Fractional Factorial vs Full Factorial DOE — When to Use Each
The 10-second answer
Full factorial (all combinations) is best when runs are affordable and you care about interactions without aliasing.
Fractional factorial (a subset of runs) is best for screening many factors quickly, accepting some aliasing (confounding) to save time and cost. support.minitab.com
Quick definitions (plain English)
Full factorial (2^k): tests every high/low combination for k factors (e.g., 5 factors → 2^5 = 32 runs, plus any center points you add).
Fractional factorial (2^(k−p)): runs a fraction (½, ¼, …) of the full set (e.g., 5 factors, half fraction → 2^(5−1) = 16 runs). You trade runs for aliasing. support.minitab.com
What “resolution” means (and why it decides everything)
Design resolution summarizes the worst-case aliasing pattern in a fractional design:
Resolution III: main effects can be aliased with 2-factor interactions.
Resolution IV: main effects are not aliased with 2-factor interactions, but 2-factor interactions may be aliased with each other.
Resolution V: main effects and 2-factor interactions are not aliased with any other main effects or 2-factor interactions (2-factor interactions may alias with 3-factor). NIST ITL+1
Rule of thumb:
Use Res IV for screening (protects main effects).
Use Res V when you expect key interactions and can afford a few more runs.
Avoid Res III unless you truly only need main-effect directionality.
Choosing between full vs fractional (practical rules)
Pick the smallest design that still estimates the effects you care about:
-
Need clean main effects and 2-factor interactions?
Full factorial or Res V fractional.
-
Just screening for the vital few factors?
Res IV fractional (then augment later if needed).
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Setup changes are costly (some factors hard to change)?
Consider split-plot structures regardless of full/fractional choice.
-
Run budget fixed?
Start with fractional to learn cheaply, then fold over or augment to break aliasing if you see promising effects. support.minitab.com+2NIST ITL+2
Typical run counts (2-level designs)
| # factors (k) | Full (2^k) | Half (2^(k−1)) | Quarter (2^(k−2)) |
|---|---|---|---|
| 3 | 8 | 4 | 2 |
| 4 | 16 | 8 | 4 |
| 5 | 32 | 16 | 8 |
| 6 | 64 | 32 | 16 |
| 7 | 128 | 64 | 32 |
Add center points if you want a curvature check (cheap and valuable). statease.com
What if you pick “too small” a fraction?
You can augment a fractional design later:
Foldover your design to break aliasing (e.g., upgrade Res III → Res IV, or untangle specific interactions).
Add targeted runs (e.g., center points; a few strategically chosen combinations) to clarify curvature or suspected interactions. NIST ITL+2NIST ITL+2
Example: 5-factor project with a tight budget
Full factorial: 32 runs (clean main + interactions).
Half-fraction Res V (common choice): 16 runs, protects main effects and 2-factor interactions from each other.
Start with the 16-run fraction → analyze → foldover if you need to resolve a key alias. NIST ITL+1
Solid how-to references (quick links)
NIST e-Handbook (resolutions & aliasing): https://www.itl.nist.gov/div898/handbook/pri/section3/pri3344.htm • https://www.itl.nist.gov/div898/handbook/pri/section3/pri3324.htm • https://www.itl.nist.gov/div898/handbook/pri/section3/pri338.htm NIST ITL+2NIST ITL+2
Minitab (full vs fractional overview; choosing designs): https://support.minitab.com/en-us/minitab/help-and-how-to/statistical-modeling/doe/supporting-topics/factorial-and-screening-designs/factorial-and-fractional-factorial-designs/ • https://support.minitab.com/en-us/minitab/help-and-how-to/statistical-modeling/doe/supporting-topics/factorial-and-screening-designs/choose-a-factorial-design/ support.minitab.com+1
JMP Learning Library (fractional factorial how-to): https://www.jmp.com/en/learning-library/topics/design-and-analysis-of-experiments/doe-fractional-factorial-design jmp.com
Stat-Ease (foldover & factorial tutorials): https://www.statease.com/docs/v25.0/tutorials/foldover-tut/ • https://www.statease.com/docs/v25.0/tutorials/two-level-factorial/ statease.com+1
Want a ready-made path?
If you’d like a guided, step-by-step workflow (screen → model → optimize) with assignments you can apply to your parts, try the Excedify DOE Training — there’s a free preview so you can test the fit first:
https://www.excedify.com/