Industry 4.0 operates based on IoT devices, sensors, and actuators, transforming the use of computing resources and software solutions in diverse sectors. Various Industry 4.0 latency-sensitive applications function based on machine learning to process sensor data for automation and other industrial activities. Sending sensor data to cloud systems is time consuming and detrimental to the latency constraints of the applications, thus, fog computing is often deployed. Executing these applications across heterogeneous fog systems demonstrates stochastic execution time behavior that affects the task completion time. We investigate and model various Industry 4.0 ML-based applications' stochastic executions and analyze them. Industries like oil and gas are prone to disasters requiring coordination of various latency-sensitive activities. Hence, fog computing resources can get oversubscribed due to the surge in the computing demands during a disaster. We propose federating nearby fog computing systems and forming a fog federation to make remote Industry 4.0 sites resilient against the surge in computing demands. We propose a statistical resource allocation method across fog federation for latency-sensitive tasks. Many of the modern Industry 4.0 applications operate based on a workflow of micro-services that are used alone within an industrial site. As such, industry 4.0 solutions need to be aware of applications' architecture, particularly monolithic vs. micro-service. Therefore, we propose a probability-based resource allocation method that can partition micro-service workflows across fog federation to meet their latency constraints. Another concern in Industry 4.0 is the data privacy of the federated fog. As such, we propose a solution based on federated learning to train industrial ML applications across federated fog systems without compromising the data confidentiality.