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DOE

Fractional Factorial Calculator

Screen 5–7 factors in a handful of runs. Build a 2-level fractional design, see its resolution and alias structure, then enter your results to rank the effects — all client-side.

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Design your screening experiment

Choose how many factors to screen and how few runs to use
Name each factor and set its low (−) and high (+) level
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Ready to design

Set your factors on the left and press Generate Design to build a fractional run sheet with its alias structure.

Watch: 2^k Factorial DOE: Test Multiple Changes Together

Simulation Lab

Fractional Factorial Screening Lab

You have many factors but limited runs. Enter the lab to see how a fractional design screens out the vital few with a fraction of the experiments.

How the fractional factorial calculator works

1

Choose your fraction

Pick how many factors to screen (5–7) and how few runs you can afford. The calculator builds a 2-level fractional design using standard generators and names each factor's low and high levels.

2

Check the confounding

It works out which effects get mixed together in this smaller design (called confounding) and gives the design a resolution rating — so before you run a single trial, you know exactly which effects you can trust and which ones are tangled up with each other.

3

Rank the effects

Run your experiment in random order, record the result for each test, and the calculator shows which factors have the biggest effect (by comparing the average result when each factor is 'on' versus 'off'). This tells you what to focus on.

Complete guide

Fractional Factorial Guide

A fractional factorial design lets you screen many factors in a fraction of the runs a full factorial would need. It is the workhorse of the early Analyse and Improve phases, where the goal is to separate the vital few factors that matter from the trivial many before committing to a detailed study.

What it is

What is a fractional factorial design?

A fractional factorial runs a carefully selected fraction — a half, a quarter, an eighth — of all the combinations a full factorial would test. By giving up the ability to estimate high-order interactions (which are usually negligible), you screen many factors in very few runs. A 2⁵⁻¹ design tests five factors in just 16 runs instead of 32, and a 2⁷⁻⁴ design screens seven factors in only 8.

How it works

How the runs are chosen — and the trade-off

A fractional design runs only a carefully chosen half (or quarter) of all the possible factor combinations, so you can test many factors in far fewer runs. The trade-off is 'confounding': because you skipped runs, some effects get tangled together and cannot be told apart. The design's 'resolution' is a grade for how serious that tangling is — higher resolution means the main factor effects stay clear of one another. Use a fractional design to screen lots of factors quickly, find the vital few, then run a fuller experiment on just those to confirm the details.

Worked example

Worked example: testing 4 factors without running 16 experiments

An engineer wants to test temperature, pressure, speed, and humidity — each at two settings. A full test of every combination would need 16 runs. A fractional factorial design cuts this to 8 carefully chosen runs.

The results still identify temperature and speed as the two factors that matter most, with pressure having almost no effect.

What to do with this: Focus improvement on temperature and speed only. You got 80% of the insight from 50% of the effort — that's the whole point of fractional factorial.

Why it matters

Operational impact

Experiments cost time, material and machine capacity. Fractional designs let a team learn which factors actually drive a result in a handful of runs rather than dozens, freeing budget for the deeper studies that follow. They turn "we think it might be temperature" into hard, ranked evidence.

Decision making

When to use it

Reach for a fractional factorial in the Analyse and early Improve phases of DMAIC, whenever you have many candidate factors and limited runs. It is the standard screening tool: identify the vital few, then switch to a higher-resolution or full factorial, or a response surface design, to optimise them.

Lean Six Sigma

Link to Six Sigma

DOE is a core Black Belt skill, and fractional factorials are where most real projects start because of their efficiency. Reporting resolution and alias structure alongside the ranked effects shows tollgate reviewers that your conclusions account for confounding rather than ignoring it.

Industry examples

Where fractional factorials are used

ManufacturingScreen machine settings — temperature, pressure, speed, feed — to find which few drive yield or defect rate before a detailed optimisation study.
Chemicals & processInvestigate many recipe and condition factors (catalyst, concentration, time, mixing) cheaply to isolate the drivers of conversion or purity.
Product & R&DTest numerous design or formulation factors in early development to focus effort on the handful that affect performance.
Software & servicesScreen many configuration or process options affecting throughput or error rate, then study the important ones in depth.
Common mistakes

Common fractional factorial mistakes

  • Choosing a fraction that confounds (mixes up) the main effects with two-factor interactions — always check the confounding pattern before running the experiment.
  • Running too small a fraction to detect all the effects you care about — if interactions between factors matter, you may need a larger fraction.
  • Randomising the run order but forgetting to record what changed between runs — unexpected factors (operator fatigue, temperature drift) can bias the results.
  • Analysing results as if you ran a full factorial — a fractional design gives you estimates, not exact answers. Some effects are aliased with others.
  • Not running a few centre-point replicates — without them you can't detect whether the relationship between factors and response is curved rather than straight.
What to do next

After screening

Once the calculator ranks your effects, separate the vital few large effects from the trivial many. Check the alias of any big effect to be sure you are crediting the right cause. Then run a follow-up experiment on the survivors — a higher-resolution or full factorial to confirm interactions, or a response surface design to find optimal settings. Fix the unimportant factors at their most convenient or cheapest levels and document the decision.

Resources

Templates, videos and learning

Combine fractional factorial screening with full factorial and response surface studies inside a structured DMAIC project.

Frequently asked questions

What is the difference between a full and fractional factorial design?

A full factorial tests every combination of your factors — 2^k runs for a 2-level design, so a 7-factor study needs 128 runs. A fractional factorial runs a carefully chosen fraction (2^(k−p)) of those combinations, for example 16 runs instead of 128. You give up the ability to estimate every interaction cleanly, but in return you screen many factors with far fewer runs — ideal when experiments are expensive and most high-order interactions are negligible.

What is design resolution?

Resolution describes how badly effects are tangled together (aliased). In a Resolution III design main effects are aliased with two-factor interactions, so use it only for rough screening. In Resolution IV main effects are clear of two-factor interactions but those interactions are aliased with each other. In Resolution V main effects and two-factor interactions are all estimated cleanly — the best fractional designs. Higher resolution means less confounding.

What is aliasing (confounding)?

Aliasing means two or more effects are estimated by the same column of the design, so the calculator cannot tell them apart — their estimates are added together. It arises because you ran only a fraction of the full design. The alias (confounding) structure lists which effects share a column. When an important effect appears large, you check its aliases to decide whether the main effect or an interaction is the true cause, often with a small follow-up experiment.

When should I use a screening design?

Use a screening (fractional) design early in an investigation when you have many candidate factors — typically five or more — and want to find the vital few that actually matter before spending runs on a detailed study. Screening relies on the sparsity-of-effects principle: usually only a handful of factors dominate. Once screening identifies them, follow up with a higher-resolution or full factorial, or a response surface design, to optimise the survivors.

Want to screen many factors in a handful of runs inside a real improvement project? The Black Belt covers fractional factorial designs, screening experiments, and the advanced Design of Experiments toolkit.

View Black Belt →