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The ability to accurately estimate the residual life of partially degraded components is arguably the most challenging problem in prognostic condition monitoring. This paper focuses on the development of a neural network-based degradation model that utilizes condition-based sensory signals to compute and continuously update residual life distributions of partially degraded components. Initial predicted failure times are estimated through trained neural networks using real-time sensory signals. These estimates are used to derive a prior failure time distribution for the component that is being monitored. Subsequent failure time estimates are then utilized to update the prior distributions using a Bayesian approach. The proposed methodology is tested using real world vibration-based degradation signals from rolling contact thrust bearings. The proposed methodology performed favorably when compared to other reliability-based and statistical-based benchmarks.