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Poisson Shock Model with Applications to Preventive Maintenance

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Part of the book series: Springer Series in Reliability Engineering ((RELIABILITY))

Abstract

In this chapter, we study in detail and more generality a Poisson shock model that describes the impact of stochastic environment.

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References

  • Aalen OO, Borgan Ø, Gjessing H (2008) Survival and event history analysis: a process point of view. Springer, New York

    Book  MATH  Google Scholar 

  • Cha JH, Finkelstein M (2009) On terminating shock process with independent wear increments. J Appl Probab 46:353–362

    Article  MathSciNet  MATH  Google Scholar 

  • Cha JH, Lee EY (2010) An extended stochastic failure model for a system subject to random shocks. Oper Res Lett 38:468–473

    Article  MathSciNet  MATH  Google Scholar 

  • Cha JH, Finkelstein M (2011) On new classes of extreme shock models and some generalizations. J Appl Probab 48:258–270

    Article  MathSciNet  MATH  Google Scholar 

  • Cha JH, Mi J (2011) On a stochastic survival model for a system under randomly variable environment. Method Comput Appl Probab 13:549–561

    Article  MathSciNet  MATH  Google Scholar 

  • Cha JH, Finkelstein M, Levitin G (2017a) On preventive maintenance of systems with lifetimes dependent on a random shock process. Reliab Eng Syst Saf 168:90–97

    Article  Google Scholar 

  • Cha JH, Finkelstein M, Levitin G (2017b) Bivariate preventive maintenance of systems with lifetimes dependent on a random shock process. Eur J Oper Res, in press. https://doi.org/10.1016/j.ejor.2017.09.021

  • Cha JH, Finkelstein M, Levitin G (2017c) Bivariate preventive maintenance for repairable systems subject to random shocks. J Risk Reliab, in press. https://doi.org/10.1177/1748006X17721797

  • Finkelstein M (2008) Failure rate modelling for reliability and risk. Springer, London

    MATH  Google Scholar 

  • Finkelstein M, Cha JH (2013) Stochastic modelling for reliability: shocks, burn-in and heterogeneous populations. Springer, London

    Book  MATH  Google Scholar 

  • Kalbfleisch JD, Prentice RL (1980) The statistical analyses of failure time data. Wiley, New York

    MATH  Google Scholar 

  • Lehmann A (2009) Joint modeling of degradation and failure time data. J Stat Plann Infer 139:1693–1705

    Article  MathSciNet  MATH  Google Scholar 

  • Nakagawa T (2007) Shock and damage models in reliability theory. Springer, London

    MATH  Google Scholar 

  • Shaked M, Shanthikumar J (2007) Stochastic orders. Springer, New York

    Book  MATH  Google Scholar 

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Correspondence to Ji Hwan Cha .

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Cha, J.H., Finkelstein, M. (2018). Poisson Shock Model with Applications to Preventive Maintenance. In: Point Processes for Reliability Analysis. Springer Series in Reliability Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-73540-5_6

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  • DOI: https://doi.org/10.1007/978-3-319-73540-5_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-73539-9

  • Online ISBN: 978-3-319-73540-5

  • eBook Packages: EngineeringEngineering (R0)

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