, Volume 74, Issue 3, pp 361–380 | Cite as

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

  • Mohammad Z. RaqabEmail author
  • Tomasz Rychlik


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  = (Xt|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.


Mean residual life function Characterization Cauchy–Schwarz inequality Monotone approximation method 


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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of JordanAmmanJordan
  2. 2.Institute of MathematicsPolish Academy of SciencesToruńPoland

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