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Imperfect repair and lifesaving in heterogeneous populations

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  • Finkelstein, Maxim

Abstract

In this theoretical paper we generalize the notion of minimal repair to the heterogeneous case, when the lifetime distribution function can be modeled by continuous or a discrete mixture of distributions. The statistical (black box) minimal repair and the minimal repair based on information just before the failure of an object are considered. The corresponding failure (intensity) rate processes are defined and analyzed. Demographic lifesaving model is also considered: each life is saved (cured) with some probability (or equivalently a proportion of individuals who would have died are now resuscitated and given another chance). Those who are saved experience the statistical minimal repair. Both of these models are based on the Poisson or non-homogeneous Poisson processes of underlying events, which allow for considering heterogeneity. We also consider the new model of imperfect repair in the homogeneous case and present generalizations to the heterogeneous setting.

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  • Finkelstein, Maxim, 2007. "Imperfect repair and lifesaving in heterogeneous populations," Reliability Engineering and System Safety, Elsevier, vol. 92(12), pages 1671-1676.
    • Handle: RePEc:eee:reensy:v:92:y:2007:i:12:p:1671-1676
    DOI: 10.1016/j.ress.2006.09.018
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    References listed on IDEAS

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    1. E. Arjas & I. Norros, 1989. "Change of Life Distribution Via a Hazard Transformation: An Inequality with Application to Minimal Repair," Mathematics of Operations Research, INFORMS, vol. 14(2), pages 355-361, May.
    2. 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.
    3. James Vaupel & Anatoli Yashin, 1987. "Repeated resuscitation: How lifesaving alters life tables," Demography, Springer;Population Association of America (PAA), vol. 24(1), pages 123-135, February.
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    Cited by:

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    2. 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.
    3. Adel Mottahedi & Farhang Sereshki & Mohammad Ataei & Ali Nouri Qarahasanlou & Abbas Barabadi, 2021. "Resilience analysis: A formulation to model risk factors on complex system resilience," 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. 12(5), pages 871-883, October.
    4. Pulcini, Gianpaolo, 2015. "Incorrect modeling of the failure process of minimally repaired systems under random conditions: The effect on the maintenance costs," Reliability Engineering and System Safety, Elsevier, vol. 144(C), pages 178-182.
    5. Bebbington, Mark & Lai, Chin-Diew & Zitikis, RiÄ ardas, 2009. "Balancing burn-in and mission times in environments with catastrophic and repairable failures," Reliability Engineering and System Safety, Elsevier, vol. 94(8), pages 1314-1321.
    6. 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.
    7. Giorgio, M. & Guida, M. & Pulcini, G., 2014. "Repairable system analysis in presence of covariates and random effects," Reliability Engineering and System Safety, Elsevier, vol. 131(C), pages 271-281.

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