Historically, the maintenance of marine vessels has been expensive and time-consuming due to the use of periodic Preventative Maintenance (PM) and Reliability-Centred Maintenance (RCM). Therefore, alternative approaches such as Risk-based Maintenance (RBM) are needed. The data-driven RBM system described in this Thesis addresses this need by quantifying risk using a supervised classification algorithm and scheduling maintenance using risk-based decision-making. The system incorporates a combination of Machine Learning, Decision Theory and Utility Theory. Decision Theory and Utility Theory can be used to create and evaluate decision trees which incorporate probabilistic elements, known as lotteries‚ÄövÑvp. Accordingly, this enables the system to include all probabilistic information that is disregarded in maintenance decision-making and maintenance scheduling using periodic PM and RCM. The novelties of this approach include: a supervised classification algorithm for risk-quantification; a novel doubt matrix as part of a tool set to interpret the probabilities generated by the classification algorithm; the incorporation of all probabilities simultaneously in risk-based decision-making within decision trees; and the development of a solution method for a special case of Infinite Compound Ordinary Lottery (ICOL). An ICOL is a lottery which is used to represent the infinite series of events that may occur while maintenance is deferred. The present RBM system is developed for the shipboard Number 2 General Service Pump. The completed maintenance system is used to analyse the CM data collected from the pump and produce a list of maintenance Policies. Additional results showed that the system can also be used to make decisions in ambiguous situations beyond human capacity, considering all probable faults. With additional data and research this RBM methodology can be expanded to deliver predictive maintenance for a series of pumps, engines, sub-systems, systems and ultimately marine vessels or any mechanical asset.