Design of Experiments (DOE)

Design of experiments (DOE) is a planned way to change several process inputs (factors) at once, in a structured pattern of runs, so you can estimate the effect of each factor and of their interactions on an output with the fewest trials.

In Six Sigma it is the main Improve-phase tool for finding the settings that move the Y, after Analyze has narrowed the list of candidate X’s.

An original worked example. Raising temperature helps at either time, but it helps much more at 20 seconds. That difference is the interaction, and one-factor-at-a-time testing would have missed it.

Key terms

Term	Meaning
Response (Y)	The output you measure, such as bond strength, yield, or cycle time
Factor (X)	An input you deliberately set, such as temperature or supplier
Level	A setting of a factor, often coded −1 (low) and +1 (high)
Run	One combination of factor levels that you actually try
Main effect	Average response at a factor’s high level minus the average at its low level
Interaction	When the effect of one factor depends on the level of another
Replicate	A repeat of the whole set of runs, used to estimate pure error
Randomization and blocking	Random run order protects against drift; blocks group runs made under one known nuisance condition, such as one shift or batch

Which DOE design should you use?

Full factorial (2^k): every combination of k factors at two levels: 4 runs for 2 factors, 8 for 3, 16 for 4. Estimates all main effects and interactions.
Fractional factorial (2^k−p): a planned fraction of the full design, used to screen many factors. Some effects are aliased (confounded) with others, and the design’s resolution tells you which.
Screening designs such as Plackett-Burman, used to find the vital few among many factors.
Response surface designs (central composite, Box-Behnken) to model curvature and find an optimum once the key factors are known.
Taguchi robust designs, which seek settings that make the output insensitive to noise factors.
EVOP, which runs small factorial changes during normal production.

How do you plan and run a DOE?

State the objective and the response, and confirm the response can be measured well (see measurement system analysis).
Choose factors and levels from Analyze-phase evidence, such as a fishbone, process knowledge, or earlier hypothesis tests. Set levels far enough apart to show an effect, but still safe to run.
Pick a design and the number of replicates, then randomize the run order.
Run the experiment exactly as planned and record anything unusual.
Analyze effects with ANOVA or regression, check residuals, and look at main-effect and interaction plots.
Confirm the best settings with confirmation runs, then lock them into the control plan.

Worked example: a 2² factorial on bond strength

A team wants stronger adhesive bonds. Factor A is cure temperature (180 or 200 °C), and factor B is cure time (10 or 20 s). They run all four combinations twice in random order (8 runs) and measure bond strength in newtons.

Run	A: temp	B: time	Replicate 1	Replicate 2	Mean
1	− (180)	− (10)	61	63	62
2	+ (200)	− (10)	72	70	71
3	− (180)	+ (20)	66	64	65
4	+ (200)	+ (20)	86	88	87

Main effect of A = (71 + 87)/2 − (62 + 65)/2 = 79.0 − 63.5 = 15.5 N
Main effect of B = (65 + 87)/2 − (62 + 71)/2 = 76.0 − 66.5 = 9.5 N
AB interaction = (62 + 87)/2 − (71 + 65)/2 = 74.5 − 68.0 = 6.5 N

Replicates give a pure-error mean square of 2.0 on 4 degrees of freedom. The ANOVA F-ratios are 240 for A, 90 for B, and 42 for AB, with p-values of about 0.0001, 0.0007, and 0.003, so all three effects are real at α = 0.05. The fitted model in coded units is ŷ = 71.25 + 7.75A + 4.75B + 3.25AB, and it predicts 87 N at 200 °C and 20 s.

Reading the interaction

At 10 s, raising temperature adds 9 N. At 20 s, it adds 22 N. The effect of temperature depends on time, which is what a significant AB term means. A one-factor-at-a-time study that held time at 10 s would have shown only a modest temperature effect and might have stopped there. Because a factorial design changes factors together, it finds interactions, and every run contributes to every effect estimate.

DOE in DMAIC

DOE sits mainly in the Improve phase of DMAIC. Screening designs can start late in Analyze, and the confirmed settings feed Control. Check the improved output with process capability and keep it stable with control charts. To practice, try the Improve-phase practice test.

Frequently asked questions

Why not test one factor at a time?

One-factor-at-a-time testing needs more runs for the same precision and cannot detect interactions. A factorial design changes factors together, so it uses every run to estimate every effect and shows when one factor changes the effect of another.

What is a fractional factorial design?

It runs a planned subset of a full factorial, for example 8 of the 16 runs for four factors. It saves runs at the cost of aliasing, where some effects cannot be separated from others. It is used to screen many factors before a fuller study.

Do you need replicates in a DOE?

Replicates give an estimate of pure error, so you can test whether effects are larger than noise. Without them, analysts often pool small high-order interactions as error or use a normal probability plot of effects. Replicate when runs are affordable.

Is DOE on the Green Belt or Black Belt exam?

Both, at different depths. Green Belt items usually cover terms, main effects, and interactions in 2-level factorials. Black Belt items add fractional factorials, resolution and aliasing, blocking, and response surface ideas.

Last updated: November 11, 2026 · Published by Lean Six Sigma Training Guide (sixsigmatrainingfree.com)