DoE Basic Terms
Key Takeaways
- DOE systematically changes input factors at planned levels while measuring responses so cause-and-effect can be estimated with far less ambiguity than one-factor-at-a-time trials.
- Independent variables (factors) are the controlled inputs; the dependent variable (response) is the Y you measure—often a CTQ such as yield, cycle time, or defect rate.
- A treatment is a unique combination of factor levels; replication repeats entire treatments to estimate pure error, while repetition is multiple measurements within one run.
- Randomization protects against time-order bias; blocking isolates known nuisance sources (shift, batch, machine) so they do not inflate experimental error.
- CSSGB BoK V.A.1 is Understand level: Green Belts must define factors, levels, responses, treatments, error, blocks, randomization, effects, and replication—and know DOE’s role in Improve before claiming causation.
DoE Basic Terms
Quick Answer: Design of Experiments (DOE) is a structured plan for changing process inputs and measuring outputs so you can estimate effects and interactions with quantified error. CSSGB BoK V.A.1 (Understand) requires fluent definitions of independent and dependent variables, factors and levels, responses, treatments, experimental error, repetition vs. replication, blocks, randomization, and effects—and a clear sense of Green Belt scope for DOE in Improve.
Why DOE Beats One-Factor-at-a-Time
In Improve, teams often “tweak” one setting, run a few parts, then tweak another. That one-factor-at-a-time (OFAT) habit confounds time order with factor changes, misses interactions (when the effect of X1 depends on X2), and burns samples without a clean error estimate. DOE replaces ad-hoc tweaking with a pre-written matrix of runs so:
- Each factor’s influence on Y can be compared on a common scale
- Interactions become visible instead of hidden
- Unexplained variation (error) is estimated, not ignored
- Randomization and blocking defend against nuisance shifts
DOE answers: If we deliberately set these inputs, what happens to the response—and how sure are we?
Independent vs. Dependent Variables
| Role | DOE name | Meaning | Example |
|---|---|---|---|
| Independent variable | Factor (input, X) | A process or design setting the experimenter controls or deliberately chooses | Temperature, pressure, supplier, training method |
| Dependent variable | Response (output, Y) | The measured outcome that may depend on the factors | Bond strength (N), fill weight (g), first-pass yield (%) |
You may track multiple responses (quality + cost + cycle time). Each response needs an operational definition, units, and a trustworthy measurement system (MSA first when the CTQ is instrumented).
CSSGB tip: “Independent” does not mean “unrelated to other factors.” It means the factor is treated as an input you set. Factors can still interact in their effect on Y.
Factors and Levels
A factor is an independent variable under study. A level is a specific value or setting of that factor in the design.
- Continuous factor levels: oven at 180 °C and 200 °C; speed at 40 and 60 units/min
- Categorical factor levels: Supplier A vs. B; fixture type 1 vs. 2; operator training “old” vs. “new”
Most Green Belt screening designs use two levels per factor (low/− and high/+) because that efficiently estimates main effects and two-factor interactions. Three or more levels support curvature studies (beyond basic V.A vocabulary, but know that two levels assume approximate linearity between endpoints).
How many factors? Screening often starts with the vital few from Analyze (multi-vari, FMEA, process knowledge). Putting ten half-understood knobs into a full factorial explodes run count; putting only one factor reverts to OFAT.
Responses, Treatments, and the Run Matrix
The response is the dependent Y (or vector of Ys) recorded for each experimental run.
A treatment (or treatment combination) is one unique set of factor levels. Example two-factor, two-level design:
| Run | Temp | Speed | Treatment label |
|---|---|---|---|
| 1 | Low | Low | A−B− |
| 2 | High | Low | A+B− |
| 3 | Low | High | A−B+ |
| 4 | High | High | A+B+ |
Each row is a run when executed once. The same treatment can appear more than once if you replicate.
Experimental Error, Repetition, and Replication
Experimental error (residual error) is the unexplained variation in the response when the same treatment is applied under supposedly identical conditions. It comes from measurement noise, uncontrolled inputs, and inherent process variation. Without an error estimate you cannot judge whether an apparent effect is real or noise.
| Term | Meaning | Why it matters |
|---|---|---|
| Repetition | Multiple measurements of Y within the same run (same setup, same parts batch under one treatment) | Improves measurement precision for that run; does not fully capture setup-to-setup process error |
| Replication | Repeating the entire treatment (reset factors, re-run the condition) as a new experimental unit | Provides independent estimates of pure error and more reliable effect estimates |
Exam trap: Calling three thickness readings on one molded part “three replications” is usually wrong—that is repetition (or multiple samples within a run). True replication re-creates the treatment (new setup/cycle as defined by the protocol).
Blocks and Randomization
Randomization is the random assignment of run order (and, when applicable, material or units) so time trends, warm-up, tool wear, and learning effects are not systematically aligned with one factor level. If all “high temperature” runs happen on Monday and all “low” on Friday, temperature is confounded with day.
Blocking deliberately accounts for a known nuisance factor you do not want to study as a primary improvement lever—or cannot hold constant—such as raw-material lot, shift, or machine. You run complete (or balanced) sets of treatments within each block so block differences are removed from the error used to test factor effects.
| Technique | Purpose |
|---|---|
| Randomize run order | Protect against unknown time-order bias |
| Block on known nuisance | Isolate shift/batch/machine variation from factor comparisons |
| Hold constants | Fix factors not in the study at standard settings |
Randomization and blocking are complementary: block what you know, randomize against what you do not.
Effects (Main Effects Preview)
An effect describes how the response changes when a factor (or combination) changes.
- Main effect of factor A: average change in Y when A moves from low to high, averaged over the levels of the other factors in the design.
- Interaction effect (e.g., A×B): the effect of A depends on the level of B (and vice versa). Covered in depth with plots in the next section.
At Understand level, know that effects are estimated contrasts from the design matrix, not casual “we tried it and it looked better” stories. Magnitude is compared to experimental error before you declare a factor “significant” in project language.
Green Belt Scope of DOE
ASQ places basic DOE terms in Improve (V.A). For CSSGB, expect to:
- Define the experimental objective and response(s) tied to the project Y/CTQ
- Select factors and levels from Analyze evidence (not random knobs)
- Use correct vocabulary for treatments, replicates, blocks, and randomization when reading or planning a simple factorial/screening study
- Interpret main effects and interaction plots (V.A.2 Apply—next section)
- Recommend settings and confirm with follow-up runs or a pilot—not declare victory from one unreplicated “best” cell alone
Typically outside deep Green Belt hand calculation: full ANOVA table derivation for large designs, complex optimal designs, and heavy response-surface optimization (more Black Belt). You still must understand what software output means: which factors matter, whether interactions change the story, and whether the design was randomized/blocked sensibly.
Where DOE sits in DMAIC:
- Measure/Analyze → candidate Xs, MSA, multi-vari, correlation
- Improve → planned DOE to confirm cause-and-effect and set improved levels
- Control → lock the winning settings in standards, poka-yoke, and SPC
Mini Worked Vocabulary Walk-Through
A team studies adhesive cure. Factors: temperature (150 °C / 170 °C) and cure time (20 min / 30 min). Response: peel strength (N). They run each of the four treatments twice (replication), randomize the eight run order, and block by adhesive lot (Lot 1: four treatments; Lot 2: four treatments).
- Independent variables: temperature, time
- Dependent variable: peel strength
- Four treatments; eight runs after replication
- Lot is a block, not a process improvement “knob” in this study
- Difference in average strength high vs. low temperature = estimate of temperature main effect
Common Pitfalls
- Confusing factor (input) with response (output)
- Treating repetition as replication
- Skipping randomization and then “discovering” a huge effect that is really a time trend
- Studying factors the process cannot actually control in production
- Running DOE before MSA—so “effects” are gage theater
Master these terms and you meet BoK V.A.1 at the Understand level—and you are ready to apply plot interpretation for main effects and interactions.
In a paint-line DOE, booth temperature and line speed are set according to a run matrix, and dry-film thickness is recorded for each run. Which labeling of variables is correct?
A Green Belt measures five consecutive parts during a single machine setup at one treatment combination and labels those five values “five replications.” What is the best correction?