Article

Metrika

, Volume 74, Issue 3, pp 361-380

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

  • Mohammad Z. RaqabAffiliated withDepartment of Mathematics, University of Jordan Email author 
  • , Tomasz RychlikAffiliated withInstitute of Mathematics, Polish Academy of Sciences

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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  = (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.

Keywords

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