The emergence of highly instrumented manufacturing systems has enabled the paradigm of smart manufacturing that provides high levels of prognostics functionality. Of particular interest is to precisely determine geometric conformance or non-conformance of workpieces during manufacturing. This paper presents a new dimensional product health monitoring system that learns from in-process sensor data and updates the prediction of the product quality as the product is manufactured. The system uses data from multiple manufacturing stages, unlike from a single stage at a time, to predict the dimensional quality of the finished product that is updated with subsequent measurements such as On-Machine Measurements (OMMs), in on-line incremental learning fashion. It is based on self-supervised neural networks for dimensionality reduction, Gaussian Process Regression (GPR) models for probabilistic prediction about the end product condition and the associated uncertainty, and Bayesian information fusion for updating the conditional probability distribution of the end product quality in the light of new information. The monitoring approach was tested on the prediction of diameter deviations with validation results showing its ability to achieve an average accuracy better than 5 μm in terms of the Root Mean Squared Error (RMSE). Having obtained a Probability Density Function (PDF) for the measurand of interest, the conformance and non-conformance probabilities given the tolerance specifications are computed to support the principle of inspection by exception. This ability to construct a conformance probability-based product quality monitoring system using probabilistic machine learning methods constitute a step change to manufacturing prognostics.