(untitled) (REC 2026 - 11th International Workshop on Reliable Engineering Computing: Reliability Computations in a Data and Model-Driven World, 2026)
Probability boxes, or p-boxes, provide a useful representation of uncertainty when a precise probability distribution cannot be justified from the available information. Although p-box propagation is well established theoretically, its practical implementation remains challenging for users who require transparent and reproducible computational workflows. This paper presents a tutorial-style Python workflow for constructing and propagating p-boxes and for approximating propagated response bounds using Interval Prediction Models via a newly developed Python package PyUncertainNumber. The aim is not to introduce a new propagation theory, but to clarify how p-box inputs can be defined, propagated through nonlinear models, extracted as probability-level-dependent response intervals, and represented by a compact interval model. The workflow is first demonstrated using the Rosenbrock function, which provides a simple nonlinear benchmark. It is then extended to an excavation-induced tunnel displacement problem, where a first-level Interval Prediction Model is used as a surrogate of numerical simulation data and soil-parameter uncertainty is propagated to tunnel displacement predictions. The results show how p-box propagation and interval modelling can be combined into a reproducible workflow for conservative engineering response assessment. The paper is intended as a practical guide for researchers and engineers implementing imprecise-probability propagation in software-based uncertainty analysis.