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 un- derlying 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 refuel- ing system. We develop a detailed physics-based model of the pneumatic valve, and perform comprehensive simulation experiments to illustrate our prognostics approach and evalu- ate its effectiveness and robustness. The approach is demon- strated using historical pneumatic valve data from the refuel- ing system.