Sequential Design for Quantile Estimation in Multifactor Sensitivity Experiments

Cavitation in hydrofoil experiments is a critical physical phenomenon, which is primarily influenced by three key factors. Efficiently identifying the combination of factor levels at which cavitation occurs with 50% probability presents a significant challenge in sensitivity testing, particularly when constrained by the high cost of hydrofoil experiments. Despite its importance, sensitivity experiments with multiple factors have received scant attention in literature. In order to tackle this challenge, we propose a novel sequential design based on the upper credible bound criterion for the generalised Gaussian process models, which is used to model the hydrofoil experimental data. Some numerical simulation studies demonstrate that the proposed method effectively balances exploitation and exploration, achieving superior performance compared to existing approaches. Finally, a practical application to hydrofoil cavitation experiments validates the superiority of the proposed method.