Modern manufacturing processes are increasing becoming cyber-physical in nature, where a computational system monitors the system performance, provides real-time process control by analyzing sensor data collected regarding process and product characteristics, in order to increase the quality of the manufactured product. Such real-time process monitoring and control techniques are useful in precision and ultra-precision machining processes. However, the output product quality is affected by several uncertainty sources in various stages of the manufacturing process such as the sensor uncertainty, computational system uncertainty, control input uncertainty, and the variability in the manufacturing process. The computational system may be a single computing node or a distributed computing network; the latter scenario introduces additional uncertainty due to the communication between several computing nodes. Due to the continuous monitoring process, these uncertainty sources aggregate and compound over time, resulting in variations of product quality. Therefore, characterization of the various uncertainty sources and their impact on the product quality are necessary to increase the efficiency and productivity of the overall manufacturing process. To this end, this paper develops a two-level dynamic Bayesian network methodology, where the higher level captures the uncertainty in the sensors, control inputs, and the manufacturing process while the lower level captures the uncertainty in the communication between several computing nodes. In addition, we illustrate the use of a variance-based global sensitivity analysis approach for dimension reduction in a high-dimensional manufacturing process, in order to enable real-time analysis for process control. The proposed methodologies of process control under uncertainty and dimension reduction are illustrated for a cyber-physical turning process.