Choosing pH with temperature fixed at 30°C, then choosing agitation speed with that pH fixed, is familiar. Even if each graph is smooth, the final combination is not guaranteed to be good across the full range. The effect of one factor may change at another factor's level.

Align experimental language with four terms

• factor: an input variable the experimenter changes or controls
• level: the actual condition assigned to a factor
• response: the output measured in a run
• run: one application of a treatment combination to an independent experimental unit

Combining 30/37°C with pH 6.8/7.4 gives two factors, two levels each, and four treatment combinations. Reading several plate wells at each combination does not by itself create more independent runs. The design defines the experimental unit: independently treated culture, batch, donor, or another unit.

OFAT sees only axes extending from the reference point

OFAT changes A alone at a reference condition, then B alone again at that reference. With two factors at two levels, it sees the reference, A-high, and B-high corners, but not A-high/B-high.

If response is additive, Y=β₀+βAA+βBB, the missing corner can be predicted from the two axis effects. But when βAB×A×B exists, the A effect changes with B's level. This is interaction.

• no interaction: lines joining A low and high are parallel at B levels
• interaction: slopes differ or cross

Interaction does not mean “both factors are individually significant.” It means one factor's effect depends on the other's condition.

DOE is an information-allocation strategy, not a synonym for minimum runs

DOE starts by specifying the research objective and candidate model, then lays out treatment combinations and run order so effects can be separated. It is not a technique for reducing runs at any cost. Full factorial designs observe every combination; fractional factorial designs select some combinations while accepting assumptions that some effects are small and some terms are aliased.

A sound DOE plans all of the following:

1. the question and measurement definition of the response
2. controllable factors and realistic ranges
3. candidate main effects, interactions, and curvature
4. independent experimental units and replication
5. randomization and blocking constraints
6. analysis, diagnostics, and confirmation experiments

Distinguish statistical exploration space from regulatory design space

An area within factor ranges where a fitted model predicts the response criteria will be met may be called a “design space” in an educational setting. Regulatory design space in ICH Q8, or MODR in ICH Q14, however, are domain concepts with development evidence, multivariate understanding, and submission/approval context. Do not automatically call the inside of a simple contour a regulatory-approved design space.

This course calls it precisely a statistical exploration region within the experimented factor ranges. QbD terms such as CQA and CPP are not prerequisites for DOE mathematics and should not support process claims without domain validation.

In-Silico Lab: see one hidden process in two ways

The Lab's hidden response is Y=70+8A+5B+γAB.

1. At γ=0, compare whether OFAT and factorial effects agree.
2. At γ=6 or 10, inspect the high-high response that OFAT does not see.
3. Consider under ±1 coding why the AB effect is twice γ.
4. Answer whether γ can be calculated from only the three OFAT points.

JMP figures reveal DOE's purpose in advance

An Interaction Plot shows nonparallelism; contours and surfaces show combination space; a Prediction Profiler shows fitted-model predictions by condition. This unit is not a menu or optimization-clicking guide. A figure becomes meaningful only after understanding which points were measured and why.

DOE does not automatically turn observational data into an experiment

Having several factor columns in already-produced historical data does not make it DOE. Causal effect interpretation needs the experimenter to assign combinations and control run order, experimental units, and noise sources. Even within DOE, record and diagnose run failure, noncompliance, and measurement drift.

Takeaways

• Define factor, level, response, and run together with the experimental unit.
• OFAT observes only axes from a reference point.
• Interaction means one factor's effect depends on another factor's level.
• DOE arranges combinations to separate information for a candidate model.
• Question, replication, and randomization come before minimizing runs.
• Do not equate a statistical exploration region with regulatory design space.

The next unit reads 2² and 2³ full-factorial tables directly and calculates balance, orthogonality, main effects, and interactions.

Official supplementary resources

• NIST/SEMATECH · Choosing an experimental design
• NIST/SEMATECH · DOE terminology

The process and Lab in this article are educational synthetic models.