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Shocks in homogeneous and heterogeneous populations

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  • Finkelstein, Maxim

Abstract

A system subject to a point process of shocks is considered. Shocks occur in accordance with a non-homogeneous Poisson process. Different criterions of system failures are discussed in a homogeneous case. Two natural settings are analyzed. Heterogeneity is modeled by an unobserved univariate random variable (frailty). It is shown that reliability (safety) analysis for a heterogeneous case can differ dramatically from that for a homogeneous setting. A shock burn-in procedure for a heterogeneous population is described. The corresponding bounds for the failure rates are obtained.

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  • Finkelstein, Maxim, 2007. "Shocks in homogeneous and heterogeneous populations," Reliability Engineering and System Safety, Elsevier, vol. 92(5), pages 569-574.
    • Handle: RePEc:eee:reensy:v:92:y:2007:i:5:p:569-574
    DOI: 10.1016/j.ress.2006.05.006
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    1. James Vaupel & Kenneth Manton & Eric Stallard, 1979. "The impact of heterogeneity in individual frailty on the dynamics of mortality," Demography, Springer;Population Association of America (PAA), vol. 16(3), pages 439-454, August.
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    1. 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.
    2. Delia Montoro-Cazorla & Rafael Pérez-Ocón, 2022. "Analysis of k-Out-of-N-Systems with Different Units under Simultaneous Failures: A Matrix-Analytic Approach," Mathematics, MDPI, vol. 10(11), pages 1-13, June.
    3. Rezgar Zaki & Abbas Barabadi & Javad Barabady & Ali Nouri Qarahasanlou, 2022. "Observed and unobserved heterogeneity in failure data analysis," Journal of Risk and Reliability, , vol. 236(1), pages 194-207, February.
    4. Rezgar Zaki & Abbas Barabadi & Ali Nouri Qarahasanlou & A. H. S. Garmabaki, 2019. "A mixture frailty model for maintainability analysis of mechanical components: a case study," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 10(6), pages 1646-1653, December.
    5. Levitin, Gregory & Finkelstein, Maxim & Dai, Yuanshun, 2018. "Heterogeneous standby systems with shocks-driven preventive replacements," European Journal of Operational Research, Elsevier, vol. 266(3), pages 1189-1197.
    6. Che, Haiyang & Zeng, Shengkui & Guo, Jianbin, 2019. "Reliability assessment of man-machine systems subject to mutually dependent machine degradation and human errors," Reliability Engineering and System Safety, Elsevier, vol. 190(C), pages 1-1.
    7. Finkelstein, Maxim, 2013. "On some comparisons of lifetimes for reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 119(C), pages 300-304.
    8. Maxim Finkelstein & Gregory Levitin, 2018. "Optimal Mission Duration for Partially Repairable Systems Operating in a Random Environment," Methodology and Computing in Applied Probability, Springer, vol. 20(2), pages 505-516, June.
    9. Cha, Ji Hwan & Finkelstein, Maxim, 2013. "The failure rate dynamics in heterogeneous populations," Reliability Engineering and System Safety, Elsevier, vol. 112(C), pages 120-128.
    10. Maxim Finkelstein & Gregory Levitin, 2018. "Optimal mission duration for systems subject to shocks and internal failures," Journal of Risk and Reliability, , vol. 232(1), pages 82-91, February.
    11. Levitin, Gregory & Finkelstein, Maxim & Dai, Yuanshun, 2018. "Optimizing availability of heterogeneous standby systems exposed to shocks," Reliability Engineering and System Safety, Elsevier, vol. 170(C), pages 137-145.
    12. Nader Ebrahimi & S.N.U.A. Kirmani & Ehsan S. Soofi, 2011. "Predictability of operational processes over finite horizon," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(6), pages 531-545, September.
    13. 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).
    14. van der Weide, J.A.M. & Pandey, M.D. & van Noortwijk, J.M., 2010. "Discounted cost model for condition-based maintenance optimization," Reliability Engineering and System Safety, Elsevier, vol. 95(3), pages 236-246.
    15. Montoro-Cazorla, Delia & Pérez-Ocón, Rafael, 2014. "A reliability system under different types of shock governed by a Markovian arrival process and maintenance policy K," European Journal of Operational Research, Elsevier, vol. 235(3), pages 636-642.
    16. Rodrigues, Augusto J.S. & Cavalcante, Cristiano A.V. & Lee, Chi-Guhn, 2024. "A general inspection and replacement policy for protection systems subject to shocks with state dependent effect," Reliability Engineering and System Safety, Elsevier, vol. 251(C).
    17. 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.
    18. Cha, Ji Hwan & Finkelstein, Maxim, 2014. "Some notes on unobserved parameters (frailties) in reliability modeling," Reliability Engineering and System Safety, Elsevier, vol. 123(C), pages 99-103.
    19. Montoro-Cazorla, Delia & Pérez-Ocón, Rafael, 2014. "Matrix stochastic analysis of the maintainability of a machine under shocks," Reliability Engineering and System Safety, Elsevier, vol. 121(C), pages 11-17.

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