I thought this website had a nice summary of what DOE is:

http://www.qualitytrainingportal.com/resources/problem_solving/problem-solving_tools-doe.htm

Here’s an example of a full factorial table. The Problem Statement here could be “What is the most fuel efficient way of driving my car”.

The factors and levels are:

Speed: 55mph or 60mph

Petrol Octane: 85 or 90

Tire Pressure: 30psi or 35psi

The response or read out for the experiment is the mpg.

As we can see the best combination of factors and levels that offers us the highest mpg (miles per gallon) is Speed 55mph, Petrol Octane 90 and Tire Pressure 35psi as this offers us 40mpg.