## 1 Introduction  
The fourth industrial revolution represented by Big Data, artificial intelligence, and Internet of Things (IoT) technologies is dramatically transforming global industries. Particularly in the manufacturing industry, many countries including Germany, the United States, and Japan are striving to achieve competitive advantage in manufacturing by establishing future-oriented and advanced manufacturing paradigms such as \"Industry 4.0,\" \"Smart Manufacturing,\" and \"Smart Factory\" [1; 2]. Factories designed to support the automation of defined production processes are foreseen to become the smart factories of the future by evolving into next-generation autonomous and adaptive factories capable of real-time production monitoring, real-time process optimization, customized flexible production, and real-time quality diagnosis and prediction by analyzing the Big Data collected via the IoT [3; 4; 5]. The production paradigm is changing from low variety high-volume production to high variety low-volume production, and to customized, personalized production owing to the increasingly versatile customer needs, resulting market fluctuations, and extreme competition in the global environment. Accordingly, manufacturers need to introduce the concepts of flexibility and variability to respond to various changes [6]. Typical examples of next-generation smart factories preparing for future production paradigms are the Adidas speed factory [7] and the EU's F3 (Flexible, Fast, Future) factory [7]. In particular, the F3 factory is a smart factory that implements modular equipment and constructs and operates the production line similar to assembling Lego blocks in accordance with customer needs. A factory with modular production equipment for variability and flexibility and the ability to immediately implement an optimized production system through the integration of Big Data and artificial intelligence could be referred to as an autonomous and adaptive smart factory that satisfies customized, personalized production. However, the actualization of an autonomous and adaptive smart factory would be expected to complicate the process operation and management because of the increased variation of the process. In addition, it would be difficult to determine whether the composition of the dynamic production line and scheduling and dispatching results are optimal in the long run. Likewise, anomalies of the current process would be difficult to identify. This is because to determine a process anomaly would require the predefined process model to be compared with the process that is actually implemented; however, in an autonomous and adaptive process, it is difficult to define or derive a standard process model from start to finish, and anomalies cannot be detected by the traditional method. Traditionally, for process anomaly detection, structural or property differences (e.g., lead time, bottlenecks) of the process are discovered by comparing the predefined process or the process model derived from logs with the actually implemented process instances (or cases) [8; 9; 10; 11]. At this time, the process mining technique could be used appropriately. Process mining is an activity that derives a process model from logs accumulated in the operational database and compares the predefined process model with the actually implemented process log (conformance checking), and enhances the process model by identifying bottlenecks or anomalous aspects of the process [12]. Recent studies have developed methods to derive a process model in real time [13; 14; 15] and discover anomalies by aligning on-stream data with the process model in real time [16; 17]. However, applying these results to autonomous and adaptive manufacturing processes is problematic. This is because process anomaly detection using the process mining technique targets various process instances (cases) that have actually been performed in situations where the start and finish positions of the process are mostly identical as the object of analysis.