Experimentation is arguably one of the fundamental pillars of the scientific method. The appropriate execution and analysis of a carefully controlled experiment is the main way to establish a cause-effect relationship. Experiments, however, are not limited to the scientific community only, but are also carried out in many industrial scenarios on a regular basis. For example, companies in the baking industry are usually interested in studying the influence of the production settings on the quality of the dough produced. These settings consider the initial moisture content of the dough, the screw speed of the mixer, the feed flow rate of water being added to the mix, etc. The main objective is to identify the affordable settings that lead to a high-quality dough and therefore to a good product.
In general, the purpose of an experiment is to identify the influence that a set of experimental variables has on the process under study. By systematically manipulating the settings of these variables, it is possible to quantify how and to which extent they affect one or more response variables that measure the process’s behaviour. The design of an experiment mainly consists in determining the number of experimental runs, the settings of the experimental variables in each run, and the sequence in which the runs need to be executed. This should be done with the purpose of maximizing the amount of information produced by the experiment. The "optimal design of experiments" approach achieves this by generating a design that is specifically tailored to the characteristics of the process. This is a very challenging task since it requires solving a very complex optimization problem.