In this paper, a model-based prognosis method where the degradation cannot be directly measured but only detectable through the drift of a model parameter is considered. This parameter drift is viewed as an unknown input, whose reconstruction allows the estimation of the degradation state. Model-based prognosis is divided into a filtering step where the current degradation state is estimated, and an uncertainty propagation step where the future degradation state is predicted. During these two steps, model uncertainty and measurement uncertainty are taken into account within the set-membership framework using interval techniques. The filtering step is performed with an interval unknown input observer for linear time-invariant discrete systems. Then, based on a set-membership constraint satisfaction methodology , interval propagation is performed to estimate the bounds that include the future degradation state until some failure threshold is reached, allowing the deduction of the interval including the remaining useful life. In order to demonstrate the efficiency of the proposed model-based prognosis methodology, the degradation of a suspension system is studied.