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Sharp bounds for NBUE distributions

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  • Mark Brown

Abstract

Let F be a new better than used in expectation (NBUE) distribution function with mean μ. In a previous paper (Brown in Probab. Eng. Inf. Sci. 20:195–230, 2006 ), the author derived the following bound. For any t≥μ, $$\overline{F}(t)=\mathit{Pr}(X \ge t) \le e^{-[{t\over\mu}-1]}. $$ The main result of this paper is to show that this bound is sharp. Other sharp bounds for NBUE distributions are also derived. Copyright Springer Science+Business Media, LLC 2013

Suggested Citation

  • Mark Brown, 2013. "Sharp bounds for NBUE distributions," Annals of Operations Research, Springer, vol. 208(1), pages 245-250, September.
    • Handle: RePEc:spr:annopr:v:208:y:2013:i:1:p:245-250:10.1007/s10479-012-1151-0
    DOI: 10.1007/s10479-012-1151-0
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    References listed on IDEAS

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    1. Michael N. Katehakis & Cyrus Derman, 1989. "On the Maintenance of Systems Composed of Highly Reliable Components," Management Science, INFORMS, vol. 35(5), pages 551-560, May.
    2. Michael N. Katehakis & Cyrus Derman, 1984. "Optimal Repair Allocation in a Series System," Mathematics of Operations Research, INFORMS, vol. 9(4), pages 615-623, November.
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    Cited by:

    1. Lando, Tommaso, 2024. "Nonparametric inference for NBUE distributions based on the TTT transform," Statistics & Probability Letters, Elsevier, vol. 212(C).
    2. Charles Wells, 2015. "Bounds on uptime distribution based on aging for systems with finite lifetimes," Annals of Operations Research, Springer, vol. 235(1), pages 757-769, December.
    3. Johnson, Tobias & Peköz, Erol, 2022. "Concentration inequalities from monotone couplings for graphs, walks, trees and branching processes," Stochastic Processes and their Applications, Elsevier, vol. 152(C), pages 1-31.

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