## 6 Conclusions  
In this study, we incorporated the DEA method and cost and time notions for the purpose of evaluating the risk associated with failure modes in FMEA. Firstly, a detailed study of the RFID system was performed. This was carried out in order to shed light on its possible failures and their causes and effects by means of a modified FMEA that considers the relationships among the sub-failures and eliminates the ranking gaps between them. Secondly, the DEA method was employed to calculate the efficiency rates of each failure mode, as well as the coefficients of the risk factors and the risk indicators. The cost and time needed to fix them served as inputs/outputs for the DEA model.  
To provide an illustration, the RFID showed that the final FM ranks resulting from the FMEA-DEA method are based on both risk and efficiency, and they are reliable and rational more often than those obtained by the traditional FMEA. Therefore, this method is effective and useful, and it may be generalized and used for assigning risk priority rates of failure modes in different applications, equipment, or processes.  
In future research, attention should be directed towards six specific areas. Initially, this will include model rate failure mode risk factors utilizing five-point numeric scales. Given the intricacy of risk analysis problems, FMEA team members often encounter challenges in providing precise assessment information for failure modes concerning each risk factor. Consequently, future exploration could involve integrating the proposed FMEA with fuzzy theories like linguistic fuzzy sets. Secondly, within the proposed FMEA framework, the assumption is that the relative weights of risk assessors are equal. In some situations, the team members have varying backgrounds and knowledge. Therefore, it is crucial to devise efficient techniques for determining the suitable weights of experts, such as AHP or DEA, in future research. Third, other methods can be used to model the interrelationships between failure, causes, and effects, such as DEMATEL. Fourth, a variety of MCDM methods can be incorporated; different combinations can be obtained from Appendix B. Fifth, improved methods for RPN calculation can be used, such as PRISM instead of the traditional method, as presented in Appendix B. Sixth, apart from the RFID system, conducting additional case studies in the future will be beneficial to further validate the proposed risk priority model.  
The following supporting information can be downloaded at: [[https://www.mdpi.com/article/10.3390/app14020584/s1](https://www.mdpi.com/article/10.3390/app14020584/s1)]([https://www.mdpi.com/article/10.3390/app14020584/s1](https://www.mdpi.com/article/10.3390/app14020584/s1)).  
Conceptualization, K.C. and S.D.; methodology, K.C. and S.D.; software PIM DEA version 3.2, S.D.; validation, K.C. and S.D.; formal analysis, K.C. and S.D.; investigation, K.C. and S.D.; resources, K.C. and S.D.; data curation, K.C.; writing--original draft preparation, K.C. and S.D.; writing--review and editing, K.C. and S.D.; visualization, K.C. and S.D.; supervision, S.D.; project administration, S.D.; funding acquisition, K.C. and S.D. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The data presented in this study are available in supplementary material [02-Data collection--Step 1.6].  
The authors express their appreciation to the Editors and unnamed reviewers for their invaluable remarks and suggestions that greatly enhanced the article's quality.  
The authors declare no conflict of interest.