Probabilistic design spaces from small DoEs – A boundary-focused workflow using quantile surrogates

Probabilistic design spaces enable pharmaceutical manufacturers to balance regulatory compliance and operational efficiency. In this context, the "edge-of-failure" separating compliant from non-compliant operation is not a fixed line, but an uncertain region driven by model parameter uncertainty. Traditional methods typically map this probability of failure across the whole design space, which is a computationally expensive task. We propose a more direct approach, reformulating the problem using quantile functions to search for a deterministic boundary at a desired confidence level. These functions are approximated via Gaussian process surrogates using a novel adaptive sampling strategy. An industrial peptide acylation case study identifies the probabilistic design space using 13 experiments versus 18 from a traditional DoE; a 28% reduction. The framework quantifies trade-offs between operational robustness and yield optima.