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Life distribution properties of a new δ - shock model

Author

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  • Hamed Lorvand
  • Alireza Nematollahi
  • Mohammad Hossien Poursaeed

Abstract

In this paper, the mixed δ-shock models for the multi-state systems is generalized to a model for which the system switches to a lower partially working state as soon as the occurrence of each interarrival time between two successive shocks lying in [δ1,δ2]. The system fails in three ways: first, k out of interarrival times between two successive shocks are in [δ1,δ2], second, upon the occurrence of each interarrival time between two successive shocks less than δ1 and third upon the occurrence of each shock with magnitude bigger than the other critical threshold γ. The survival functions of the system’s lifetime, the time used by the system in a perfectly functioning state, and the total time used by the system in partially working states are derived under the proposed model. The first two moments are also calculated. A simulation study is conducted to illustrate the behavior of the survival functions of the system’s lifetime.

Suggested Citation

  • Hamed Lorvand & Alireza Nematollahi & Mohammad Hossien Poursaeed, 2020. "Life distribution properties of a new δ - shock model," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(12), pages 3010-3025, June.
    • Handle: RePEc:taf:lstaxx:v:49:y:2020:i:12:p:3010-3025
    DOI: 10.1080/03610926.2019.1584316
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    Cited by:

    1. Mohsen Bohlooli-Zefreh & Majid Asadi & Afshin Parvardeh, 2021. "On the reliability and optimal maintenance of systems under a generalized mixed δ -shock model," Journal of Risk and Reliability, , vol. 235(5), pages 909-922, October.
    2. Zhiyuan Zuo & Liang Wang & Yuhlong Lio, 2022. "Reliability Estimation for Dependent Left-Truncated and Right-Censored Competing Risks Data with Illustrations," Energies, MDPI, vol. 16(1), pages 1-25, December.
    3. Wang, Xiaoyue & Zhao, Xian & Wu, Congshan & Wang, Siqi, 2022. "Mixed shock model for multi-state weighted k-out-of-n: F systems with degraded resistance against shocks," Reliability Engineering and System Safety, Elsevier, vol. 217(C).

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