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On some properties of shock processes in a ‘natural’ scale

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  • Cha, Ji Hwan
  • Finkelstein, Maxim

Abstract

We consider shocks modeling in a ‘natural’ scale which is a discrete scale of natural numbers. A system is subject to the shock process and its survival probability and other relevant characteristics are studied in this scale. It turns out that all relations for the probabilities of interest become much easier in the new scale as compared with the conventional chronological time scale. Furthermore, it does not matter what type of the point process of shocks is considered. The shock processes with delays and the analog of a shot-noise process are discussed. Another example of the application of this concept is presented for systems with finite number of components described by signatures.

Suggested Citation

  • Cha, Ji Hwan & Finkelstein, Maxim, 2016. "On some properties of shock processes in a ‘natural’ scale," Reliability Engineering and System Safety, Elsevier, vol. 145(C), pages 104-110.
    • Handle: RePEc:eee:reensy:v:145:y:2016:i:c:p:104-110
    DOI: 10.1016/j.ress.2015.09.009
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    References listed on IDEAS

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    1. Finkelstein, Maxim & Marais, Francois, 2010. "On terminating Poisson processes in some shock models," Reliability Engineering and System Safety, Elsevier, vol. 95(8), pages 874-879.
    2. Maxim Finkelstein, 2008. "Failure Rate Modelling for Reliability and Risk," Springer Series in Reliability Engineering, Springer, number 978-1-84800-986-8, January.
    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.
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    8. Montoro-Cazorla, Delia & Pérez-Ocón, Rafael, 2012. "A shock and wear system under environmental conditions subject to internal failures, repair, and replacement," Reliability Engineering and System Safety, Elsevier, vol. 99(C), pages 55-61.
    9. 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, September.
    10. Austin J. Lemoine & Michael L. Wenocur, 1986. "Technical Note—A Note on Shot-Noise and Reliability Modeling," Operations Research, INFORMS, vol. 34(2), pages 320-323, April.
    11. Finkelstein, Maxim, 2007. "Shocks in homogeneous and heterogeneous populations," Reliability Engineering and System Safety, Elsevier, vol. 92(5), pages 569-574.
    12. van der Weide, J.A.M. & Pandey, M.D., 2011. "Stochastic analysis of shock process and modeling of condition-based maintenance," Reliability Engineering and System Safety, Elsevier, vol. 96(6), pages 619-626.
    13. Montoro-Cazorla, Delia & Pérez-Ocón, Rafael & del Carmen Segovia, Maria, 2009. "Replacement policy in a system under shocks following a Markovian arrival process," Reliability Engineering and System Safety, Elsevier, vol. 94(2), pages 497-502.
    14. 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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