Predictive Analytics and Machine Learning (ML) are at the heart of some of the most popular Industry 4.0 applications such as condition-based monitoring, predictive maintenance, and quality management. To support the implementation of such use cases, various ML models have been proposed and validated in the research literature. This paper introduces a novel set of machine learning algorithms for Industry4.0 use cases, namely the QARMA algorithms, which are capable of mining of quantitative rules. QARMA models present several advantages when compared to conventional ML and Deep Learning mechanisms, including computational performance, predictive accuracy and "explainability". In the scope of this paper, we discuss these advantages based on practical experiences from the field deployment and validation of QARMA models in two different production lines. The deployment has been supported by a state-of-the-art Industrial Internet of Things platform, which is also presented in the paper.