Traditional approaches to reliability analysis are based on life tests that record only time-to-failure. With very few exceptions, all such analyses are aimed at estimating: a population characteristic, or characteristics of a system, subsystem, or component. For some components, degradation measurements can be obtained over time, and these measurements contain useful information regarding component reliability. Then, one can define component failure in terms of a specified level of degradation, and estimate the reliability of that particular component based on its unique degradation measures. This paper provides a unique approach that allows 'determination of a component's reliability as it degrades with time' by monitoring its degradation measures. The concepts have been implemented using: 'finite-duration impulse response multi-layer perceptron neural networks' for modeling degradation measures, self-organizing maps for modeling degradation variation. The specific application considered is in-process monitoring of the condition of the drill-bit in a drilling process, using the torque & thrust signals. An approach to compute prediction Limits for any feed-forward neural network, critical for on-line performance reliability monitoring of systems using neural networks, is introduced by combining the network with a self-organizing map. Experimental results show that neural networks are effective in: modeling the degradation characteristics of the monitored drill-bits, predicting conditional & unconditional performance reliabilities as they degrade with time or usage. In contrast to traditional approaches, this approach to on-line performance reliability monitoring opens new avenues for better understanding and monitoring 'systems that exhibit failures through degradation'. Essentially, implementation of this 'performance reliability monitoring' reduces overall operations costs by facilitating optimal component-replacement and maintenance strategies.