Prognostics is crucial to providing reliable condition-based maintenance decisions. To obtain accurate predictions of component life, a variety of sensors are often needed. However, it is typically difficult to add enough sensors for reliable prognosis, due to system constraints such as cost and weight. Model-based prognostics helps to offset this problem by exploiting domain knowledge about 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. We develop a model-based prognostics methodology using particle filters, and investigate the benefits of a model-based approach when sensor sets are diminished. We apply our approach to a detailed physics- based model of a pneumatic valve, and perform comprehensive simulation experiments to demonstrate the robustness of model-based approaches under limited sensing scenarios using prognostics performance metrics.