Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 342940, 11 pages
Research Article

On Extreme Residual Lives after the Failure of the System

1Department of Industrial Engineering, Atilim University, Incek, 06836 Ankara, Turkey
2Department of Mathematics, Izmir University of Economics, 35330 Izmir, Turkey

Received 25 January 2012; Revised 18 May 2012; Accepted 20 May 2012

Academic Editor: Alexander Pogromsky

Copyright © 2012 Serkan Eryilmaz and Ismihan Bayramoglu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The concept of residual lifetime has attracted considerable research interest in reliability theory. It is useful for evaluating the dynamic behavior of a system. In this paper, we study the extreme residual lives, that is, the minimum and maximum residual lives of the remaining components after the failure of the system. The system is assumed to have an arbitrary structure. We obtain signature-based distributional and ordering results for the extreme residual lives.