QM BenchQuality engineering tools

DOE Calculator: 2^k Full Factorial Design, Main Effects and Interactions

Plan a 2-level factorial experiment, run it in random order, and find which factors and interactions really move the result and which settings are best.How to use ↓Full guide with case study →

Run the trial and enter the results

0 of 8 results entered
StdRunA: Factor AB: Factor BC: Factor CResponse
14− Low− Low− Low
28+ High− Low− Low
35− Low+ High− Low
43+ High+ High− Low
56− Low− Low+ High
62+ High− Low+ High
77− Low+ High+ High
81+ High+ High+ High

Run the trials in the run order, so that drift over time does not look like a factor effect. You can paste a whole column of results into the first field.

No results yet

Set up the factors with a low and a high setting, run the 8 trials and enter each result. The analysis appears when every run has a value.

  1. 1Enter or paste dataor click Load sample
  2. 2Read the verdictcharts and key figures
  3. 3Download the PDFwith your logo

Where this tool fits

Before this
Regression and CorrelationConfirm the cause with an experimentMulti-Vari Chart and Box PlotTest the suspected factors
DOE: 2-Level Factorial Design
Next step
Control PlanFix the best settings in the control planProcess Capability & Control ChartsCheck the capability at the new settings
In-depth guide: theory, step by step and a worked case studyWritten by Ľubomír Blažek, automotive quality managerRead →

Design of experiments online: 2^k full factorial

This DOE tool plans and analyses two-level full factorial experiments with 2 to 5 factors. It builds the run plan in standard and randomised order, lets you enter the results run by run, and shows which factors and interactions really change the response.

You get the Pareto of standardised effects, main effects and interaction plots, a table of effects and coefficients, and the best combination of settings for maximising, minimising or hitting a target, as used in Six Sigma Green and Black Belt projects.

How it works in 4 steps: DOE: 2-Level Factorial Design

  1. Plan3 factors × 2 levels8 runs, random order
  2. Run16 resultseach setting twice
  3. AnalyseA, B and AB significantPareto of effects
  4. DecideBest settingconfirm, then update the control plan
Example: shrinkage against melt temperature, pressure and cooling time, 2^3 with 2 replicates.

How the DOE: 2-Level Factorial Design works

Effects are estimated by least squares on the coded −1 / +1 model with every interaction. With replicates the error comes from the repeated runs and every effect gets a t-test; without replicates the tool uses Lenth’s pseudo standard error.

The calculations are validated against least-squares t-tests in SciPy and the published 2^4 filtration-rate example of Montgomery.

When to use it

Use a factorial DOE to optimise a process setting, to screen which of several suspected factors matter, to find interactions that one-factor-at-a-time trials miss, during process development before PPAP, and in Six Sigma Improve phases.

PDF report in one click

Export the experiment as a PDF with the factors and levels, the verdict, the effect plots, the effects table, the best settings and the full run sheet.

Private: everything runs in your browser

The design and the results stay in your browser. Nothing is uploaded and no account is needed.

How to run a DOE with this tool

  1. Choose 2 to 5 factors and give each a low and a high setting that are far enough apart to show an effect.
  2. Decide on replicates: 2 replicates give a real noise estimate; 1 replicate is enough for screening 4 or 5 factors.
  3. Run the trials in the run order shown and type each result into the table.
  4. Read the Pareto of effects: bars past the red line are significant. Use the interaction plots to see how factors work together.
  5. Confirm the best settings with a few confirmation runs, then update the control plan.

Before the trial, make sure the measurement system can see the differences you expect (Gage R&R). To find candidate factors from existing production data, start with regression or a multi-vari study.

Frequently asked questions

›What is a 2^k factorial design?

Each of k factors is tested at a low and a high setting, in every combination: 2 factors need 4 runs, 3 factors 8, 4 factors 16. This shows the effect of every factor and every interaction with far fewer trials than changing one factor at a time.

›What is an interaction?

Two factors interact when the effect of one depends on the setting of the other, for example a higher pressure that helps only at high temperature. On the interaction plot the lines are not parallel.

›Do I need replicates?

Replicates measure the pure noise and give real p-values. Without them the tool uses Lenth’s method, which judges the effects against the small ones and works well from 3 factors up.

›Why randomise the run order?

So that anything that drifts during the trial (tool wear, temperature, operator) is spread over all settings instead of looking like a factor effect.

›Are the results validated?

Yes. The effects and significance are checked against least-squares t-tests in SciPy / NumPy and against the published 2^4 filtration-rate example of Montgomery.