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Prognostics is the scientific study of component and system degradation with use, and the prediction of when failure may occur. In this work, we propose a new data-driven method for predicting a system’s remaining useful life (RUL) without needing an accurate system model or expert knowledge. Instead, we use system operational data to estimate how the system’s performance metrics change with time. Although this is a purely data-driven approach, the method’s design is inspired by model-based techniques. First, we frame a novel Multitask Machine Learning architecture to simultaneously learn the general pattern of performance degradation and the individual trajectories from run-to-failure performance trajectory data. We apply this method to the set of performance metrics that determine the system’s end-of-life (EOL), building a performance trajectory library of the system operation under different operational conditions. We leverage the performance metric library as prior belief and develop a Bayesian deep learning approach to update the performance measures over time and predict the system EOL. We evaluate our method on two datasets of the N-CMAPSS benchmark, achieving satisfactory results in terms of overall performance and uncertainty estimation accuracy. Overall, our approach illustrates a generalized deep learning architecture that can more effectively predict the system RUL for a collection of identical systems.