The purpose of this paper is to develop a new Failure Mode and Effect Analysis (FMEA) framework for identification, prioritization and improvement of failure modes. A hybrid multiple criteria decision-making (MCDM) method combining Stepwise Weight Assessment Ratio Analysis (SWARA) and VlseKriterijumska optimizacija I KOm-promisno Resenje (VIKOR) is used to rank the risk of failure modes identified in FMEA. For this purpose, the SWARA method is utilized to obtain the influential weights and then VIKOR technique is employed to give the prioritization levels for the failure modes in safety equipment. A case study of a gas company in Lorestan Province (Iran) is provided to illustrate the potential application and benefits of the proposed FMEA approach. The obtained results show that the new risk priority model can be effective to find high risk failure modes and create suitable maintenance strategies. The proposed FMEA also can overcome the shortcomings, improve the effectiveness of the traditional FMEA and provide useful information to help in managing risks of safety equipment.