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Inequalities for NBUE and NWUE Life Distributions

Author

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  • Robert L. Launer

    (U.S. Army Research Office, Research Triangle Park, North Carolina)

Abstract

This paper presents a procedure for developing reliability inequalities for several known classes of failure distributions. The inequalities are rational functions of the moments and conditional tail moments of the underlying failure distribution. The introduction of four new classes of failure distributions based on the variance behavior facilitates the development of certain inequalities for the NBUE and NWUE distributions.

Suggested Citation

  • Robert L. Launer, 1984. "Inequalities for NBUE and NWUE Life Distributions," Operations Research, INFORMS, vol. 32(3), pages 660-667, June.
    • Handle: RePEc:inm:oropre:v:32:y:1984:i:3:p:660-667
    DOI: 10.1287/opre.32.3.660
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    Citations

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    Cited by:

    1. Ramesh C. Gupta, 2006. "Variance residual life function in reliability studies," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 343-355.
    2. Belzunce, F. & Candel, J. & Ruiz, J. M., 1996. "Dispersive orderings and characterization of ageing classes," Statistics & Probability Letters, Elsevier, vol. 28(4), pages 321-327, August.
    3. M. Khorashadizadeh & A. Roknabadi & G. Borzadaran, 2013. "Variance residual life function based on double truncation," METRON, Springer;Sapienza Università di Roma, vol. 71(2), pages 175-188, September.
    4. Francisco Germán Badía & María Dolores Berrade, 2022. "On the Residual Lifetime and Inactivity Time in Mixtures," Mathematics, MDPI, vol. 10(15), pages 1-20, August.
    5. Henry W. Block & Thomas H. Savits & Harshinder Singh, 2002. "A Criterion for Burn-in that Balances Mean Residual Life and Residual Variance," Operations Research, INFORMS, vol. 50(2), pages 290-296, April.
    6. Willmot, Gordon E., 1997. "Bounds for compound distributions based on mean residual lifetimes and equilibrium distributions," Insurance: Mathematics and Economics, Elsevier, vol. 21(1), pages 25-42, October.
    7. Balu, Mini N. & Sabnis, S. V., 1997. "Preservation of certain dependent structures under bivariate homogeneous Poisson shock models," Statistics & Probability Letters, Elsevier, vol. 35(1), pages 91-100, August.
    8. Kan Cheng & Yeh Lam, 2002. "Reliability bounds for the NBUE distributions," Naval Research Logistics (NRL), John Wiley & Sons, vol. 49(8), pages 781-797, December.
    9. Chadjiconstantinidis, Stathis, 2023. "Some bounds for the renewal function and the variance of the renewal process," Applied Mathematics and Computation, Elsevier, vol. 436(C).
    10. Al-Zahrani, Bander & Stoyanov, Jordan, 2008. "Moment inequalities for DVRL distributions, characterization and testing for exponentiality," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1792-1799, September.
    11. Li, Xiaohu & Li, Zehui & Jing, Bing-Yi, 2000. "Some results about the NBUC class of life distributions," Statistics & Probability Letters, Elsevier, vol. 46(3), pages 229-237, February.

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