This paper presents a similarity-based approach for prognostics of the Remaining Useful Life (RUL) of a system, i.e. the lifetime remaining between the present and the instance when the system can no longer perform its function. Data from failure dynamic scenarios of the system are used to create a library of reference trajectory patterns to failure. Given a failure scenario developing in the system, the remaining time before failure is predicted by comparing by fuzzy similarity analysis its evolution data to the reference trajectory patterns and aggregating their times to failure in a weighted sum which accounts for their similarity to the developing pattern. The prediction on the failure time is dynamically updated as time goes by and measurements of signals representative of the system state are collected. The approach allows for the on-line estimation of the RUL. For illustration, a case study is considered regarding the estimation of RUL in failure scenarios of the Lead Bismuth Eutectic eXperimental Accelerator Driven System (LBE-XADS)