Design of experiments in formulation: optimization

The first article on planning experiments in formulation of this treatise was devoted to the presentation and application of techniques for selecting the ingredients of a formula and highlighting, among the factors characterizing a manufacturing process, those which have a real effect on the properties of the final product.

This second article is devoted to the development of a formula, which corresponds to its optimization and is often the next step. It requires the use of a predictive mathematical model to be able to simulate the behavior of the properties studied in the experimental field. The fact that the proportions of a mixture cannot vary independently, since their sum is constant and equal to 1, obliges the experimenter to use experiment matrices and specific mathematical models. These techniques, known as Scheffé matrices and models, are presented here.

However, there are many circumstances which often make it impossible to implement these tools. Experimental domains are generally subject to numerous constraints on the proportions of components, due to technical (instability of the mixture), sanitary (standard to be respected), economic (expensive component), etc. necessities. We will therefore study the impact of these constraints on the shape of the experimental domain and the "tailor-made" planning techniques that must then be used.

Sometimes, the techniques mentioned above (Scheffé matrices and models, or custom matrices) are "just" inappropriate. This is particularly the case when studying the behavior of a mixture around a given composition, especially when optimizing a formula that has already been manufactured, and which we will study in the paragraph entitled "Modeling in the vicinity of a given formula".

In addition to the composition of the formula, the experimenter must also take into account so-called "process" factors, such as molding temperature, extrusion speed, drying time, etc. We'll devote an entire section to this problem, entitled "Mixed factor/component problems". We will devote an entire paragraph to this problem, entitled "Mixed factor/component problems", in which we will also show how a very small component can be taken into account.

Finally, experimental planning would not be complete without the analysis and interpretation of results. We will illustrate a wide range of analysis techniques, depending on the type of problem presented, with particular emphasis on graphical methods. In particular, we will demonstrate the use of the "desirability" technique, which enables us to find the best compromise between several sometimes contradictory properties.

Readers are reminded that this presentation consists of two...