Currently, the manufacturing management board applies technologies in line with the concept of Industry 4.0. Cyberphysical production systems (CPSs) mean integrating computational processes with the corresponding physical ones, i.e., allowing work at the operational level and at the strategic level to run side by side. This paper proposes a framework to collect data and information from a production process, namely, the burnishing one, in order to monitor real-time deviations from the correct course of the process and thus reduce the number of defective products within the manufacturing process. The proposed new solutions consist of (i) the data and information of the production process, acquired from sensors, (ii) a predictive model, based on the Hellwig method for errors in the production process, relying on indications of a machine status, and (iii) an information layer system, integrating the process data acquired in real time with the model for predicting errors within the production process in an enterprise resource planning (ERP) system, that is, the business intelligence module. The possibilities of using the results of research in managerial practice are demonstrated through the application of an actual burnishing process. This new framework can be treated as a solution which will help managers to monitor the production flow and respond, in real time, to interruptions.