Digital technologies are becoming more pervasive and industrial companies are exploiting them to enhance the potentialities related to Prognostics and Health Management (PHM). Indeed, PHM allows to evaluate the health state of the physical assets as well as to predict their future behaviour. To be effective in developing PHM programs, the most critical assets should be identified so to direct modelling efforts. Several techniques could be adopted to evaluate asset criticality; in industrial practice, criticality analysis is amongst the most utilised. Despite the advancement of artificial intelligence for data analysis and predictions, the criticality analysis, which is built upon both quantitative and qualitative data, has not been improved accordingly. It is the goal of this work to propose an ontological formalisation of a multi-attribute criticality analysis in order to i) fix the semantics behind the terms involved in the analysis, ii) standardize and uniform the way criticality analysis is performed, and iii) take advantage of the reasoning capabilities to automatically evaluate asset criticality and associate a suitable maintenance strategy. The developed ontology, called MOCA, is tested in a food company featuring a global footprint. The application shows that MOCA can accomplish the prefixed goals; specifically, high priority assets towards which direct PHM programs are identified. In the long run, ontologies could serve as a unique knowledge base that integrate multiple data and information across facilities in a consistent way. As such, they will enable advanced analytics to take place, allowing to move towards cognitive Cyber Physical Systems that enhance business performance for companies spread worldwide.