# DOE Variables

Common terminology in a DOE.

## Variables

System parameters that can be changed to improve the system performance.

## Reduced Variables

In DOE terminology, it is standard practice to work with reduced variables that have a range of -1 to 1 for each real variable. Reduced variables are associated to real variables with the following formula:
$y=\frac{x-\frac{\left({x}_{\mathrm{max}}+{x}_{\mathrm{min}}\right)}{2}}{\frac{{x}_{\mathrm{max}}-{x}_{\mathrm{min}}}{2}}$

where x is the initial variable, and y is the reduced variable.

## Levels

Values taken by y in the range [-1; +1]. The number of levels per variable to be considered depends on the level of non-linearity in the problem; for a linear model two levels are sufficient; for a quadratic model three levels are needed.