Design of Experiments (Full Factorial)

What it does

A 2-level full factorial experiment tests every combination of the low and high settings of 2 to 5 factors. Unlike changing one factor at a time, it measures each factor’s effect and also the interactions, where the effect of one factor depends on the setting of another.

The tool builds the run table (with a random run order if you want it), then analyses the results you paste in: which effects are significant, the model equation in coded and original units, and the main-effects and interaction plots. It works with or without replicates.

Method

The analysis follows Montgomery’s treatment of 2^k factorial designs, with exact p-values when the runs are replicated and an established method for experiments without replicates. The calculation reproduces the effects, sums of squares and p-values of the book’s worked examples.

Worked example

The data behind “Try an example” is Montgomery’s plasma etch experiment: etch rate (Å/min) with factors A gap, B C2F6 flow and C power, 2 replicates, 16 runs.

Power has the biggest effect, and gap matters mostly through its interaction with power: at high power a wider gap lowers the etch rate sharply, while at low power it raises it slightly, so the two must be set together. Flow has no significant effect and can be set for cost.