# The main principles of statistical Design of Experiments (DoE)

## The underlying ideas of statistical Design of Experiments (DoE)

Varying simultaneously all potential influence factors within the statistical Design of Experiments (DoE) guarantees an optimal coverage of the factor region. The experimental designs are chosen so that a minimal number of experiments yield maximum information. A very efficient way to use statistical Design of Experiments (DoE) is to follow a sequential approach. Our user-friendly DoE tool STAVEX consequently implements this approach.

## Sequential statistical Design of Experiments (DoE)

First, the number of investigated influence factors is reduced in screening and modelling stages. As soon as a small enough number of factors is reached, a new series of experiments is performed as the final optimisation step. The choice of the DoE stage depends on the number of included factors and the desired amount of information.

### *DoE screening stage (at > 8 factors):*

A relatively small number of experiments, compared to the number of included factors, i.e. also relatively few information. In this DoE stage the only aim is to reduce the number of factors.

*DoE modelling stage (approx. 4-8 factors):*

An intermediate number of experiments, compared to the number of included factors. Here, a linear model with interactions is fitted. The aim of this DoE stage is still to reduce the number of factors.

### *DoE optimisation stage (approx. 1-3 factors):*

Here, a quadratic model is used. Such a model allows to identify minima (lowest point of a "cup") and maxima ("peaks"), i.e. in this stage the optimum is found. This cannot be achieved within the modelling stage, as there the model is not quadratic, but linear.

## It's your competence - DoE is your tool!

Employ the above mentioned principles optimally according to your applications. Depending on the application, it is sometimes possible and even recommended to try an optimisation already at a larger number of factors (e.g. in bio-technology).

Moreover, do not be misled by the software stating the "best factor combination" in the modelling stage analysis. A linear model (with or without interactions) can be used for a first investigation of the underlying factor relations and the general tendency. For the final optimisation of a product or process, it is necessary to proceed to the DoE optimisation stage. Only there, a "peak" or a "lowest point of a cup" can be calculated. Only here you obtain reliable predictions.

## Higher flexibility due to sequential Design of Experiments (DoE)

One of the many advantages of the sequential approach to statistical Design of Experiments (DoE) is that the "region of interest" (i.e. the investigated factor area) can be adapted at the start of each experimental stage.

This area should not be chosen too wide in order to obtain a good approximation. However, if one stage shows that a higher temperature leads to better results, the next experimental stage can be performed e.g. at 60-80°C instead of the current 30-60°C.