Distributed machine learning algorithms that employ Deep Neural Networks (DNNs) are widely used in Industry 4.0 applications, such as smart manufacturing. The layers of a DNN can be mapped onto different nodes located in the cloud, edge and shop floor for preserving privacy. The quality of the data that is fed into and processed through the DNN is of utmost importance for critical tasks, such as inspection and quality control. Distributed Data Validation Networks (DDVNs) are used to validate the quality of the data. However, they are prone to single points of failure when an attack occurs. This paper proposes QUDOS, an approach that enhances the security of a distributed DNN that is supported by DDVNs using quorums. The proposed approach allows individual nodes that are corrupted due to an attack to be detected or excluded when the DNN produces an output. Metrics such as corruption factor and success probability of an attack are considered for evaluating the security aspects of DNNs. A simulation study demonstrates that if the number of corrupted nodes is less than a given threshold for decision-making in a quorum, the QUDOS approach always prevents attacks. Furthermore, the study shows that increasing the size of the quorum has a better impact on security than increasing the number of layers. One merit of QUDOS is that it enhances the security of DNNs without requiring any modifications to the algorithm and can therefore be applied to other classes of problems.