Accurate reliability modeling and assessment of manufacturing systems leads to lower maintenance costs and higher profits. However, the complexity of modern Smart Manufacturing Systems poses a challenge to traditional expert-driven reliability modeling techniques. The growing research field of data-driven reliability modeling seeks to harness the abundance of data from such systems to improve and automate the reliability modeling processes. In this paper, we propose the use of Process Mining techniques to support the extraction of reliability models from event data generated in Smart Manufacturing Systems. More specifically, we extract a stochastic Petri net which can be used to analyze the overall system reliability as well as to test new system configurations. We demonstrate our approach with an illustrative case study of a flow shop manufacturing system with parallel operations. The results indicate, that using Process Mining techniques to extract accurate reliability models is feasible.