Design Of Experiments

Design of Experiments

Overview

Factorial DOE helpers:

• Full factorial design enumeration for an arbitrary number of factors at

arbitrary level counts.

• Two-level factorial design (2^k) with optional randomization.
• Main-effect estimates from a fitted run (simple averaging contrast).

Suitable for hands-on screening campaigns with a small number of factors; not a replacement for full RSM (central composite, Box-Behnken) or optimal-design software.

Prerequisites

1. uv available.

When to Use

• Planning a 2-5 factor screening campaign with clear inputs and a single

response.

• Generating a randomised run sheet for a small experiment.
• Computing the rough magnitude of main effects after a small run.

Don't use for

• Response-surface methodology (RSM, central composite, Box-Behnken).
• Plackett-Burman or fractional-factorial confounding analysis.
• Observational data — DOE assumes you control the factor levels.
• Mixture experiments (constrained simplex designs).

Utility Scripts

• uv run scripts/doe.py full-factorial --factor "T=300,320" --factor "P=1e5,2e5" --output /tmp/fact.json
• uv run scripts/doe.py two-level --factors "A,B,C" --randomize --seed 42 --output /tmp/2k.json

Procedure

1. List factors and their levels (2 for screening, more for full

factorial).

1. Choose the design (full factorial for small k; two-level if you only

want main effects and 2-factor interactions).

1. Randomise the run order to mitigate time-order effects.
2. Add replication externally if you need pure-error estimates or curvature checks.
3. After the run, compute main effects.
4. If main effects are statistically significant, iterate to RSM with a

different tool.

Pitfalls

• Choosing two levels that are too close; main effects fall in the noise.
• Forgetting to randomise; time-order confounds the factor effects.
• Reporting effects without replicate variability.
• Confusing main effect (averaged over the other factors) with

conditional slope (computed at fixed values of the other factors).

• Treating a two-level design as a curvature test; this script does not add

centre points or run an RSM analysis.

• Using a 2^k design when you have only one shot per condition (no

replicates) and treating ±SE as meaningful.

• Picking response that is correlated with multiple physical phenomena

without thinking about what the design is testing.

• Forgetting blocking when the experiment spans multiple days /

raw-material lots.

Fallback Strategies

• If the number of factors exceeds 5, switch to fractional-factorial or

Plackett-Burman screening (use pyDOE2 outside this skill).

• For curvature exploration, switch to a central composite design with a

dedicated package.

Verification

• Run the listed script with representative inputs and an --output file when a deterministic calculation is available.
• Confirm the JSON result contains ok: true, expected units, and no unhandled warnings.
• Check result magnitudes against the stated assumptions, references, and a hand calculation or known operating range before reporting them.

References

• references/factorial_designs.md — design conventions and analysis

outline.

• Montgomery, Design and Analysis of Experiments (any edition).

Anti-Patterns

• Reporting "the effect of T is X" without naming the level range and

the other factors held fixed.

• Designing an experiment without randomization and reporting the

estimates as if independent.

• Using 2-level factorial for a known curved response.

Source & license

This open-source skill is cataloged on AgentStack and links to its original source — we do not rehost the code.

• Author: jskherman
• Source: jskherman/engg-skills
• License: Apache-2.0

Install and usage instructions live in the source repository linked above.