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Asymptotic properties of imperfect repair models and estimation of repair efficiency

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  • Laurent Doyen

Abstract

The aim of this articles is to study the asymptotic behavior of two imperfect repair models, called Arithmetic Reduction of Intensity and Arithmetic Reduction of Age models. These models have been proposed by Doyen and Gaudoin (Reliab Eng Syst Safe 84 (2004) 45–56) and include many usual virtual age models. First, it is proved that the failure intensity of these models is asymptotically almost surely equivalent to a deterministic increasing function with a cumulative error proportional to a logarithm. Second, the almost sure convergence and asymptotic normality of several estimators of repair efficiency are derived, when the wear‐out process without repair is known. Finally, the coverage rate of the asymptotic confidence intervals issued from those estimators is empirically studied. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010

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  • Laurent Doyen, 2010. "Asymptotic properties of imperfect repair models and estimation of repair efficiency," Naval Research Logistics (NRL), John Wiley & Sons, vol. 57(3), pages 296-307, April.
    • Handle: RePEc:wly:navres:v:57:y:2010:i:3:p:296-307
    DOI: 10.1002/nav.20406
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    References listed on IDEAS

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    1. Kijima, Masaaki & Morimura, Hidenori & Suzuki, Yasusuke, 1988. "Periodical replacement problem without assuming minimal repair," European Journal of Operational Research, Elsevier, vol. 37(2), pages 194-203, November.
    2. Pham, Hoang & Wang, Hongzhou, 1996. "Imperfect maintenance," European Journal of Operational Research, Elsevier, vol. 94(3), pages 425-438, November.
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    Cited by:

    1. Wu, Shaomin, 2021. "Two methods to approximate the superposition of imperfect failure processes," Reliability Engineering and System Safety, Elsevier, vol. 207(C).
    2. Liu, Xingheng & Vatn, Jørn & Dijoux, Yann & Toftaker, Håkon, 2020. "Unobserved heterogeneity in stable imperfect repair models," Reliability Engineering and System Safety, Elsevier, vol. 203(C).

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