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Bounds for the mean residual life function of a k-out-of-n system

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Abstract

In the reliability studies, k-out-of-n systems play an important role. In this paper, we consider sharp bounds for the mean residual life function of a k-out-of-n system consisting of n identical components with independent lifetimes having a common distribution function F, measured in location and scale units of the residual life random variable X t  = (X−t|X > t). We characterize the probability distributions for which the bounds are attained. We also evaluate the so obtained bounds numerically for various choices of k and n.

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Authors and Affiliations

  1. Department of Mathematics, University of Jordan, Amman, 11942, Jordan

    Mohammad Z. Raqab

  2. Institute of Mathematics, Polish Academy of Sciences, Toruń, 87100, Poland

    Tomasz Rychlik

Authors
  1. Mohammad Z. Raqab
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  2. Tomasz Rychlik
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Correspondence to Mohammad Z. Raqab.

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Raqab, M.Z., Rychlik, T. Bounds for the mean residual life function of a k-out-of-n system. Metrika 74, 361–380 (2011). https://doi.org/10.1007/s00184-010-0307-7

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  • DOI: https://doi.org/10.1007/s00184-010-0307-7

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