Design of Experiments (DOE) and Bayesian Optimisation

Design of Experiments (DOE) lets you change several factors at once and untangle their individual and joint effects with far fewer runs than one-factor-at-a-time testing. This guide covers the design choices that matter most in practice.

A 3D wireframe cube with eight glowing vertex spheres representing a two-level, three-factor full factorial design, floating in deep navy space with electric blue edges and cyan vertex glow. — A two-level, three-factor full factorial — eight corners of the design space.

Choosing a design

Full factorial — every combination of every factor at every level. Best for small factor counts (≤ 4).
Fractional factorial — a carefully chosen subset that preserves main-effect estimates and key interactions. Look at the resolution (III, IV, V) to know what gets aliased.
Split-plot — when one factor is hard to change between runs (oven temperature, batch material). Two error strata; ANOVA must respect them.
Completely Randomised Design (CRD) — when all factors can be randomised freely.

Analysis essentials

Run order randomisation — protects against time-correlated noise.
ANOVA with % contribution — quantifies how much of the response variance each effect explains, not just whether it is statistically significant.
Residual diagnostics — residuals vs fitted, residuals vs run order, normal Q-Q. Patterns reveal missed effects, non-constant variance, or order effects.
Main effects and interaction plots — translate the ANOVA into pictures the team can act on.
Normal Probability Plot of effects — separates active effects from noise without an ANOVA F-test, especially useful for unreplicated designs.

A smooth 3D optimization landscape surface with gentle hills and valleys, six glowing cyan exploration points connected by a thin path showing a Bayesian search trajectory across the surface. — Bayesian optimisation places each new run where it will teach the model most.

Bayesian optimisation

Once a screening DOE identifies the active factors, Bayesian optimisation iteratively suggests the next experimental point that best balances exploration of unknown regions with exploitation of promising ones. It is well suited to expensive experiments where each run costs hours or days.

How Ops Excellence handles this

The DOE tool generates the design and run order, accepts response data, runs ANOVA with % contribution, plots residual diagnostics, main effects, interactions, and a Normal Probability Plot, and includes a Bayesian optimisation engine for follow-up runs. Build your first design.