## 5 Conclusions  
Assessing the effectiveness of safety barriers (SBs) holds significance in guiding their configuration and subsequently reducing the failure risks within process systems. In this study, we proposed an integrated method to evaluate the effectiveness of SBs in process systems. This method incorporated IVIFNs into the BT model. Due to the limited data availability concerning safety barriers in practical processes, this method addresses the challenge of obtaining fundamental probability data by employing expert elicitation. Furthermore, it manages uncertainties in opinions by utilizing IVIFNs. The effectiveness of safety barriers is measured by comparing the relative change in failure risk due to the addition of the barrier. The method was applied to analyze the SBs of a natural gas storage tank. The results show that multiple SBs are more effective than a single SB, and preventive SBs have a greater effect on system risks than protective SBs. Therefore, preventive SBs should be prioritized in order to avoid a critical event. However, as it is not possible to fully control all sources of hazards, it is desirable to also have protective SBs to control and mitigate the effects of failure consequences. The combinational analysis of SBs can also provide a comprehensive understanding of the effectiveness of each SB so that the most appropriate combination of SBs can be found to meet the requirements of safe production and cost control. The accuracy of this method still depends on the model structure and the probabilities of bottom events, which means that the selection of experts and the supplementation of data are very important. Therefore, it is necessary to consider experts' professional background and practical experience comprehensively, giving as comprehensive information as possible to eliminate the influence of expert bias when determining the expert group. A panel of three experts was used in this study, who met the criteria for professionalism and diversity, but consulting more experts can make the model results more objective and reliable. In fact, expert elicitation is used to solve the challenge of lacking accurate and reliable objective data, and IVIFNs in further analysis are used in this method to reduce the bias and uncertainty of experts' opinions. Moreover, if objective data exist for some events of the BT model, direct assignment can make the evaluation more reliable. Therefore, in future studies, we plan to propose more effective methods to mitigate the influence of expert biases and to obtain objective actual data as comprehensively as possible to replace experts' opinions. Due to the feasibility of the IVIFN-BT method, it can be extended to other process industry scenarios where SBs are required, and actual data are difficult to obtain. It can also provide support for safety management and risk assessment in other process industry environments. In addition, in the current work, the SB effectiveness analysis based on the BT model is static. However, in practice, safety barriers evolve over time. Therefore, future research should further consider the changes in safety barrier functions during the evolution of an event, so as to conduct a more comprehensive assessment in the process industry. **Author Contributions:** Conceptualization, J.L. ; methodology, J.L. ; software, H.Y. and X.G. ; validation, H.Y. ; formal analysis, H.Y. ; investigation, Y.Z. and X.L. ; resources, X.L. ; data curation, X.G. ; writing--original draft preparation, J.L. ; writing--review and editing, H.Y., Y.Z., X.L., Y.L., X.G. and W.W.; visualization, Y.Z. ; supervision, W.W.; project administration, Y.L. ; funding acquisition, X.L. and W.W. All authors have read and agreed to the published version of the manuscript. **Funding:** This work was funded by the Natural Science Basic Research Program of Shaanxi Province of China (Program No. 2023-JC-YB-447), the Science and Technology Program of the State Administration for Market Regulation (2022 MK200), and the Science and Technology Program of CSEI (2022 key03).