This is a forward-looking approach that uses a multiple-criteria decision analysis (MCDA) model as an assessment tool for risk identification. This study proposes an indifference threshold-based attribute ratio analysis and technique for order preference by similarity to an ideal solution (ITARA-TOPSIS)-based assessment model to identify critical failure modes in products and systems. The improved indifference threshold-based attribute ratio analysis (ITARA) method can generate more reliable weights for risk factors. In addition, the modified technique for order preference by similarity to an ideal solution (TOPSIS) is used to obtain the risk levels of the failure modes. The gray correlation coefficient is applied to replace the conventional Euclidean distance, and a new index is used to determine the priority of failure modes. The determination of risk factors is based on the failure mode and effect analysis (FMEA) theory, including severity, occurrence, and detection. An important indicator, the expected cost, is also included in the framework. The case of a steam turbine for a nuclear power plant is used to demonstrate the approach, and the analysis results show that the proposed model is practical and effective. Moreover, the advantages of our integrated model are illustrated through model comparisons and sensitivity analysis. This paper can help decision-makers, risk engineers, and related researchers to better understand how a systematic risk assessment can be conducted.