The Industry 4.0 revolution has been made possible via AI-based applications (e.g., for automation and maintenance) deployed on the serverless edge (aka fog) computing platforms at the industrial sites -- where the data is generated. Nevertheless, fulfilling the fault-intolerant and real-time constraints of Industry 4.0 applications on resource-limited fog systems in remote industrial sites (e.g., offshore oil fields) that are uncertain, disaster-prone, and have no cloud access is challenging. It is this challenge that our research aims at addressing. We consider the inelastic nature of the fog systems, software architecture of the industrial applications (micro-service-based versus monolithic), and scarcity of human experts in remote sites. To enable cloud-like elasticity, our approach is to dynamically and seamlessly (i.e., without human intervention) federate nearby fog systems. Then, we develop serverless resource allocation solutions that are cognizant of the applications' software architecture, their latency requirements, and distributed nature of the underlying infrastructure. We propose methods to seamlessly and optimally partition micro-service-based application across the federated fog. Our experimental evaluation express that not only the elasticity is overcome in a serverless manner, but also our developed application partitioning method can serve around 20% more tasks on-time than the existing methods in the literature.