In the context of Design of Experiments (DOE), center points are used. These are extra runs in the mathematical centre of two continuous variables. Let’s look at this further to understand the importance of center points in setting up your DOE.

## Overview: What are the center points?

Design of experiments (DOE), is a great tool to understand the relationships between your input and output variables. DOE is simply a more advanced version of linear predictive. It is assumed that the relationship is linear.

DOE creates a series of experiments or runs that allow for exploration of all possible combinations in real-time. A linear relationship is also the assumption of most designs. However, this assumption might not be true. This is where the idea about center points comes into play.

Basic DOE designs typically use a 2-level experiment to obtain center points. This allows for continuous data at both a low- and high-level level. If you want to study the relationship between temperature, pressure and line speed in relation to lamination thickness, then you could set your experimental levels at:

- For pressure, 90 and 120 PSI
- Temperature ranges between 120 and 180 degrees Fahrenheit
- Line speed can be between 200 and 400 feet per minute

Your experiment would be run under the assumption that there is a linear relationship between levels of the three factors, lamination thickness, and the other variables. What if this wasn’t the case? Your prediction equation would be incorrect, and your estimate of lamination thickness wouldn’t be accurate.

These are simply additional runs that are performed at the mathematical center for the high and low settings of each continuous factor.

That would be the pressure at 105 psi. This is between 90 and 120. It would also be 140°F for temperature and 300 fps to determine line speed.

Each center point can be run one to many times. The final calculations of your DOE will show whether the relationship is linear or curvilinear. If the relationship is curvilinear you will need to switch from your fractional and full factorial DOE methods and use a more advanced tool like Response Surface Modeling (RSM).

## A case study from an industry that demonstrates the importance of center points

A chemical company was testing the manufacturing yield of a new formulation. The temperature was one of the factors that they used in their Design of Experiments (DOE) to get center points. They were unsure if the relationship between yields and temperature was linear or curvilinear. They decided to run three runs at the middle point of their high and low-temperature settings.