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Reliability analysis and optimal replacement for a k-out-of-n system under a δ -shock model

Author

Listed:
  • Hamed Lorvand
  • Maryam Kelkinnama

Abstract

Consider a k -out-of- n system which is subject to shocks that arrive at random times. This study develops δ -shock model, among the variants of well-known shock models, for such system which consists of independent components. In a δ -shock model, the system fails when the inter-arrival between two consecutive shocks is less than a critical threshold value of δ . Depending on the number of components that fail due to the occurrence of the shocks, we introduce two δ -shock models. The reliability function and mean time to failure of the system are discussed when the time between shocks has an arbitrary distribution. Furthermore, the problem of finding the optimal preventive time concerned with minimizing a mean cost per unit time is investigated. Numerical examples based on a simulation study are also provided to illustrate theoretical achievement.

Suggested Citation

  • Hamed Lorvand & Maryam Kelkinnama, 2023. "Reliability analysis and optimal replacement for a k-out-of-n system under a δ -shock model," Journal of Risk and Reliability, , vol. 237(1), pages 98-111, February.
    • Handle: RePEc:sae:risrel:v:237:y:2023:i:1:p:98-111
    DOI: 10.1177/1748006X221082762
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    References listed on IDEAS

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    1. Cha, Ji Hwan & Finkelstein, Maxim & Levitin, Gregory, 2017. "On preventive maintenance of systems with lifetimes dependent on a random shock process," Reliability Engineering and System Safety, Elsevier, vol. 168(C), pages 90-97.
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    3. Levitin, Gregory & Finkelstein, Maxim, 2017. "Optimal backup in heterogeneous standby systems exposed to shocks," Reliability Engineering and System Safety, Elsevier, vol. 165(C), pages 336-344.
    4. Bai Jing Pan & Ma Ming & Yang Ya Wen, 2017. "Parameter estimation of the censored δ-shock model on uniform interval," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(14), pages 6936-6946, July.
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    Cited by:

    1. Zebin Hu & Linmin Hu, 2025. "Reliability assessment of a multi-state mixed $$\delta $$ -shock model based on discrete PH distribution," Annals of Operations Research, Springer, vol. 353(3), pages 885-916, October.
    2. Mizuki Kasuya & Lu Jin, 2025. "Structural Properties of Optimal Maintenance Policies for k -out-of- n Systems with Interdependence Between Internal Deterioration and External Shocks," Mathematics, MDPI, vol. 13(5), pages 1-23, February.

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