DOE

Design of experiments (DOE) is the most efficient approach for organizing experimental work. DOE selects a diverse and representative set of experiments in which all factors are independent of each other despite being varied simultaneously. The result is a causal predictive model showing the importance of all factors and their interactions. These models can be summarized as informative contour plots highlighting the optimum combination of factor settings. DOE is used for three primary objectives:

Screening
Which factors are most influential and over what range?

Optimization
How can we find the optimum settings taking into account conflicting demands of different responses?

Robustness testing
Once the optimum is found, can we guarantee robustness close to that point or do we need to change specifications to achieve robustness?

Let's continue with a comparison of two experimental situations, with and without DOE.

Imagine that all possible results from some experimental reaction are known to you and summarised as a contour plot. The axes relate to two independently controlled factors, temperature and time. Changes in these factors cause the yield of the reaction to vary from low values (dark blue) to high (red).

Let’s see what happens when someone begins experimenting with the process, without knowing about the contour map. Will they reach the optimum?

Our experimenter begins by fixing temperature and varying time. The yield rises from 30% to over 40%, but soon begins to drop off again. Time is fixed at its best level and now temperature is varied. This affects the yield in a similar way and the best temperature is chosen. At this point, the experimenter concludes that the optimum has been found.

With the contour map to look at, it is easy to see what went wrong. Increasing time would have had a much greater impact on yield at a lower temperature. In other words, the key to understanding the system lies in the interaction between the two factors.

Let's start again but use design of experiments this time. With an experimental design, you plan a set of experiments where all the factors are varied in a systematic and balanced manner. In a simple factorial design, for example, each factor is ascribed a low and a high level and you carry out all combinations of all factors at the two levels. Hence, two factors describe a square array of experiments, three describe a cube and four or more a hypercube.

As before, the experiments are marked on the contour plot (red dots). This time, the design allows the effects of the two factors and their interaction to be calculated using a multiple regression model, making part of the map visible.

With the newly found window into the contour map, it is easy to locate the best direction for finding the optimum.

As mentioned previously, interaction is the key to understanding the system. When you apply DOE to your own systems, you will discover how common and influential these interactions are in practice.

Finally, let's work out the number of experiments required for this design. There are the four corner points defining the square plus three additional centre points for diagnostic purposes. So just seven experiments in all!

The quickest way to get started with design of experiments is to take a basic, three-day training course with Umetrics Academy.

Look up our Course Calendar to find a convenient location and date.

You can also find More Reading about design of experiments, or order Literature for Self-training.

To find out more about multivariate technology, continue with multivariate data analysis at MVDA – How it Works.

Our state-of-the-art software for design of experiments is MODDE. Read more about it here.

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