In this paper, an assessment of two methods of uncertainty quantification in prognostics is undertaken. The two methods, the Inverse First Order Reliability Method (IFORM) and set-based reachability analysis for prognostics are considered. The IFORM approach permits the generation of confidence bounds that allows for the calculation of RUL values corresponding to the specified user-defined probability levels. On the other hand, uncertainty quantification can be achieved by means of set-based reachability analysis. A Zono-topic Kalman filter (ZKF) is proposed to take into account a damage-model such that at each propagation time, with the estimated state (degradation) and its uncertainty, a propagation of zonotopic sets can be produced. Coming from two different schools of thought, the statistical and set-based theory, both schemes are explored and tested on a case study in simulation.