Anomaly detection is essential for realizing modern and secure cyber-physical production systems. By detecting anomalies, there is the possibility to recognize, react early, and in the best case, fix the anomaly to prevent the rise or the carryover of a failure throughout the entire manufacture. While current centralized methods demonstrate good detection abilities, they do not consider the limitations of industrial setups. To address all these constraints, in this study, we introduce an unsupervised, decentralized, and real-time process anomaly detection concept for cyber-physical production systems. We employ several 1D convolutional autoencoders in a sliding window approach to achieve adequate prediction performance and fulfill real-time requirements. To increase the flexibility and meet communication interface and processing constraints in typical cyber-physical production systems, we decentralize the execution of the anomaly detection into each separate cyber-physical system. The installation is fully automated, and no expert knowledge is needed to tackle data-driven limitations. The concept is evaluated in a real industrial cyber-physical production system. The test result confirms that the presented concept can be successfully applied to detect anomalies in all separate processes of each cyber-physical system. Therefore, the concept is promising for decentralized anomaly detection in cyber-physical production systems.