Machine Learning (ML) is increasingly applied in industrial manufacturing, but often performance is limited due to insufficient training data. While ML models can benefit from collaboration, due to privacy concerns, individual manufacturers cannot share data directly. Federated Learning (FL) enables collaborative training of ML models without revealing raw data. However, current FL approaches fail to take the characteristics and requirements of industrial clients into account. In this work, we propose a FL system consisting of a process description and a software architecture to provide \acrfull{flaas} to industrial clients deployed to edge devices. Our approach deals with skewed data by organizing clients into cohorts with similar data distributions. We evaluated the system on two industrial datasets. We show how the FLaaS approach provides FL to client processes by considering their requests submitted to the Industrial Federated Learning (IFL) Services API. Experiments on both industrial datasets and different FL algorithms show that the proposed cohort building can increase the ML model performance notably.