t), for any arbitrary t>0 in various scale units generated by central absolute moments. The results are derived by using the greatest convex minorant approximation combined with the Hölder inequality. We also determine the distributions for which the bounds are attained. The optimal bounds are numerically evaluated and compared with other classical rough bounds."> t), for any arbitrary t>0 in various scale units generated by central absolute moments. The results are derived by using the greatest convex minorant approximation combined with the Hölder inequality. We also determine the distributions for which the bounds are attained. The optimal bounds are numerically evaluated and compared with other classical rough bounds.">
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Evaluations of the mean residual lifetime of an m-out-of-n system

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  • Raqab, Mohammad Z.
Abstract
The mean residual lifetime is an important measure in the reliability theory and in studying the lifetime of a living organism. This paper presents sharp upper bounds on the deviations of the mean residual lifetime of an m-out-of-n system from the mean of a residual life random variable Xt=(X-tX>t), for any arbitrary t>0 in various scale units generated by central absolute moments. The results are derived by using the greatest convex minorant approximation combined with the Hölder inequality. We also determine the distributions for which the bounds are attained. The optimal bounds are numerically evaluated and compared with other classical rough bounds.

Suggested Citation

  • Raqab, Mohammad Z., 2010. "Evaluations of the mean residual lifetime of an m-out-of-n system," Statistics & Probability Letters, Elsevier, vol. 80(5-6), pages 333-342, March.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:5-6:p:333-342
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    1. Mohammad Z. Raqab, 2000. "On the moments of record values," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 29(7), pages 1631-1647, January.
    2. Raqab, Mohammad Z., 1997. "Bounds based on greatest convex minorants for moments of record values," Statistics & Probability Letters, Elsevier, vol. 36(1), pages 35-41, November.
    3. Unknown, 1986. "Letters," Choices: The Magazine of Food, Farm, and Resource Issues, Agricultural and Applied Economics Association, vol. 1(4), pages 1-9.
    4. Arnold, Barry C., 1985. "p-Norm bounds on the expectation of the maximum of a possibly dependent sample," Journal of Multivariate Analysis, Elsevier, vol. 17(3), pages 316-332, December.
    5. Abouammoh, A. & El-Neweihi, E., 1986. "Clusure of the NBUE and DMRL classes under formation of parallel systems," Statistics & Probability Letters, Elsevier, vol. 4(5), pages 223-225, August.
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    1. Bayramoglu, Ismihan, 2020. "Joint distribution of a random sample and an order statistic: A new approach with an application in reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 193(C).

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