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On mixed δ-shock models

Author

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  • Parvardeh, A.
  • Balakrishnan, N.

Abstract

In this note, we study the system lifetime mixed δ-shock models. In this model, the system fails when the time between two successive shocks is smaller than a critical threshold δ, or the magnitude of the shock (the cumulative magnitude of shocks) is larger than another critical threshold γ. We then obtain the survival function of the system under these new shock models.

Suggested Citation

  • Parvardeh, A. & Balakrishnan, N., 2015. "On mixed δ-shock models," Statistics & Probability Letters, Elsevier, vol. 102(C), pages 51-60.
    • Handle: RePEc:eee:stapro:v:102:y:2015:i:c:p:51-60
    DOI: 10.1016/j.spl.2015.04.006
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    References listed on IDEAS

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    1. Jian-Ming Bai & Zhe Zhang & Ze-Hui Li, 2014. "Lifetime properties of a cumulative shock model with a cluster structure," Annals of Operations Research, Springer, vol. 212(1), pages 21-41, January.
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    Cited by:

    1. Eryilmaz, Serkan, 2017. "δ-shock model based on Polya process and its optimal replacement policy," European Journal of Operational Research, Elsevier, vol. 263(2), pages 690-697.
    2. repec:bpj:demode:v:6:y:2018:i:1:p:131-138:n:8 is not listed on IDEAS
    3. Coskun Kus & Altan Tuncel & Serkan Eryilmaz, 2022. "Assessment of Shock Models for a Particular Class of Intershock Time Distributions," Methodology and Computing in Applied Probability, Springer, vol. 24(1), pages 213-231, March.
    4. Chen, Yunxia & Zhang, Wenbo & Xu, Dan, 2019. "Reliability assessment with varying safety threshold for shock resistant systems," Reliability Engineering and System Safety, Elsevier, vol. 185(C), pages 49-60.
    5. Dheeraj Goyal & Nil Kamal Hazra & Maxim Finkelstein, 2022. "On the Time-Dependent Delta-Shock Model Governed by the Generalized PóLya Process," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1627-1650, September.
    6. Eryilmaz, Serkan & Unlu, Kamil Demirberk, 2023. "A new generalized δ-shock model and its application to 1-out-of-(m+1):G cold standby system," Reliability Engineering and System Safety, Elsevier, vol. 234(C).

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