# Design of Experiments (DOE) / Statistical Design of ExperimentsExploring and discovering the virtual world

Statistical design of experiments is a methodology that allows to find optimal working points of a system depending on several input variables. In contrast to classical optimization, no objective function is defined. Only the system response related to input variables has to be described mathematically.

## Example

For an illustrative representation, a system with two parameters is assumed below. The efficiency of a motor is considered as a function of rotational speed and torque. In this case, the efficiency in a three-dimensional coordinate system is presented as a generally curved surface. It is also described as the response surface.

## Demarcation

With a DOE study, the efficiency degree is only evaluated at discrete points, so that a maximum value can always be specified from the amount of evaluated efficiencies. This is a significant advantage compared to a classical optimization. However, it is possible that local maxima are overlooked. In this case, the determined maximum value does not match the maximum efficiency degree. Maxima beyond the specified test room are also not recorded. The Statistical Design of Experiments can be understood in first approximation as a limited optimization, if also no boundary conditions can be formulated in dependence on which a system should be optimized.