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On preventive maintenance of systems subject to shocks

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  • Maxim Finkelstein
  • Ilya Gertsbakh

Abstract

A system of identical components is subject to an external shock process, described by the number of shocks in each time interval. Each shock destroys one of the components with probability p and has no effect on a system with probability 1 − p . Signatures are defined and used for description of the system’s structure and for dealing with the corresponding optimal maintenance problems. Two optimal maintenance strategies are discussed. The first strategy is based on the obtained optimal number of a shock, after which the maintenance is performed unless the failure of a whole system occurs earlier. In the latter case the system is replaced. The second strategy is periodic when preventive maintenance is performed periodically with respect to the observed shock numbers. Several numerical examples are presented.

Suggested Citation

  • Maxim Finkelstein & Ilya Gertsbakh, 2016. "On preventive maintenance of systems subject to shocks," Journal of Risk and Reliability, , vol. 230(2), pages 220-227, April.
    • Handle: RePEc:sae:risrel:v:230:y:2016:i:2:p:220-227
    DOI: 10.1177/1748006X15624593
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    References listed on IDEAS

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    1. Hongzhou Wang & Hoang Pham, 2006. "Reliability and Optimal Maintenance," Springer Series in Reliability Engineering, Springer, number 978-1-84628-325-3, March.
    2. Maxim Finkelstein, 2008. "Failure Rate Modelling for Reliability and Risk," Springer Series in Reliability Engineering, Springer, number 978-1-84800-986-8, March.
    3. Maxim Finkelstein & Ji Hwan Cha, 2013. "Burn-in for Heterogeneous Populations," Springer Series in Reliability Engineering, in: Stochastic Modeling for Reliability, edition 127, chapter 0, pages 261-312, Springer.
    4. Toshio Nakagawa, 2008. "Advanced Reliability Models and Maintenance Policies," Springer Series in Reliability Engineering, Springer, number 978-1-84800-294-4, March.
    5. Francisco J. Samaniego, 2007. "System Signatures and their Applications in Engineering Reliability," International Series in Operations Research and Management Science, Springer, number 978-0-387-71797-5, April.
    6. Maxim Finkelstein & Ji Hwan Cha, 2013. "Shocks as Burn-in," Springer Series in Reliability Engineering, in: Stochastic Modeling for Reliability, edition 127, chapter 0, pages 313-361, Springer.
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    Cited by:

    1. Zarezadeh, Somayeh & Ashrafi, Somayeh, 2019. "On preventive maintenance of networks with components subject to external shocks," Reliability Engineering and System Safety, Elsevier, vol. 191(C).
    2. Zarezadeh, Somayeh & Asadi, Majid, 2019. "Coherent systems subject to multiple shocks with applications to preventative maintenance," Reliability Engineering and System Safety, Elsevier, vol. 185(C), pages 124-132.
    3. Cha, Ji Hwan & Finkelstein, Maxim & Levitin, Gregory, 2018. "Bivariate preventive maintenance of systems with lifetimes dependent on a random shock process," European Journal of Operational Research, Elsevier, vol. 266(1), pages 122-134.
    4. 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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