DOE (Design of Experiments) can be defined as a set of statistical tools that deal with the planning, executing, analyzing, and interpretation of controlled tests to determine if there is a casual relationship between your process factors or variables and your process output.

## Overview: What is DOE?

Two common approaches to DOE are a full factorial DOE and a fractional factorial DOE. The purpose of the full factorial DOE is to determine what settings of your process inputs will optimize the values of your process outcomes. As an example, if your output is drilling of holes in a metal part, and your primary process variables are drill speed, temperature, and drill bit size, then what combination of those factors will give you the desired consistent hole size?

With the three variables above, how many different unique combinations would you have to test to explore all the possibilities? Which combination of the three factors will give you the most consistent drill hole? The experimentation using all possible factor combinations is called a full factorial design.

But what if you aren’t able to run the entire set of combinations of a full factorial? What if you have monetary or time constraints, or too many variables? This is when you might choose to run a fractional factorial, also referred to as a screening DOE, which uses only a fraction of the total runs.

The output of your DOE will indicate which individual factors have a significant impact on your outcomes. These are referred to as main effects. You will also be able to determine whether there are any significant interaction effects. Interactions occur if the impact of one factor on your response is dependent upon the setting of another factor.

## An industry example of DOE

Charlie works for a company that helps NASCAR drivers perform better. He decided to see if he could improve the gas mileage of a car, so they didn’t have to come off the track to refuel as often. Charlie decided to try and use DOE to see if he could improve performance.

He narrowed down the key factors to be the octane of the fuel, track speed, tire pressure, and time of day. Charlie chose to do a 2 level, 4 factor full factorial experiment. This experiment required 16 runs which he could accomplish over the course of two days using a nearby test track.

After running his 16 trials, he concluded that speed was a significant main effect while there was an additional interaction between tire pressure and time of day. After fully analyzing his DOE, he was able to adjust his combination of factors to increase fuel performance by an additional 5 mpg thus eliminating 2 pit stops during a typical race.

### What is the difference between correlation and DOE?

Correlation establishes whether there is a significant relationship between your dependent and independent variables. It does not establish causation. DOE also establishes whether there is a significant relationship between your variables, but it determines the causal relationship by using controlled experiments.

### What are DOE main effects?

The main effects of a DOE are the individual factors that have a statistically significant effect on your output.

### How can I calculate how many experiments or runs I would have to do if I did a two level, full factorial experiment with 4 factors?

The formula for calculating the number of runs of a full factorial DOE is # Runs = X^K where X is the number of levels or settings, and K is the number of variables for factors. Therefore, you would be 2^4 or 16 runs.