## 1 Introduction  
A system is considered complex if it comprises of several interacting components whose series/parallel breakdown is impossible and the overall task cannot be obtained by the summation of individual components' activities [1]. Regardless of the degree of intricacy of the complex system under study, some components are deemed critical, relative to others, regarding the safety and functionality of the entire system. Due to the increasing complexity of engineering systems, the identification and evaluation of risks associated with the failure of individual components is usually the starting point for efficient reliability and safety analysis. For this purpose, several advanced techniques such as Fault Tree Analysis (FTA), Failure Mode and Effects Analysis (FMEA), Reliability Block Diagram (RBD), Reliability-Centered Maintenance (RCM), Monte-Carlo Simulation (MCS), Markov Analysis (MA) and Bayesian Networks (BN) have been developed in the literature [2; 3; 4].  
FTA is a 'top down' Boolean logic tool commonly used to identify possible causes for potential operating hazards or an undesired event. FMEA is another risk analysis technique that is extensively used across different industries, such as aerospace, automotive, energy, transport, etc. for determining failure modes and corresponding effects on system performance. The successful application of both the FTA and FMEA techniques has increased their adoption in several reliability and safety engineering analyses studies. However, due to inherent limitations of each technique, coupled with the growing complexity of engineering systems, the use of hybrid models has become very popular in recent years.  
Integrated FTA and FMEA has been employed coherently and concurrently to enhance and complement each other in several reliability applications. Forward integration (i.e., FMEA to FTA) and backward integration (i.e., FTA to FMEA) have been proposed, with divers' advantages associated with each integration direction [5; 6]. Lutz & Woodhouse [7] also propounded a bi-directional intertwine of both techniques and used it to certify safety-critical software, paving the way for numerous studies on integrating the software domains of both tools. The combination has successfully been applied in civil aerospace and automotive domains. To effectively achieve a set reliability goal, ensure thoroughness and completeness of analysis, and improve quality of analysis without compromise on overall safety, it is necessary to redefine the underlying criteria governing techniques in a combinatorial framework. In [PERSON] et al. [8], only the occurrence (O) of a failure is taken into consideration because the complex system under consideration was non-repairable. Equal importance was given to all minimal cut sets in terms of their effect on system performance, which caused the severity (S) of failure for all the system components to be same.  
By using the minimal cut sets theory and [PERSON]'s measure of importance, this paper aims to develop a modified FMEA approach in the backward integration with FTA tool for the identification, evaluation and prioritization of failure risks in safety-critical systems. In order to appropriately identify and rank components according to their criticality, a weight will be assigned to the Risk Priority Number (RPN) associated with each component's failure mode. This weight represents the importance of the component in overall system functionality. A case study of a subsea Blowout Preventer (BOP) is presented to illustrate the applicability of the proposed model.  
The rest of the paper continues with a background review of risk analysis techniques in Section 2, followed by a full presentation of our proposed FTA-FMEA methodology in Section 3. Section 4 presents the case study and Section 5 concludes our paper.