Control and Cybernetics
42 (2013) No. 3
On new aging lasses based on the reversed mean residual
life order∗
Kambiz Ahmadi
and Majid Rezaei
Department of Statistis, University of Birjand, Iran
K.Ahmadibirjand.a.ir, Mjrezaeibirjand.a.ir
Abstrat: In this paper, we introdue new onepts of aging
for lifetime distributions. The main idea is the omparison between
reversed mean residual life of the random variables X and (X − t |
X > t), for all t > 0. Firstly, with some examples, we highlight
the role of the proposed aging lasses in reliability and life testing.
Then, we try to nd the onnetion between the new aging lasses
and other aging lasses well-known from the literature. Reliability
properties of the new lasses are studied. Formally, we derive the
preservation property under monotoni transformations. Some other
haraterization and impliations are studied.
Keywords: reversed mean residual life, stohasti order, aging
lass, preservation, haraterizations, IRMR.
1. Introdution and denitions
Stohasti orderings have long been a topi of interest in the reliability theory, eonomis, atuarial sienes, survival analysis and many other branhes of
statistis. Beause the aurate distribution of the life of an element or a system
is often unavailable pratially, nonparametri aging properties are quite useful
for modeling aging or wear-out proesses, and for onstruting maintenane poliies. Suh aging lasses are derived via several notions of omparison between
random variables. In the ontext of lifetime distributions, some stohasti orderings of probability distributions have been used to give haraterizations and
new denitions of aging lasses. By aging we mean the phenomenon whereby
an older system has a shorter remaining lifetime, in some statistial sense, than
a younger one, Bryson and Siddiqui (1969). The main goal of this work is to
provide another onept of aging for lifetime distributions along with some reliability properties of this onept. The new aging onept is based on stohasti
omparison of new lifetime unit and the used one, aording to the reversed
mean residual life order.
∗ Submitted:
Marh 2013; Aepted: June 2013