One of the challenges of maintenance management of a marine machinery system is the problem of selecting the optimum interval for replacement of equipment items. Most of the approaches that are given in the literature for selecting optimum replacement intervals are based on a single criterion model such as cost. This approach may be satisfactory for some industries but for the marine industry disruption in services will result in a considerable cost penalty and, as such, other factors such as system downtime and system reliability must be taken into consideration when determining the optimum replacement interval for the system. These decision criteria have been proven to be in conflict with one another. On this basis, a multi-criteria decision-making tool, Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS), is proposed in this article for aggregating multiple criteria in order for them to be used simultaneously in determining the optimum scheduled replacement interval for the equipment items of the system. The use of a multi-criteria decision-making tool allows the decision-maker to express preference for the decision criteria in terms of their levels of importance. To achieve this aim, a compromise decision weighting technique is integrated with TOPSIS. The compromise weighting technique was obtained from a combination of the variance method (an objective decision criteria weighting technique) and analytical hierarchy process (a subjective decision criteria weighting technique). In order to demonstrate the applicability of the proposed innovative methodology for determining the optimum replacement intervals for a marine machinery system and also validate the technique, a case study involving some equipment items of a marine diesel engine is presented. Although results show that it produces the same optimum solution as the methods in the literature, the proposed method is more flexible and less computationally intensive.