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Preservation of DMRL and IMRL aging classes under the formation of order statistics and coherent systems

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  • Navarro, Jorge

Abstract

If the random variable X represents the lifetime of a unit, the mean residual life (MRL) function m(t)=E(X−t|X>t) is a basic tool to study the aging process. The decreasing/increasing mean residual life (DMRL/IMRL) aging classes are defined by the corresponding monotonicity properties of function m. In this paper, sufficient properties are provided for the preservation of these aging classes under the formation of order statistics and coherent systems with identically distributed (ID) components. We consider both the cases of independent and dependent components. In the last case, the sufficient conditions are based on properties of the copula which determines the dependence structure.

Suggested Citation

  • Navarro, Jorge, 2018. "Preservation of DMRL and IMRL aging classes under the formation of order statistics and coherent systems," Statistics & Probability Letters, Elsevier, vol. 137(C), pages 264-268.
    • Handle: RePEc:eee:stapro:v:137:y:2018:i:c:p:264-268
    DOI: 10.1016/j.spl.2018.02.005
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    References listed on IDEAS

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    1. Jorge Navarro & M. Carmen Gomis, 2016. "Comparisons in the mean residual life order of coherent systems with identically distributed components," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 32(1), pages 33-47, January.
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    Cited by:

    1. Walid B. H. Etman & Mohamed S. Eliwa & Hana N. Alqifari & Mahmoud El-Morshedy & Laila A. Al-Essa & Rashad M. EL-Sagheer, 2023. "The NBRULC Reliability Class: Mathematical Theory and Goodness-of-Fit Testing with Applications to Asymmetric Censored and Uncensored Data," Mathematics, MDPI, vol. 11(13), pages 1-22, June.
    2. Chen Li & Xiaohu Li, 2020. "Weak aging properties for coherent systems with statistically dependent component lifetimes," Naval Research Logistics (NRL), John Wiley & Sons, vol. 67(7), pages 559-572, October.
    3. Bo H. Lindqvist & Francisco J. Samaniego, 2019. "Some new results on the preservation of the NBUE and NWUE aging classes under the formation of coherent systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(5), pages 430-438, August.

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