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[Process Optimisation]
Free tool

Design of Experiments

Build a full or fractional factorial experimental plan for 2–7 process factors, see how many runs each costs, and export the design matrix ready to fill in.

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Factors

List each input you want to vary and the two settings you will test it at. Two levels per factor — this design tells you which factors matter and how they interact, not where the optimum curve peaks.

FactorLow levelHigh levelRemove factor
Design type

Why it matters: it protects you from anything that drifts over time — a warming room, a settling feedstock, an operator getting better at the job — being mistaken for a factor effect. Randomise unless a factor is genuinely impractical to change between runs.

Your design
Runs required
8
Factors
3
Full factorial
8runs
Runs saved
—

Run the experiments in the order shown and record your Product Yield (%) against each one.

Design matrix

RunTemperaturePressureCatalystProduct Yield (%)
1150−2−1−—
2150−2−3+—
3150−5+1−—
4150−5+3+—
5200+2−1−—
6200+2−3+—
7200+5+1−—
8200+5+3+—

The small + and − show the coded level behind each real setting. Coded levels are what the analysis works in; the real values are what you set on the plant.

Factor balance

Factor balance: Temperature 0.00, Pressure 0.00, Catalyst 0.00. Zero is perfectly balanced.Temperature0.00Pressure0.00Catalyst0.00mean coded level — 0 is balanced

Every factor is tested equally often high and low — the design is balanced, so each effect can be read independently of the others.

Design space — first two factors

Design space for Temperature against Pressure: 4 distinct settings across 8 runs.222215020025TemperaturePressure
Each marker is a corner of the design space; the number in it is how many runs sit there.
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Results are indicative

Figures assume typical conditions and the stated method. For measured, guaranteed numbers on your plant, our engineers run site surveys, heat loss audits, and full process models.

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Send us the result — we'll tell you what it means for your plant.

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One factor at a time cannot find what you are looking for

The instinct when a process misbehaves is to change one thing, see what happens, change it back, change the next thing. It is careful, it feels rigorous, and it is almost the worst way to spend the experiments.

It fails for a specific reason: it cannot see interactions. If a higher temperature only helps when the catalyst loading is also high, no amount of varying temperature at fixed catalyst will reveal it. And on real chemical and thermal processes, interactions are usually where the money is.

A factorial design varies everything together, in a pattern, so that every factor is tested equally often at both settings. Each run contributes to the estimate of every effect rather than just one — which is why factorial designs get more information from fewer experiments, not more.

What the designs cost

Two levels per factor, full factorial:

FactorsFull factorialRes IV fractionRes V fraction
3888
41688
532816
664816
7128816

Seven factors as a full factorial is 128 experiments. As a resolution IV fraction it is 8 — a 1/16th fraction that still estimates all seven main effects.

That saving is real, and it is not free.

What a fraction gives up: aliasing

A fractional design builds its extra factors as products of the base ones. In the 2⁷⁻⁴ design, factor 4 is the product of factors 1 and 2. The consequence is that the design cannot tell the effect of factor 4 apart from the interaction between factors 1 and 2 — they are aliased, and the number the analysis returns is their sum.

Resolution names how bad the aliasing is:

  • Resolution IV — main effects are clear of two-factor interactions, but two-factor interactions are confounded with each other. Right for screening, when you want to know which of many factors matter at all.
  • Resolution V — main effects and two-factor interactions are all clear of one another. Right when you already know which factors matter and need to understand how they combine.

The honest workflow is usually two stages: screen seven or eight candidates in 8 runs at resolution IV, then take the three or four that survive and run a full factorial with replication on those.

Randomising the run order

The randomise option shuffles the order in which you actually perform the runs, and it matters more than it looks.

Anything that drifts over the course of a day — a warming room, a settling feedstock, a catalyst slowly deactivating, an operator getting better at the job — will be read as a factor effect if you happen to run that factor's settings in time order. Randomising breaks the correlation, so drift becomes noise rather than a false result.

Randomise unless a factor is genuinely impractical to change between runs. If one is (a furnace that takes six hours to change temperature, for instance), that is a split-plot design, and it needs analysing as one — the calculator does not build split-plot designs.

Reading the design

Coded levels are −1 and +1 for the low and high setting of each factor. The analysis works in coded units, which is what makes the effects directly comparable regardless of whether a factor is measured in °C or bar. The table shows both the coded level and the real value you set on the plant.

Balance is the mean coded level per factor. Every one should be exactly zero: that is what "each factor tested equally often high and low" means, and it is the property that keeps the estimated effects independent of each other and of the overall mean. The calculator plots it so an unbalanced design cannot slip through unnoticed.

Limits worth stating before you run anything

  • Two levels only. Two-level designs assume the response is roughly linear between your settings. They find which factors matter and how they interact — they cannot locate an optimum inside the range or detect curvature. That needs centre points, and then a response-surface design (central composite, Box–Behnken).
  • No replication. Without repeated runs you have no independent estimate of experimental error, so you cannot tell a real effect from noise. Add replicates or centre points if you need a significance test rather than a ranking.
  • It plans, it does not analyse. The design matrix and an empty response column come out; the effects, the ANOVA and the model do not.
  • It does not know your constraints. Some combinations of settings will be unsafe, impossible, or will wreck a batch. Read every row before you run it.
  • Choose your levels well. Too narrow and a real effect vanishes into measurement noise; too wide and you leave the operating envelope or hit a non-linearity the design cannot represent.

An hour spent choosing factors and levels is worth more than any amount of sophistication in the design that follows.

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Frequently asked questions

By how many factors you have and how sure you are about them. Up to about four factors, run the full factorial: 16 runs is affordable and you get every interaction cleanly. With five or more, a fraction usually wins — seven factors drops from 128 runs to 8. The rule of thumb is to screen many factors with a resolution IV fraction, then run a full factorial on the two or three that survive. Full factorial when you need certainty about interactions; fractional when you need to find out which factors matter at all.

It tells you what is confounded with what. Resolution IV keeps main effects clear of two-factor interactions but confounds two-factor interactions with each other — fine for screening, where you only want to know which factors matter. Resolution V keeps main effects and two-factor interactions all clear of one another, which you need once you are trying to understand how factors combine. Higher resolution costs runs: for six factors, IV is 8 runs and V is 16.

To stop time-varying effects being mistaken for factor effects. If the room warms through the day, the feedstock settles, or the catalyst slowly deactivates, and you happen to run all the high-temperature trials in the afternoon, that drift shows up as a temperature effect. Randomising breaks the correlation so the drift becomes noise instead of a wrong answer. The exception is a factor that is genuinely impractical to change between runs — that is a split-plot design and needs analysing as one.

No, and it is important to be clear about that. Two-level factorial designs assume a straight line between your low and high settings, so they identify which factors matter and how they interact — but they cannot see a peak in the middle of the range. Finding an optimum needs centre points to detect curvature and then a response-surface design such as a central composite or Box–Behnken. This tool is the screening step that tells you which factors are worth taking to that stage.

This generator builds two-level designs without replication, which is the standard screening starting point. Without replicates you have no independent estimate of experimental error, so you get a ranking of effects rather than a significance test. If you need to say an effect is statistically real, add replicate runs or centre points — centre points are especially efficient, since they also tell you whether the response is curved.

Wide enough that a genuine effect is bigger than your measurement noise, narrow enough to stay inside a safe and physically sensible operating envelope. Too narrow is the more common mistake: a timid range makes real effects look like nothing and wastes the whole experiment. If you know the process is non-linear across the range you want, split it into two experiments rather than stretching one design across a bend in the response.

No. The design is generated in your browser and the CSV export is built locally — no factor names, levels or results are sent to a server. The earlier version of this calculator downloaded a Python runtime to do the same arithmetic; this one does not need it, so it also works offline.