## 2 Research Background
### FTA and FMEA  
Recently, applying both the FTA and FMEA techniques either simultaneously or in succession has been proven to be complementary, effective and increasingly popular. Employed systematically, an integrated FTA-FMEA technique can provide a thorough evaluation of system safety concerns [18]. FTA yields a comprehensive breakdown of faults leading to the undesired top event, whilst FMEA furnishes the exact fashion in which these faults exists and their direct effects on the top event, making the combination appropriate for safety and reliability analyses.  
The backward integration of both tools seemingly provides stronger advantages, though many researchers argue advantages depend on the specific application [9]. [PERSON] and [PERSON] [19] carried out FTA in parallel and FMEA sequentially, to analyze and diagnose the different causes of failures in a gas leak detection system. Limitations of the individual techniques were however not explored. [PERSON] et al. [20] in a unified bouncing approach considered multiple point failures through interaction matrices, a major enhancement to the traditional FMEA. The interaction between the techniques grows in complexity, requiring in-depth knowledge of the tools and particularly of the system under study.  
Employing the combination of FTA and FEMA for identifying critical components and reliability analysis of highly complex systems has received little attention. [PERSON] et al. [21] combined three methods of critical component identification, namely reliability prediction, FMEA and FTA in a reliability tolerance design program for light-emitting diode (LED). [PERSON] et al. [5] used the combination of FTA and FMEA techniques to identify critical components in the manufacturing processes of a photovoltaic power station in the bi-directional fashion, revising minimal cut sets and continually refining them. Though software usage is incorporated, the process remains long and complex. As clearly seen, these methodologies are not without limitations. Therefore, there still exists a crucial need to manage different criteria of risk analysis techniques in a combinatorial framework to efficiently furnish and complement each other, and be pertinent to specific safety and reliability requirements. In order to tap maximum benefits of an FTA-FMEA integration, minimal cut set theory will be used in this study.  
Weights (\(w\)) are assigned to RPN values in the FMEA technique to incorporate the importance of each component in the system. Therefore, the weighted RNP value is calculated by Equation (2), that is,  
\[\text{WRPN}=w\times\text{S}\times\text{O}\times\text{D} \tag{2}\]  
where as shown, \(w\) is factored into traditional RPN values to prioritize failure modes and thereafter critical components. These weights are vital as they are representative of the importance of minimal cut sets and hence all components are represented by the latter. The FTA methodology is selected for this purpose, as it readily provides and ranks minimal cut sets in terms of importance to system performance. Subsequent breakdown of minimal cut sets allows all components to be analyzed in FMEA worksheets. Simplicity and ease of use are introduced through underlying theory that links both techniques and the complex system under consideration, and is streamlined to component level. The criticality of components is then calculated, not based on RPN but on the weighted RPN. The details of the methodology are presented in the next Section.