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Stress-strength reliability inference of multi-state system with multi-type components based on copula theory

Author

Listed:
  • Xuchao Bai
  • Yuxian Wang
  • Chunfang Zhang
  • Jing Cai
  • Haocheng Zhou

Abstract

This article considers a multi-state system which is composed by several multi-type components, it is assumed that any type of components has two strengths which is suffered from two stresses. Further, assume that two strengths have dependent relationship, as well as the two stresses, but there are no relationship among strengths and stresses for different types of components. By extending the applied scenarios, a new survival signature, that is named by improved generalized survival signature, is introduced and is used to analyze the system reliability. When stress (strength) variables follow the distributions of Weibull and exponential, the Clayton copulas are employed to depict the dependence structure of system, then the inferences of system reliability are obtained by a two-stage method. In the first stage, the dependent parameters are achieved by adopting the pseudo maximum likelihood estimation method. The second stage, the maximum likelihood estimation, two confidence intervals based on parametric bootstrap method and transformation-based method for system reliability are deduced. At last, the numerical study and real data application are conducted to illustrate the proposed methodologies.

Suggested Citation

  • Xuchao Bai & Yuxian Wang & Chunfang Zhang & Jing Cai & Haocheng Zhou, 2025. "Stress-strength reliability inference of multi-state system with multi-type components based on copula theory," Journal of Risk and Reliability, , vol. 239(6), pages 1556-1567, December.
    • Handle: RePEc:sae:risrel:v:239:y:2025:i:6:p:1556-1567
    DOI: 10.1177/1748006X251322580
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    References listed on IDEAS

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    1. M. E. Ghitany & D. K. Al-Mutairi, 2008. "Size-biased Poisson-Lindley distribution and its application," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 299-311.
    2. Yan Shen & Ancha Xu, 2018. "On the dependent competing risks using Marshall–Olkin bivariate Weibull model: Parameter estimation with different methods," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(22), pages 5558-5572, November.
    3. Marichal, Jean-Luc & Mathonet, Pierre & Waldhauser, Tamás, 2011. "On signature-based expressions of system reliability," Journal of Multivariate Analysis, Elsevier, vol. 102(10), pages 1410-1416, November.
    4. Serkan Eryilmaz & Altan Tuncel, 2016. "Generalizing the survival signature to unrepairable homogeneous multi‐state systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 63(8), pages 593-599, December.
    5. Yao, Can-Zhong & Li, Min-Jian, 2023. "GARCH-MIDAS-GAS-copula model for CoVaR and risk spillover in stock markets," The North American Journal of Economics and Finance, Elsevier, vol. 66(C).
    6. Faghih-Roohi, Shahrzad & Xie, Min & Ng, Kien Ming & Yam, Richard C.M., 2014. "Dynamic availability assessment and optimal component design of multi-state weighted k-out-of-n systems," Reliability Engineering and System Safety, Elsevier, vol. 123(C), pages 57-62.
    7. Ghitany, M.E. & Al-Mutairi, D.K. & Nadarajah, S., 2008. "Zero-truncated Poisson–Lindley distribution and its application," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(3), pages 279-287.
    8. Ghitany, M.E. & Atieh, B. & Nadarajah, S., 2008. "Lindley distribution and its application," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 78(4), pages 493-506.
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