On order relations between reliability measures

It is well known that the three reliability measures, namely, the survival function, the failure rate function, and the mean residual life function are equivalent in the sense that knowing any one of them, the other two can be determined. This paper deals with the question of whether an ordering of two life distributions with respect to a reliability measure implies the same ordering with respect to another reliability measure. Implications of various orderings are discussed from the point of view of some properties of the life distributions involved.