With the evolution of traditional production towards smart manufacturing, humans and machines interact dynamically to handle complex production systems in semi-automated environments when full automation is not possible. To avoid undesirable side effects, and to exploit the full performance potential of experts, it is crucial to consider the human perspective when developing new technologies. Specifically, human sub-tasks during machine operation must be described to gain insights into cognitive processes. This research proposes a cognition-based framework by integrating a number of known psychological concepts. The focus is on the description of cognitive (team) processes in the resolution of anomalies within a manufacturing process with interdisciplinary experts working together. An observational eye tracking study with retrospective think-aloud interviews (N = 3) provides empirical evidence for all cognitive processes proposed in the framework, such as regular process monitoring and—in case of a detected anomaly—diagnosis, problem solving, and resolution. Moreover, the role of situation awareness, individual expertise and (cognitive) team processes is analyzed and described. Further, implications regarding a human-centered development of future production systems are discussed. The present research provides a starting point for understanding and supporting cognitive (team) processes during intelligent manufacturing that will dominate the production landscape within Industry 5.0.