This work presents an efficient computational framework for estimating the end of life (EOL) and remaining useful life (RUL) by combining the particle filter (PF)-based prognostics with the technique of Subset simulation. It has been named PFP-SubSim on behalf of the full denomination of the computational framework, namely, PF-based prognostics based on Subset Simulation. This scheme is especially useful when dealing with the prognostics of evolving processes with asymptotic behaviors, as observed in practice for many degradation processes. The effectiveness and accuracy of the proposed algorithm is demonstrated through an example for predicting the probability density function of EOL for a carbon-fibre composite coupon subjected to an asymptotic fatigue degradation process. It is shown that PFP-SubSim algorithm is efficient, and at the same time, fairly accurate in obtaining the probability density function of EOL and RUL as compared to the traditional PF-based prognostic approach reported in the PHM literature.