Benefits of Prognostics and Health Management (PHM) to support critical decisionmaking processes can be manifested by effectively implementing prognostics algorithms and accurately predicting the Remaining Useful Lives (RUL) of engineering components or systems. In general, a prognostics process requires two sequential processes: an offline training (or learning) process and an online prediction process. This paper presents a generic data-driven prognostics framework using the Relevance Vector Machine (RVM) for the offline training process and the Similarity-Based Interpolation (SBI) for the online prediction process. The RVM is a state-of-the-art technique for statistical regression that provides regression coefficients in the form of probabilistic distribution functions (PDFs). Within the proposed prognostics framework, the system health degradation process can be characterized by two health index systems: Physics Health Index (PHI) and Virtual Health Index (VHI). In the offline training process, the RVM is employed for a supervised statistical learning with system training dataset to build background health knowledge (e.g., a predictive health degradation curve) of system units in a statistical form. With this background knowledge, the SBI is then proposed for predicting and continuously updating the RUL in a statistical manner in the online prediction process. The proposed generic prognostics framework is applicable to different engineering applications and its effectiveness is demonstrated with two cases studies.