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Failure mode and effect analysis (FMEA), as a powerful and effective risk assessment tool in reliability and safety analysis, has been extensively applied in different fields to enhance the reliability of a system. However, the traditional FMEA method has exposed some significant defects in practical applications. Furthermore, the risk ranking of failure modes is not convenient for subsequent maintenance strategies, and the interactions between risk criteria are not considered in most multiple criteria decision making (MCDM)-based methods. In this paper, we construct a novel FMEA model based on criteria importance through the inter-criteria correlation (CRITIC) method and three-way decisions to improve the performance of the conventional FMEA method and aid making a maintenance plan. Firstly, we introduce the decision-theoretic rough sets (DTRSs) into an interval 2-tuple linguistic (I2TL) environment to define interval 2-tuple linguistic decision-theoretic rough sets (I2TLDTRSs). Secondly, the CRITIC method is employed to calculate the weight of risk criteria. Thirdly, the conditional probability is obtained by a similarity-based method with the help of the ideas of the TOPSIS approach, and a relative loss function is designed by introducing risk avoidance coefficient. Fourthly, the classification of failure modes is derived according to the three-way decision rules. Finally, two numerical examples of the train door system are given to verify the effectiveness and practicality of the presented model. The presented model both extends the theory and application of three-way decisions and provides a solution beneficial for making a maintenance strategy to reduce the risk of failure modes. [ABSTRACT FROM AUTHOR]