The random variable = –, which is called the residual life random variable, has gathered the
attention of most researchers in reliability. The properties of mean residual life in continuous
case have been studied by several authors. But in discrete case, only in recent years, some studies
have been done. In this paper, we present the main results concerning the statistical properties of
the discrete mean residual life ordering. such as, convolution, mixtures and convergence in
distributions. Furthermore, two results concerning discrete renewal process in connection with
the orders in the paper are obtained.