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On the behaviour of some new ageing properties based upon the residual life of k-out-of-n systems

Part of: Special processes Distribution theory

Published online by Cambridge University Press:  14 July 2016

Xiaohu Li  and
Ming J. Zuo
Xiaohu Li*
Affiliation:
Lanzhou University
Ming J. Zuo*
Affiliation:
University of Alberta
*
∗ Postal address: Department of Mathematics, Lanzhou University, Lanzhou 730000, China. Email address: [email protected]
∗∗ Postal address: Department of Mechanical Engineering, University of Alberta, Edmonton, Alberta, Canada T6G 2G8.
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Abstract

In this paper, we investigate k-out-of-n systems with independent and identically distributed components. Some characterizations of the IFR(2), DMRL, NBU(2) and NBUC classes of life distributions are obtained in terms of the monotonicity of the residual life given that the (n-k)th failure has occurred at time t ≥ 0. These results complement those reported by Belzunce, Franco and Ruiz (1999). Similar conclusions based on the residual life of a parallel system conditioned by the (n-k)th failure time are presented as well.

Keywords

DMRLIFR(2)NBUCNBU(2)NBULtincreasing convex orderincreasing concave orderparallel systemresidual life

MSC classification

Primary: 62E10: Characterization and structure theory
Secondary: 60K10: Applications (reliability, demand theory, etc.)
Type
Short Communications
Information
Journal of Applied Probability , Volume 39 , Issue 2 , June 2002 , pp. 426 - 433
Copyright
Copyright © Applied Probability Trust 2002 

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