Factorial Experiment Lab.
A heat-sealing machine is making weak seals. Three settings could be to blame: temperature, dwell time (how long the hot jaws stay closed) and pressure. If you change one setting at a time, you can miss the best recipe when two settings work together. So here you test all eight mixes of low and high settings. That’s called a factorial experiment. See which settings really matter, then compare with the one-at-a-time way.
Change one setting at a time, and you can miss what two settings do together.
A heat sealer is making weak seals. The suspects are temperature, dwell time (how long the hot jaws stay closed) and jaw pressure. Each corner of the cube is one mix of low and high settings. Press Run 8 trials to test all eight. Then press Compare one at a time to see which settings that approach would pick.
Settings · result is peel strength, N per 15 mm of seal
| Setting | Low − | High + |
|---|---|---|
| ASeal temperature | 150 °C | 170 °C |
| BDwell time | 0.8 s | 1.2 s |
| CJaw pressure | 40 psi | 60 psi |
Run-to-run noise
Answer key
Strength here means peel strength: the force, in newtons (N), needed to pull the seal apart, per 15 mm of seal. Real runs scatter, so the same settings never give exactly the same seal. σ (sigma) is the typical size of that scatter, here 0.6 N. Each run’s random luck is fixed, so turning noise off and on reuses the same runs. The lab knows the true process, which a real factory never does. Show truth draws it next to your estimates.
Run log
No runs yet. Each round runs the eight combinations in a new random order.
Effects, largest first · change in strength, N
Run the trials to measure each effect: how much seal strength changes when a setting goes from low to high. AB, AC, BC and ABC are interactions, where one setting changes what another one does. Hover or tap a row to light up the corners on its + side.
Interaction · A × B
Parallel lines mean the two settings don’t affect each other. Lines that cross or spread apart mean one setting changes what the other one does. That’s an interaction.
All eight combinations
| # | Corner | Settings | ± | Runs | Average |
|---|---|---|---|---|---|
| 1 | 150 °C · 0.8 s · 40 psi | · | – | – | |
| 2 | 170 °C · 0.8 s · 40 psi | · | – | – | |
| 3 | 150 °C · 1.2 s · 40 psi | · | – | – | |
| 4 | 170 °C · 1.2 s · 40 psi | · | – | – | |
| 5 | 150 °C · 0.8 s · 60 psi | · | – | – | |
| 6 | 170 °C · 0.8 s · 60 psi | · | – | – | |
| 7 | 150 °C · 1.2 s · 60 psi | · | – | – | |
| 8 | 170 °C · 1.2 s · 60 psi | · | – | – |
How the model works, how it’s checked and what it leaves out
How it works
Each setting is coded as −1 (low) or +1 (high). A is seal temperature, 150/170 °C. B is dwell time, 0.8/1.2 s. C is jaw pressure, 40/60 psi. The hidden process is y = 18 + 2.4A + 0.3B + 0.25C + 2.1AB − 0.2AC + ε, in N/15 mm, where AB means A times B. ε is each run’s random noise, drawn from a bell curve: ε ~ N(0, σ²), with σ = 0.6 (or 0 with noise off).
Each round (a replicate) runs the eight corners in a new random order. The orders and the noise come from fixed seeds, so Reset replays exactly the same runs.
Each effect is the average result on its + corners minus the average on its − corners: mean(y at +) − mean(y at −). That works out to twice its coefficient in the formula. With one round, “bigger than noise” uses Lenth’s pseudo standard error (PSE), a noise guess made from the smallest effects. The margin of error is 3.764 × PSE. With two or three rounds, it uses how much repeat runs of the same corner scatter (the pooled within-cell variance). That scatter has n − 8 degrees of freedom: n runs in total, minus the 8 used up by the corner averages. It gives s, the typical scatter, and SE = 2s/√n, the typical error in one effect. The dashed line sits at SE times the cutoff from a two-sided 95% t-test, a standard check for “bigger than chance”.
How it’s checked
With noise off, the measured effects equal twice the true coefficients: A +4.80, AB +4.20, B +0.60, C +0.50, AC −0.40, BC and ABC 0. The seven columns of + and − signs are perfectly balanced against each other (orthogonal). So changing one true coefficient moves exactly one estimate. AB equals half the difference between B’s effect at 170 °C and at 150 °C.
OFAT starts with every setting low and changes one setting at a time, keeping whichever level looked better. Then it checks the final mix with a fifth run. It has its own random seed, so comparing never changes the factorial runs. With noise off, it settles on A+ B− C+ at 18.05 N. The best corner, A+ B+ C+, gives 22.85 N.
What it leaves out
Curves: there are no runs at middle settings (centre points), so it can’t tell if strength bends between low and high. Grouping runs into blocks, such as by day (blocking). Drift over the run order. Error in the strength tester itself. Settings that are hard to change. Checks on the leftover errors (residual diagnostics).
Lenth’s method assumes most effects are zero. So even with σ = 0, it still treats the small real effects B, C and AC as noise. A real study would add centre points, plus check runs at the chosen settings, before changing the recipe.