The Industry 4.0 paradigm has changed the way industrial systems with hundreds of sensor-actuator enabled devices, including industrial internet of things (IIoT), cooperate and communicate with the physical and human worlds. Given the intricacy, the diagnostics of such systems is extremely important. While anomaly detection is a valid approach to avoid unplanned maintenance or even complete breakdown, its effective realization in IIoT requires the design and implementation of frameworks for efficient monitoring, data collection, and analysis. Most of the existing anomaly detection techniques provide only a diagnosis of the fault without taking into account the uncertainty. Moreover, the lack of ground truth data (which is a typical problem in the industrial context), make their implementation even more challenging. This paper proposes an anomaly detection technique built on top of an industrial framework for the data collection and monitoring. Specifically, we address the lack of labeled data by designing a semi-supervised anomaly detection algorithm that exploits Bayesian Gaussian Mixtures to assess the working condition of the plant while measuring the uncertainty during the diagnosis process and we implement the proposed framework on a real-life IIoT testbed, namely a scale replica assembly plant. Experimental results demonstrate that our anomaly detection algorithm is able to detect the plant working conditions with 99.8% of accuracy, and the semi-supervised approach performs better than a supervised one.