Failure mode effects and criticality analysis (FMECA) is a commonly adopted approach to defining, assessing, and reducing possible failures in designs, systems, processes, products, and services. Traditional FMECA ranks the failure modes of products based on a risk priority number (RPN), which is obtained by multiplying the risk elements. Conventional FMECA has the shortcomings of badly handling unknown information and unreasonably assessing RPNs. To deal with these issues, an advanced FMECA method based on intuitionistic 2-tuple linguistic variables (I2LVs) and the triangular fuzzy analytic hierarchy process (TFAHP) is proposed. In this method, the fuzzy evaluation of risk elements given by different FMECA members is represented by I2LVs, which can efficiently handle unknown information. The TFAHP method is adopted to assess the weights of risky elements and rank the risk priorities of different failure modes. Finally, an application case of an insulated-gate bipolar transistor is used to verify the effectiveness and robustness of the proposed method.