## 6 Conclusions  
With the continuous improvement of product integration and reliability, the problem of reliability assessment for zero-failure models has become an important challenge in reliability engineering. This paper proposes a reliability assessment method for series systems with Weibull zero-failure data, addressing the low accuracy or inapplicability of the traditional method in zero-failure scenarios. The main research results are summarized as follows:  
Figure 7: Reliable life update results for IES.  
Based on the minimum lifetime distribution theory, a reliability assessment method for series systems is established when the component life follows the Weibull distribution. Closed-form expressions for the LCLs of system reliability and reliable life are derived from zero-failure data of different components. The special case of a series system containing several identical components is also discussed, and the equivalent zero-failure time conversion formula is provided.
2. A reliability updating procedure for series systems is proposed, using the system-level operation data to update the system reliability assessment results initially derived from component life data. This method further improves the accuracy of system reliability assessment.
3. Monte Carlo simulations demonstrate that the LCLs of system reliability obtained by this paper's method are very close to the real value and have higher accuracy than those obtained by the LM method. This improvement is due to the new method's ability to fully exploit the life information in the component zero-failure data, thereby effectively improving the analysis accuracy.
4. Through an engineering application in the reliability assessment of an IES, the effectiveness of the new method in integrating zero-failure life data from multiple levels (components and system) and multiple sources (field test and actual operation) is verified.  
In this study, component life is assumed to follow a Weibull distribution. Future research should aim to explore more efficient strategies to address other reliability models, such as lognormal and gamma distributions. The current update method assumes that the system operates without failures, but the probability of failure rises with increased time in service. Therefore, developing updated models that can integrate system-level failure time data is necessary. In addition, existing case studies mainly focus on aerospace products. In the future, there remains a need to scientifically validate the applicability of this method in other engineering fields (e.g., weaponry and nuclear power equipment). In conclusion, the robustness and applicability of the model are expected to be further improved by relaxing component distribution restrictions, incorporating system-level failure time data, and diversifying the engineering domains.  
Conceptualization, Z.L. and H.F.; methodology, Z.L. and H.F.; software, Z.L.; validation, Z.L., H.F. and J.G.; formal analysis, Z.L.; investigation, Z.L. and H.F.; resources, Z.L., H.F. and J.G.; data curation, Z.L.; writing--original draft preparation, Z.L.; writing--review and editing, Z.L., [PERSON] and [PERSON]; visualization, [PERSON]; supervision, [PERSON]; project administration, [PERSON]; funding acquisition, [PERSON] All authors have read and agreed to the published version of the manuscript.  
This research was funded by National Natural Science Foundation of China grant No. U2037602.  
Not applicable.  
These data were derived from the following publicly available resource: [[http://www.caphboot.com/n3433175/n3433206/n3773743/c3746865/content.html](http://www.caphboot.com/n3433175/n3433206/n3773743/c3746865/content.html)]([http://www.caphboot.com/n3433175/n3433206/n3773743/c3746865/content.html](http://www.caphboot.com/n3433175/n3433206/n3773743/c3746865/content.html)) (accessed on 4 March 2025).  
The authors declare no conflicts of interest.