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Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 142169, 8 pages
Research Article

Reliability Analysis of the Proportional Mean Residual Life Order

1Department of Statistics and Operations Research, College of Science, King Saud University, Riyadh 11451, Saudi Arabia
2Department of Mathematics, Faculty of Science, Suez University, Suez 41522, Egypt
3School of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad 91779, Iran

Received 4 April 2014; Accepted 2 August 2014; Published 28 August 2014

Academic Editor: Shaomin Wu

Copyright © 2014 M. Kayid et al. 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 mean residual life plays an important role in reliability and life testing. In this paper, we introduce and study a new stochastic order called proportional mean residual life order. Several characterizations and preservation properties of the new order under some reliability operations are discussed. As a consequence, a new class of life distributions is introduced on the basis of the anti-star-shaped property of the mean residual life function. We study some reliability properties and some characterizations of this class and provide some examples of interest in reliability.