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Keywords:

  • PF2;
  • IFR;
  • DMRL;
  • NBU;
  • NBU(2);
  • NBUC;
  • increasing convex order;
  • increasing concave order;
  • residual life;
  • right spread order

Abstract

The k-out-of-n structure is a very popular type of redundancy in fault-tolerant systems, it has founded wide applications in industrial and military systems during the past several decades. This paper will investigate the residual life length of a k-out-of-n system with independent (not necessarily identical) components, given that the (nk)th failure has occurred at time t⩾0. Behaviour of PF2, IFR, DRHR, DMRL, NBU(2) and NBUC classes of life distributions are derived in terms of the monotonicity of the residual life given the time of the (nk)th failure. Copyright © 2004 John Wiley & Sons, Ltd.