Quality-by-Design Using a Gaussian Mixture Density Approximation of Biological Uncertainties

In this contribution the uncertainties of a biological process model are taken into account explicitly to calculate optimal process trajectories. For this purpose, the initial condition and the uncertainties of the model parameters are described by a weighted sum of normal distributions. Such a so-called Gaussian mixture density (GMD) approximation is propagated through the nonlinear process model to calculate a second order approximation of the statistical properties of the planed process trajectory. A Value@Risk primary objective is used to obtain an optimal process design procedure in presence of uncertainties. In an extensive simulation study a descriptive fermentation process model is used to compare the classical trajectory planning with the robust design approaches. Here, different degrees of approximation complexity and the influence of the weighting factor in the Value@Risk dual objective criterion is investigated.