A novel Bayesian framework for the in-flight SRM Failure Decision and Prognostic (FD&P) is introduced and discussed. It is based on a combination of low-dimensional performance models (LPDMs) and a dynamical inference of the parameters of nonlinear flow of combustion products. To verify the method we introduce a high-fidelity model of the overpressure fault based on a system of stochastic partial differential equations (SPDEs). To analyze the deviations of the system parameters from the stable burn-back conditions of the SRM we derived a LPDM of the SRM obtained by integrating the SPDEs over the length of the combustion camera. We consider a few fault scenarios, including nozzle failure with neutral and progressive thrust curve, and nozzle blocking with time varying fault parameters to model "misses" or "false alarms". Prognostic is accomplished by building the distribution of the predicted values of the fault parameters as a function of the measurement time. We discuss how the novel Bayesian framework can be extended to encompass the pro pella nt cracking and the case breach faults of the SRM.