Structural and Multidisciplinary Optimization

, Volume 60, Issue 6, pp 2511–2529 | Cite as

Time-dependent reliability analysis model under fuzzy state and its safety lifetime model

  • Yingshi Hu
  • Zhenzhou LuEmail author
  • Jingyu Lei
Research Paper


In view of the lack of time-dependent reliability analysis model (TDRA) under fuzzy state, which is ubiquitous in engineering, a TDRA model under fuzzy state is proposed in this paper, followed by the corresponding safety lifetime model. To establish the TDRA model under fuzzy state, this paper firstly transforms the TDRA model under binary state into a form expressed by the time-dependent failure domain indicator function, and then the TDRA model under fuzzy state is derived based on the basic principle of the time-independent reliability analysis (TIRA) model under fuzzy state. By introducing an auxiliary variable and establishing the time-dependent generalized performance function, the TDRA model under fuzzy state is transformed into a generalized one under binary state, where the failure domain and safety domain are clearly defined. Then, the single-loop Kriging (SLK) surrogate model approach is used to efficiently estimate the time-dependent failure probability (TDFP) in the special service time interval under fuzzy state. Based on the generalized TDRA model and its efficient estimation, a safety lifetime model constrained by the target TDFP under fuzzy state and a corresponding efficient solving method are presented. Finally, examples are used to verify the rationality of the TDRA model and the safety lifetime model under fuzzy state established in this paper, and the efficiency of the algorithm is also validated.


Fuzzy state Time-dependent reliability analysis model Safety lifetime model 


Funding information

This work was supported by the National Natural Science Foundation of China (Grant 51775439) and the National Science and Technology Major Project (2017-IV-0009-0046).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of AeronauticsNorthwestern Polytechnical UniversityXi’anPeople’s Republic of China

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