Complex equipment systems are becoming common in both industrial production and social life, and complicated correlations exist between system components. With the development of information technology, data-based analysis methods have become an efficient approach to the correlation analysis, taking place the traditional model-based methods. Specifically, association rule mining is one of the most efficient correlation analysis methods. Hence, this paper presents a multi-objective association rule mining algorithm to extract hidden correlations between system components in the performance data generated by equipment systems. Based on the NSGA-III framework, five objectives are used to optimize the quantitative association rules comprehensively. Finally, a case study is carried out on a multivariate dataset generated by the propulsion plant system of a vessel. The results show that the proposed algorithm is competent to the correlation analysis of real complex equipment systems, and can assist in the fault warning and state analysis. This study has reference significance for the study on modelling, analysis, and optimization of complex equipment systems.