst decomposes. Feasibility screening is your job, not the tool's.
Aliasing is not removed by a good score. The resolution III chains above exist regardless of how the design ranks.
This is design support, not a validated result. The runs still have to happen in a lab, and nothing here substitutes for confirmation runs or a regulatory filing.

Frequently asked questions

What is the difference between a fractional factorial and a Plackett-Burman design?

Both are two-level screening designs, but a fractional factorial has run counts that are powers of two and a clean defining relation, so the aliasing is explicit and predictable. Plackett-Burman designs come in multiples of four and have complex partial aliasing spread across many interactions. For 6 factors, CovaDOE returns an 8-run resolution III fraction versus an 8-run Plackett-Burman, both resolution III.

When should I use a definitive screening design instead of a fractional factorial?

Use a DSD when curvature is plausible and you want to move into optimisation without a second screening round. For 6 factors, covadoe_compare_designs returned a 13-run DSD at resolution VI with power 0.85, versus an 11-run resolution III fraction at power 0.70. Two extra runs buy you unaliased main effects and quadratic detection.

Why does Plackett-Burman show perfect D-efficiency but very low power?

D-efficiency measures how well the design spreads information across the factors, and a saturated orthogonal array scores 1.000. Power measures whether you can distinguish an effect from noise, which needs residual degrees of freedom. At 8 runs with 7 model terms, covadoe_power_analysis returns power 0.0 with 0 residual df and warns that there are too few runs.

How many runs do I need to screen 6 factors?

It depends on what you want to estimate. CovaDOE returned a full factorial at 67 runs (power 1.0), D-optimal at 19 (power 0.98), a definitive screening design at 13 (power 0.85), a resolution III fraction at 11 (power 0.70) and Plackett-Burman at 8 (power 0.18). For most process screens, 13 to 19 runs is the practical range.

What does design resolution III mean in practice?

It means main effects are aliased with two-factor interactions and cannot be separated from them. In the 2^(6-3) fraction above, covadoe_alias_structure found 14 alias chains: the temperature estimate is temperature plus catalyst x water plus base x time. If interactions are real, resolution III effect estimates are biased and need a fold-over or an augmented design to resolve.

Can I turn a screening design into a response surface without starting over?

Yes. covadoe_augment_design extends an existing design rather than replacing it. In our documented CovaDOE example, the 13-run DSD was augmented with 8 further runs (6 axial, 2 centre) to give a 21-run central composite design on the three surviving factors. The screening runs are reused, so only the new runs cost lab time.