Statistical concepts of excipient compatibility studies

An important intermediate step  during the production of pharmaceutics is to test how the active ingredient behaves over time. Especially the inactivation by several factors (decomposition, crystallization, ...) is an important parameter.
The final drug is composed of, on the one hand, a mixture of the active ingredient with several functional excipients, and on the other hand, a mixture of fillers to achieve the desired mass and volume. As a result, the final drug can be viewed as a mixture of mixtures. On top of that, several variables from the testing procedure (e.g. humidity, temperature, length of experiment) should also be taken into account. These variables are called process variables.
The goal of this PhD is to develop a good statistical model to account for the specific problems encountered when working with a mixture of mixtures combined with process variables. Based on this model, a suitable optimality criterion can then be derived to develop an optimal experimental design. An algorithm will be developed to help design future experiments ina fast and efficient way.