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Fluctuation Analysis of a Soft-Extreme Shock Reliability Model

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  • Jewgeni H. Dshalalow

    (Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL 32901, USA)

  • Ryan T. White

    (Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL 32901, USA)

Abstract

In this paper, we deal with a mixed reliability system decaying from natural wear, occasional soft and hard shocks that eventually lead the system to failure. The aging process alone is linear and it is escalated through soft shocks such that they lead to the system’s soft failure when the combined damage exceeds a threshold M . The other threat is that posed by occasional hard shocks. When the total number of them identified as critical (each critical shock exceeds a fixed threshold H ) reaches N , the system becomes disabled. With N = 1 , a critical shock is extreme . The arrival stream of shocks is a renewal process marked by soft and hard shocks. We establish a formula for a closed form functional containing system’s time-to-failure , the state of the system upon its failure, and other useful statistical characteristics of the system using and embellishing fluctuation analysis and operational calculus. Special cases provide tame expressions that are computed and validated by simulation.

Suggested Citation

  • Jewgeni H. Dshalalow & Ryan T. White, 2022. "Fluctuation Analysis of a Soft-Extreme Shock Reliability Model," Mathematics, MDPI, vol. 10(18), pages 1-33, September.
  • Handle: RePEc:gam:jmathe:v:10:y:2022:i:18:p:3312-:d:913222
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    References listed on IDEAS

    as
    1. Eryilmaz, Serkan, 2015. "Assessment of a multi-state system under a shock model," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 1-8.
    2. Che, Haiyang & Zeng, Shengkui & Li, Kehui & Guo, Jianbin, 2022. "Reliability analysis of load-sharing man-machine systems subject to machine degradation, human errors, and random shocks," Reliability Engineering and System Safety, Elsevier, vol. 226(C).
    3. Jewgeni H. Dshalalow, 1997. "On the level crossing of multi-dimensional delayed renewal processes," International Journal of Stochastic Analysis, Hindawi, vol. 10, pages 1-7, January.
    4. Meango, Toualith Jean-Marc & Ouali, Mohamed-Salah, 2020. "Failure interaction model based on extreme shock and Markov processes," Reliability Engineering and System Safety, Elsevier, vol. 197(C).
    5. Li, Xiang-Yu & Huang, Hong-Zhong & Li, Yan-Feng & Xiong, Xiaoyan, 2021. "A Markov regenerative process model for phased mission systems under internal degradation and external shocks," Reliability Engineering and System Safety, Elsevier, vol. 215(C).
    6. Fermín Mallor & Javier Santos, 2003. "Reliability of systems subject to shocks with a stochastic dependence for the damages," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 12(2), pages 427-444, December.
    7. Yousefi, Nooshin & Coit, David W. & Song, Sanling & Feng, Qianmei, 2019. "Optimization of on-condition thresholds for a system of degrading components with competing dependent failure processes," Reliability Engineering and System Safety, Elsevier, vol. 192(C).
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    Cited by:

    1. Jewgeni H. Dshalalow & Hend Aljahani, 2023. "Discrete and Continuous Operational Calculus in N-Critical Shocks Reliability Systems with Aging under Delayed Information," Mathematics, MDPI, vol. 11(16), pages 1-27, August.
    2. Wei, Xiaohua & Bai, Sijun & Wu, Bei, 2023. "A novel shock-dependent preventive maintenance policy for degraded systems subject to dynamic environments and N-critical shocks," Reliability Engineering and System Safety, Elsevier, vol. 239(C).

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