Failure mode and effect analysis with ORESTE method under large group probabilistic free double hierarchy hesitant linguistic environment

Failure Mode and Effect Analysis (FMEA) is a prospective and systematic analytical tool widely used to improve the reliability and safety of various industries. However, the existing FMEA methods have received criticism for their inherent deficiencies that limit their flexibility and effectiveness. To address these issues, we propose a novel FMEA model that combines Probabilistic Free Double Hierarchy Hesitant Linguistic Term Set (PFDHHLTS), Extended Grey Relation Analysis (EGRA), and ORESTE to determine the priorities of Failure Modes (FMs). Firstly, the PFDHHLTSs are proposed to represent experts' assessments, improving the flexibility and accuracy of experts' expressions. Secondly, the PFDHHLTS-EGRA is proposed to determine the evaluation matrix and the weights of risk factors in a large group environment. Furthermore, the ORESTE method is extended to the PFDHHLTS environment. Lastly, we verify the effectiveness of our method through a case study on the aluminum electrolysis process. The results demonstrate the effectiveness and flexibility of our method in expressing experts' assessments and obtaining more accurate and reliable risk priorities.