This paper deals with a model-based prognosis approach for assessing the remaining useful life (RUL) of a printed circuit board (PCB) subjected to impact or vibration loads applied to its support contour. The approach deals with the interaction (coupling) of the "fast" Ball-Grid-Array (BGA) vibration model and the "slow" low cycle fatigue damage model of BGA solder joint interconnections. As the complete knowledge of these interconnected models are typically not available, a two-stage filtering process is used to estimate the fast and slow dynamics involved. The RUL of the BGA solder joint interconnections is then estimated based on the identified models. Simulation results show the efficiency of the proposed approach.