# Case Study of Expected Loss Failure Mode and Effect Analysis Model Based on Maintenance Data
## 1 Introduction  
FMEA is an efficient qualitative analysis method adopted in safety system engineering. The failure modes, failure effects, potential accidents, and the consequence of accidents can be systematically identified and evaluated by using the powerful tool [1]. The results of the FMEA can help analysts identify and correct the failure modes that have a detrimental effect on the system and improve its performance during the design and production stages [2]. Since its introduction as a methodology for preventing failures, FMEA has been broadly used in various industries, including the aerospace, automotive, semiconductor, aircraft, chemical plant, and steel industries [1, 3, 4, 5, 6, 7, 8]. Procedures for traditional FMEA are largely divided into system definition and FMEA worksheet creation. System definition identifies functions and operating modes as an introduction stage. The procedures required for FMEA worksheet creation are largely divided into failure mode analysis and risk assessment. Failure analysis has a way of enumerating failure modes for individual hardware or cataloging functional failures for products and components [9]. Next, the risk associated with a failure mode is usually evaluated using the risk priority number (_RPN_), which corresponds to the mathematical product of the occurrence (\(O\)), severity (\(S\)), and detection (\(D\)) of a failure-cause (i.e., \(RPN=O\times S\times D\)). _RPN_ evaluation of a potential failure requires evaluating three risk factors, i.e., \(O\), \(S\) and \(D\), via the 1-to-10 scale. The higher the _RPN_ of a failure, the greater is the associated risk concerning system/product reliability [10]. However, this traditional FMEA risk-evaluation approach has often been extensively discussed in the existing literature for various reasons [2]. FMEA includes the following limitations in terms of worksheet creation procedures and RPN-based approaches. First, an_RPN_-based approach include (i) no consideration of relative importance among \(O\), \(S\), and \(D\)[11; 12; 13; 14]; (ii) difficulty to obtain the exact ratings on \(O\), \(S\), and \(D\) because of the uncertainty and vagueness of FMEA group members' judgements [15; 16; 17; 18; 19; 20; 21; 22]; (iii) no reflection of the interdependence between different causes of failure and their consequent effects [6; 23; 24; 25]; and (iv) excessive reliance on expert intuition and experience instead of scientific methods for assessing three risk factors [26; 27]. Next, the limitations in terms of FMEA procedures include: (i) FMEA is an inductive and non-structured approach to identify failure modes [28]; (ii) FMEA worksheets are only practical when there are a variety of experts and team members who are knowledgeable about the system [28]; (iii) identification of failure modes, causes, and effects requires a lot of time and effort by experts. Many researchers have attempted to overcome the drawbacks mentioned above, thereby improving the FMEA risk-evaluation method in the process. Summarizing many studies that focused on improving the risk assessment method, [PERSON] et al. reported that the most popular FMEA approach correspond to the fuzzy rule-based system [29; 30; 31; 32], followed by the grey theory [13; 14], cost-based model [16; 17; 18; 33], AHP/ANP [24; 34; 35] and linear programming. Others included an integration-based approach [21; 22; 26; 27] and probability-based methodology [19; 36]. Apart from these approaches, in our previous study [10; 36], we proposed an economic expected loss model in consideration of the time between the occurrence of the cause of failure and the time it takes to be detected when targeting a step-tier system and a multi-tier system. The proposed model is a time-dependent FMEA model, which has the advantage of being able to intuitively assess the size of risk, unlike RPN, which is a traditional FMEA risk assessment index, RPN. Besides, [PERSON] et al.