Prognostics deals with the prediction of the end of life (EOL) of a system. EOL is a random variable, due to the presence of process noise and uncertainty in the future inputs to the sys- tem. Prognostics algorithms must account for this inherent uncertainty. In addition, these algorithms never know exactly the state of the system at the desired time of prediction, or the exact model describing the future evolution of the system, accumulating additional uncertainty into the predicted EOL. Prediction algorithms that do not account for these sources of uncertainty are misrepresenting the EOL and can lead to poor decisions based on their results. In this paper, we explore the impact of uncertainty in the prediction problem. We develop a general model-based prediction algorithm that incorporates these sources of uncertainty, and propose a novel approach to efficiently handle uncertainty in the future input trajecto- ries of a system by using the unscented transform. Using this approach, we are not only able to reduce the computa- tional load but also estimate the bounds of uncertainty in a deterministic manner, which can be useful to consider during decision-making. Using a lithium-ion battery as a case study, we perform several simulation-based experiments to explore these issues, and validate the overall approach using experi- mental data from a battery testbed.