The operation and maintenance of industrial plants constitute a major concern among managers, scientists, and engineers. To allow the prioritization of maintenance actions for improved continuous equipment operation, this paper presents a novel method focused on identifying the most critical components of a plant’s systems. In a complex engineering approach, this method uses tools and techniques borrowed from several fields of knowledge, including an innovative technique devised by the authors, as well as a multi-criteria decision method in the criticality determination process. To illustrate the method, a case study is presented considering a 150 MW Kaplan hydro generator from a hydroelectric power plant located in the north of Brazil. An uncertainty analysis is presented, considering variations in the scores of each criterion, to verify the robustness of the proposed method. The results show that the method responds in a solid and structured way, allowing decision making from qualitative and quantitative data and eliciting the opinion of experts on the factors that can affect the degradation of the performance of a system. In addition, the method’s robustness is confirmed since the uncertainty propagation related to the criteria scores is small for the items classified as most significant from its application.