Identifying and managing health and safety risks that threaten personnel in production systems are vital for the continuity and success of organizations. Many tools are used to accurately analyze and assess risks. Failure mode and effect analysis (FMEA) is one of the most commonly used tools in different industries. However, the accuracy and reliability of FMEA method have been fairly criticized by many researchers in the field. In this study, an approach based on FMEA that integrates the advantages of the fault tree analysis (FTA) method and belief in fuzzy probability estimations of time (BIFPET) algorithm has been proposed in order to improve the performance of the FMEA method. In order to practically apply the proposed method to real life problems, it has been employed to analyze and assess the potential risks for a finishing process in the fabric dyeing department of a textile company. The performance of the proposed FMEA-FTA-BIFPET method has been compared to the results obtained by FMEA-FTA and FMEA-FTA-program evaluation and review technique (PERT) distribution integrated methods. The results of this study show that failure related to fabric trimming adjustment in the tenter has the highest risk priority number. The proposed approach can be used in various industry for risk analysis. In addition, results obtained by the study have indicated that the proposed approach can be implemented in practice to perform comprehensive risk assessment procedures as it reflects real-life dynamics to analyze and assess potential risk.