# Failure Mode and Effects Analysis Considering Consensus and Preferences Interdependence
## 1 Introduction  
Failure mode and effects analysis (FMEA) is a very effective and useful engineering technique used for accident prevention and risk analysis, and it is applied to identify and eliminate known or potential failures to enhance the reliability and safety of a complex system [1, 2]. The major usefulness of FMEA is that it intends to provide the relative information required for risk management decision-making and risk analysis [1, 3]. As a formal system analysis approach, the technique of FMEA was originally proposed in the 1960s, and was intended to satisfy the aerospace industry's apparent safety and reliability requirements [4]. Since then, the FMEA method has been successfully used in various industries as a simple and powerful tool to enhance the safety and reliability of products, systems, and processes in industry, such as the aerospace [5], energy [6], health care and hospital [7], and manufacturing industries [8]. In the method of traditional FMEA, the risk priority of failure modes is determined by the risk priority number (RPN) that is calculated by the multiplication of the three risk factors, namely, Severity (S), Occurrence (O), and Detection (D). The RPN value is obtained by the equation \(\text{RPN}=5\times O\times D\), where \(S\) is the seriousness of effects, while \(O\) and \(D\) are the probability of occurrence and likelihood of being undetected, respectively. The conventional RPN method has been widely used in various fields because it is quite straight forward. However, it has been criticized extensively for a varietyof limitations. Numerous alternative methods have been presented in the literature to handle some of these drawbacks [2], which could explain why focusing on these shortcomings can improve the performance of traditional FMEA. However, many practical application cases have suggested that the ranking results determined by these alternative methods are not reliable and suffer from drawbacks in some situations. The main reasons are the assumption that the experts' preferences are independent and the team of experts have reached a consensus before aggregating the experts' preferences. Therefore, it is worth studying the problem of how to determine effectively the risk priority of failure modes without considering these two assumptions. It is very important for an FMEA team to adopt a suitable aggregation method to aggregate the experts' preferences into a collective evaluation matrix before determining the failure modes ranking. Many aggregation methods that assume that experts' preferences are independent have been applied to aggregate the experts' preferences. In practice, the FMEA team experts come from different departments or industries, and their subjective preferences, which are often influenced by social, power, knowledge, and other factors, usually indicate some interdependent characteristics. On the one hand, the geometric Bonferroni mean (GBM) initially proposed by [PERSON] et al. [9] is an efficient operator to deal with the aggregation of interdependent arguments. The GBM operator has a prominent characteristic that can easily capture the interrelationships among input arguments [9]. Therefore, it is significant to integrate the experts' preferences into a comprehensive preference by adopting the GBM operator that depicts the interdependent relationships between the experts' preferences before determining the risk priority of failure modes. On the other hand, group-based FMEA risk assessment is essentially a multi-criteria group decision-making problem [10]. Many different approaches based on group decision-making, which assume that FMEA team experts have reached a consensus before ranking the failure modes, have been presented by researchers and practitioners to improve the reliability of the conventional FMEA method. In reality, group decision-making consists of two processes: the consensus-reaching process and the selection process [11; 12].