Within the area of systems health management, the task of prognostics centers on predicting when components will fail. Model-based prognostics exploits domain knowledge of the system, its components, and how they fail by casting the underlying physical phenomena in a physics-based model that is derived from first principles. Uncertainty cannot be avoided in prediction, therefore, algorithms are employed that help in managing these uncertainties. The particle filtering algorithm has become a popular choice for model-based prognostics due to its wide applicability, ease of implementation, and support for uncertainty management. We develop a general model-based prognostics methodology within a robust probabilistic framework using particle filters. As a case study, we consider a pneumatic valve from the Space Shuttle cryogenic refueling system. We develop a detailed physics-based model of the pneumatic valve, and perform comprehensive simulation experiments to illustrate our prognostics approach and evaluate its effectiveness and robustness. The approach is demonstrated using historical pneumatic valve data from the refueling system.