Full and fractional factorial concepts

Learning objectives

• Explain the purpose of full and fractional factorial concepts in a garment-factory improvement project.
• Apply the described method to a representative shop-floor situation.
• Recognize the common mistakes and how to avoid them.

Concept

Full factorial designs estimate all combinations; fractional designs use a planned subset to screen more factors with aliasing tradeoffs.

A two-level full factorial with k factors needs 2^k runs before replication.

Fractions reduce runs but alias effects; higher resolution protects more important effects from confounding.

Variables, units, and assumptions

k factors at 2 levels (coded ±1); response Y in engineering units.

Effects roughly additive within levels; higher-order interactions negligible for chosen resolution.

Free-spreadsheet workflow

Use free factorial template; enter factor names/levels; run in randomized order; analyze effect magnitudes via mean differences and Pareto plot.

Interpretation and limitations

Large main effects and interactions above noise band deserve confirmation runs.

Aliased effects cannot be separated within the chosen fraction.

Garment-factory example

Five finishing factors require 32 full-factorial combinations; a justified 2^(5-1) fraction (16 runs) can screen them before a smaller confirmation design.

Method

1. Rank likely interactions from process knowledge.
2. Set run budget.
3. Choose design with a free DOE template.
4. Document generators and aliases.
5. Randomize.
6. Confirm leading settings with follow-up runs.

Common mistakes

• Using a low-resolution fraction when interactions are likely.
• Declaring an aliased effect causal without confirmation.