Factorial, fractional factorial, Plackett-Burman, central composite, Box-Behnken, definitive screening — the menu of DOE designs is intimidating, and it is easy to freeze before you have run a single experiment. This design of experiments decision guide reduces the whole choice to three questions asked in order: what is my goal, how many factors do I have, and how many runs can I afford. Answer those and the design falls out. Here is exactly how to decide which DOE design should I use.
Step 1: screening or optimizing?
Everything starts here. The screening vs optimization distinction is the single most important fork in DOE, and getting it right eliminates two-thirds of the candidate designs immediately.
Screening answers the question "which of my factors actually matter?" You have a long list of suspects — a dozen medium components, half a dozen process parameters — and you want to find the critical few cheaply. Screening designs estimate main effects for many factors in very few runs, accepting that interactions are confounded. The workhorses are the Plackett-Burman design and the fractional factorial design.
Optimization answers the question "what settings give the best result?" You already know your handful of important factors and now you want to locate the optimum precisely, including any curved sweet spot. Optimization designs fit a quadratic model with a curved response surface. The workhorses are the central composite and Box-Behnken designs, covered in the response surface methodology guide.
The canonical DOE workflow is screen first, optimise second: use a screening design to cut ten factors down to three, then run a response-surface design on those three. Trying to optimise all ten at once is the classic mistake — it wastes an enormous number of runs on factors that turn out not to matter. If your factors are ingredient proportions that must sum to 100%, neither branch applies directly; you need a mixture design instead.
By factor count (2–4 / 5–8 / 9+)
Once you know your goal, factor count narrows the choice within it. The number of factors is what decides whether you can afford to test every combination or must fraction the design.
2–4 factors → full factorial. With a handful of factors you can run a full factorial design and get the cleanest possible information: every main effect and every interaction, unconfounded. A 2³ design is 8 runs, a 2⁴ is 16 — still very manageable. This is the default whenever you can afford it, and the best design to learn on.
5–8 factors → screen, or use a DSD. A full factorial now explodes (2⁵ = 32, 2⁸ = 256 runs), so you fraction. For pure screening, a fractional factorial or Plackett-Burman finds the important factors cheaply. If your factors are continuous and runs are costly, a definitive screening design is often the smartest single choice in this range: it screens and detects curvature in about 2k+1 runs, potentially saving you a separate optimization study.
9+ factors → Plackett-Burman. With many factors, a Plackett-Burman design is purpose-built: 12 runs screen up to 11 factors, 20 runs up to 19. You accept heavily confounded interactions, which is fine because at this stage you only want to know which factors to carry into the next round. Screen aggressively, then bring the survivors into a factorial or response-surface design.
By run budget
The third axis is how many experiments you can actually run. In bioprocessing a single bioreactor run can take a week and cost hundreds in media, so run budget frequently overrides the "textbook best" design.
The rule is simple: the more expensive your runs, the more you fraction. When runs are cheap (microplates, shake flasks, fast readouts), a full factorial or a full central composite design buys you the most complete picture. When runs are expensive (large bioreactors, slow assays), you trade completeness for economy — a fractional factorial instead of a full one, a Box-Behnken instead of a central composite (fewer runs, no extreme corners), or a definitive screening design to collapse two study stages into one.
A practical way to price this before committing is to compare run counts head-to-head; our companion guide on getting started with DOE walks a beginner through setting factors and levels, and the generator below shows the exact run count for each design as you configure it, so you can see immediately whether a design fits your budget.
DOE design decision flowchart
Here is the whole design of experiments decision guide as a single flowchart. Start at the top with your goal, follow the branches by factor count, and land on a recommended design.
The designs at a glance (table)
The same logic in a lookup table. Scan the "Best for" column to confirm which DOE design should I use for your situation, then follow the linked guide for the detail.
| Design | Goal | Factors | Typical runs | Best for |
|---|---|---|---|---|
| Full factorial | Understand | 2–4 | 4–16 | Clean, complete effects + interactions when runs are affordable |
| Fractional factorial | Screen | 4–8 | 8–16 | Screening with some interaction info; tunable resolution |
| Plackett-Burman | Screen | 5–11+ | 12–20 | Many factors, main effects only, minimum runs |
| Definitive screening (DSD) | Screen + optimise | 4–8 | ~2k+1 | Continuous factors, scarce runs; detects curvature in one study |
| Central composite (CCD) | Optimise | 2–5 | ~14–30 | Precise optimum; can run beyond factor ranges (star points) |
| Box-Behnken | Optimise | 3–5 | 13–46 | Optimum without extreme corners; safer, fewer runs than CCD |
Worked decision: a CHO titer study
You suspect eight factors influence mAb titer (temperature, pH, DO, three feed components, seeding density, feed start day) and each bioreactor run is expensive.
- Goal? You do not yet know which of the eight matter → screening.
- Factor count? Eight continuous factors → a fractional factorial or, because runs are costly and factors are continuous, a definitive screening design (13 runs, and it flags curvature too).
- Next stage: the DSD points to, say, temperature, pH, and one feed component as critical. Carry those three into a Box-Behnken design (15 runs, no extreme corners) to find the optimum.
- Total: ~28 runs to go from eight unknown factors to a confirmed optimum — versus hundreds for a full factorial, or an OFAT search that would miss the interactions entirely.
Let the tool pick for you
You do not have to memorise any of this. A free design of experiments calculator encodes exactly this decision logic: tell it your goal and how many factors you have, and it recommends a design, shows the run count, builds the matrix, and randomises the run order — all in the browser with no coding.
The practical value of having the generator alongside this guide is that you can try the decision both ways. Configure a fractional factorial and a definitive screening design for the same eight factors, compare the run counts side by side, and pick the one that fits your budget. Because the same tool builds screening, factorial, and response-surface designs, you never switch software as you move from screening vs optimization and back — you screen, read the effects, and drop the survivors straight into an optimization design.
Not sure which design fits? Let the generator decide
Enter your goal and factor count; get a recommended design, its exact run count, and a randomised run sheet. Free, no install, no coding.
Frequently Asked Questions
Which DOE design should I use?
Choose by your goal first. If you are screening many factors to find the critical few, use a Plackett-Burman or fractional factorial design. If you already have 2–4 important factors and want to understand them fully, use a full factorial. If you want to fine-tune an optimum on 2–5 continuous factors, use a response-surface design (central composite or Box-Behnken). A definitive screening design is a good all-in-one choice for 4–8 continuous factors when runs are scarce. Factor count and run budget then narrow the choice within each goal.
What is the difference between screening and optimization designs?
Screening designs answer 'which factors matter?' — they estimate main effects for many factors in few runs (Plackett-Burman, fractional factorial), accepting confounded interactions. Optimization designs answer 'what settings are best?' — they fit a curved (quadratic) model to a small number of already-important factors to locate the optimum (central composite, Box-Behnken). The standard workflow is screening first, then optimization on the survivors. The screening vs optimization decision is the single most important fork in choosing a DOE design.
How many factors can a screening design handle?
A lot. A 12-run Plackett-Burman design screens up to 11 factors; larger Plackett-Burman and fractional factorial designs handle even more. That is their purpose — to test many candidate factors cheaply and identify the few that drive the response. You accept that two-factor interactions are confounded with main effects, which is an acceptable trade at the screening stage because you only need to know which factors to carry forward.
When should I use a response-surface design?
Use a response-surface design (RSM) once screening has reduced your problem to 2–5 important continuous factors and you need to locate the optimum precisely. Because RSM fits a quadratic model with a curved surface, it can find an interior optimum that two-level designs miss. Choose a central composite design when you can safely run beyond your factor ranges, or a Box-Behnken design when extreme combinations are risky and you want to stay inside a box of levels.
What is a definitive screening design and when should I choose it?
A definitive screening design (DSD) is a three-level design that estimates main effects, detects curvature, and keeps two-factor interactions clear of main effects, all in about 2k+1 runs. It effectively merges screening and optimization into one study, so it is an excellent choice for 4–8 continuous factors when runs are expensive and you would rather not run separate screening and RSM studies. It is less suited to categorical factors or very large factor counts.
Does the number of runs I can afford change which design I pick?
Yes — run budget is the third axis after goal and factor count. If runs are cheap, a full factorial gives the cleanest, most complete information. If runs are expensive, fraction the design (fractional factorial or Plackett-Burman for screening; Box-Behnken over central composite for optimization; or a definitive screening design to combine both). The art of DOE is buying the most information for the runs you can actually afford.
Related Tools
- DOE Experiment Generator — Recommends and builds factorial, screening, and response-surface designs free in the browser.
- Media & Feed Estimator — Cost the conditions you compare across a DOE.
- Fed-Batch Calculator — Plan feed strategies you might set as DOE factors.
References
- NIST/SEMATECH (2012). e-Handbook of Statistical Methods, Section 5.3.3: Choosing an experimental design. itl.nist.gov
- Jones, B. & Nachtsheim, C.J. (2011). A class of three-level designs for definitive screening. Journal of Quality Technology, 43(1), 1–15. DOI: 10.1080/00224065.2011.11917841
- Mandenius, C.F. & Brundin, A. (2008). Bioprocess optimization using design-of-experiments methodology. Biotechnology Progress, 24(6), 1191–1203. DOI: 10.1002/btpr.67