Reduction of spaceflight costs calls for development of new technologies that render rockets reusable. This new requirement and the continuous improvement of rocket engines require pro-active approach towards the possibility of integrating health monitoring systems on-board. These health monitoring strategies should also take into consideration the state of degradation and the remaining useful life prediction. In this paper, an Extended Kalman Filter is used to estimate the state of health and the dynamics of the degradation, and the remaining useful life is predicted with respect to failure thresholds pre-set by the user. The first-order inverse reliability method is employed to assess the quality of the remaining useful life prediction by quantifying the associated uncertainty. The overall method is validated using simulation study involving degradation data provided by Centre National d'Etudes Spatiales (CNES) applied to liquid propulsion rocket engine (LPRE) combustion chamber.