Failure mode and effect analysis (FMEA) is a powerful risk discerning technique for identifying, evaluating, and reducing possible failures of products or processes. However, the classical FMEA has been criticized for inherent limitations, such as equal weights of risk elements and lack of capability in handling inaccurate information. Although fuzzy-based modified FMEA methods are frequently utilized to handle vagueness of experts' judgments, they still have some drawbacks, for example, requiring extra assumptions, neglecting experts' bounded rationality and psychological effects, lacking consideration of randomness, and only considering three classical risk elements among most of them. Therefore, this study develops an extended risk assessment method to enhance the performance of FMEA, which integrates the superiority of rough number theory in handling subjective and inaccurate information and the advantage of cloud model theory in reflecting the randomness of qualitative evaluations. Moreover, two synthetic weighting methods are developed to determine the weights of risk elements and handle the experts' individual effects, respectively, which consider both subjective and objective aspects. In addition, maintenance is added into the classical risk elements, and then a hierarchical structure containing four risk dimensions is built to evaluate failures' risk levels comprehensively. Finally, an application case to demonstrate the effectiveness of the developed FMEA model is presented. K E Y W O R D S cloud model, failure mode and effect analysis, hierarchical TOPSIS, rough number theory, synthetic weight 1 | INTRODUCTION Failure mode and effect analysis (FMEA) is a reliable risk assessment technique to determine the known and/or potential failure modes, causes, and effects on the stability and performance of a system, design, service, and process to identify the most crucial ones and conduct actions to eliminate them. 1 In the 1960s, it was firstly used by NASA in the aerospace industry to ensure the safety and quality of products. 2 FMEA is commonly performed by a cross-functional team contained experts with different knowledge and experience to analyze and quantify the relationships between