The coupling of individual models in terms of end-to-end calculations for unit operations in manufacturing processes is a challenging task. We present a probability distribution-based approach for the combined outcomes of parametric and non-parametric models. With this so-called Bayesian predictive ensemble, the statistical moments such as mean value and standard deviation can be accurately computed without any further approximation. It is shown that the ensemble of different model predictions leads to an uninformed prior distribution, which can be transformed into a predictive posterior distribution using Bayesian inference and numerical Markov Chain Monte Carlo calculations. We demonstrate the advantages of our method using several numerical examples. Our approach is not restricted to certain unit operations, and can also be used for the more robust interpretation and assessment of model predictions in general.

Determining process variances in biopharmaceutical manufacturing is challenging due to limited data availability. To address this, we introduce a Bayesian hierarchical model designed for meta-analysis of process variance. This approach can improve process variance estimation by integrating data from multiple products, providing more reliable estimates of critical quality attributes in cases of data scarcity. Additionally, our model aids in evaluating process models, ensuring quality in process development. The paper demonstrates the new method using a simulation study, showcasing its potential to leverage historical data for both upstream and downstream phases of future CMC drug development. The new statistical model has great potential to expedite the market introduction of therapies while ensuring patient safety, allowing new treatments to reach patients more quickly without compromising quality or efficacy.