Smart factories are evolving into Cyber-Physical Systems (CPS), demanding increased autonomy. This necessitates real-time decision making, facilitated by insights derived from sensor data. Process mining offers a valuable approach to gain such insights and guide actions. The edge computing paradigm supports this real-time requirement by enabling network communication between sensors and leveraging nearby computing resources. This paper investigates the implications of performing real-time process mining algorithms on the edge. Within this paper, we first propose a formalism to describe relevant datasets and the computing topology. We then evaluate the edge computing approach through a case study involving an edge-based conformance checking algorithm. The results demonstrate the feasibility and benefits of edge-based real-time process mining for enhanced autonomous control in smart factories.