The integration of Fog-Cloud computing in manufacturing has given rise to a new paradigm called Fog manufacturing. Fog manufacturing is a form of distributed computing platform that integrates Fog-Cloud collaborative computing strategy to facilitate responsive, scalable, and reliable data analysis in manufacturing networks. The computation services provided by Fog-Cloud computing can effectively support quality prediction, process monitoring, and diagnosis efforts in a timely manner for manufacturing processes. However, the communication and computation resources for Fog-Cloud computing are limited in Fog manufacturing. Therefore, it is significant to effectively utilize the computation services based on the optimal computation task offloading, scheduling, and hardware autoscaling strategies to finish the computation tasks on time without compromising on the quality of the computation service. A prerequisite for adapting such optimal strategies is to accurately predict the run-time metrics (e.g., Time-latency) of the Fog nodes by capturing their inherent stochastic nature in real-time. It is because these run-time metrics are directly related to the performance of the computation service in Fog manufacturing. Specifically, since the computation flow and the data querying activities vary between the Fog nodes in practice. The run-time metrics that reflect the performance in the Fog nodes are heterogenous in nature and the performance cannot be effectively modeled through traditional predictive analysis. In this thesis, a multi-task learning methodology is adopted to predict the run-time metrics that reflect performance in Fog manufacturing by addressing the heterogeneities among the Fog nodes. A Fog manufacturing testbed is employed to evaluate the prediction accuracies of the proposed model and benchmark models. The proposed model can be further extended in computation tasks offloading and architecture optimization in Fog manufacturing to minimize the time-latency and improve the robustness of the system.