Metrika

, Volume 74, Issue 3, pp 361–380

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

Article

DOI: 10.1007/s00184-010-0307-7

Cite this article as:
Raqab, M.Z. & Rychlik, T. Metrika (2011) 74: 361. doi:10.1007/s00184-010-0307-7

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 Xt = (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 functionCharacterizationCauchy–Schwarz inequalityMonotone approximation method

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

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