## Design of Experiments (DoE)

#### Why experimental design?

When collecting new data for multivariate modeling, one should pay attention to the following criteria:

#### Focusing

from fewer experiments
Collect only the information that is really needed

There are four basic ways to collect data for an analysis:

1. Obtain historical data
2. Collect new data
3. Run specific experiments by disturbing (exciting) the system being studied
4. Design experiments in a structured, mathematical way

With designed experiments there is a better possibility of testing the significance of the effects and the relevance of the whole model.

Experimental design (commonly referred to as DOE) is a useful complement to multivariate data analysis because it generates “structured” data tables, i.e. data tables that contain an important amount of structured variation. This underlying structure will then be used as a basis for multivariate modeling, which will guarantee stable and robust models.

More generally, careful sample selection increases the chances of extracting useful information from the data. When one has the possibility to actively perturb the system (experiment with the variables), these chances become even greater. The critical part is to decide which variables to change, the intervals for this variation, and the pattern of the experimental points.

#### What is experimental design?

Experimental design is a strategy to gather empirical knowledge, i.e. knowledge based on the analysis of experimental data and not on theoretical models. It can be applied when investigating a phenomenon in order to gain understanding or improve performance.

Building a design means carefully choosing a small number of experiments that are to be performed under controlled conditions. There are four interrelated steps in building a design: : e.g. "better understand" or "sort out important variables" or "find the optimum conditions"

 Define the objective of the investigation: e.g. “better understand” or “sort out important variables” or “find the optimum conditions” Define the variables that will be controlled during the experiment (design variables), and their levels or ranges of variation. Define the variables that will be measured to describe the outcome of the experimental runs (response variables), and examine their precision Choose among the available standard designs the one that is compatible with the objective, number of design variables and precision of measurements, and has a reasonable cost

Design-Expert® which is available from The Unscrambler® X provides a large variety of experimental designs to solve most common problems. The user specifies the experimental objective, the number (and nature) of the design variables, the nature of the responses and the economical number of experimental runs have been defined. Generating such a design will provide the user with the list of all experiments to be performed in order to gather the required information to meet the objectives.

The figure above shows the Box-Behnken design drawn in two different ways. In the left drawing one can see how it is built, while the drawing to the right shows how the design is rotatable.

#### DOE with The Unscrambler® X

CAMO software has teamed up with Stat-Ease to provide the customers access to their leading Design-Expert® software for experimental design. This extension lets the users access many powerful statistical tools to optimize their products or processes. It supports designs such as factorial screening designs, factorial studies, response surface methods, mixture design techniques and their combinations. When setting up the experimental design, the user will be automatically redirected to Design-Expert®. After specifying the experiment, the data can either be further analyzed with classical statistics such as ANOVA and MLR or transferred back to The Unscrambler® X for multivariate analysis.

### The Unscrambler® X with Design-Expert

The Unscrambler® X provides powerful statistical tools to help you optimize your product or process, such as:

• Two-level factorial screening designs: Identify the vital factors that affect your process or product so you can make breakthrough improvements.
• General factorial studies: Discover the best combination of categorical factors, such as source versus type of raw material supply.
• Response surface methods (RSM): Find the optimal process settings to achieve peak performance.
• Mixture design techniques: Discover the ideal recipe for your product formulation.
• Combinations of process factors, mixture components, and categorical factors: Mix your cake (with different ingredients) and bake it too!

Your Design-Expert program offers rotatable 3D plots to easily view response surfaces from all angles. Use your mouse to set flags and explore the contours on interactive 2D graphs. Our numerical optimization function finds maximum desirability for dozens of responses simultaneously!

You'll find a wealth of statistical details within the program itself via various Help screens. Take advantage of this information gold mine that is literally at your fingertips. Also, do not overlook the helpful annotations provided on all reports.

For details of Design-Expert® features, visit the Stat-Ease website.