On some properties of the bathtub failure rate family of life distributions

In this paper, some of the basic issues concerning the bathtub failure rate (BFR) life distributions, thus far unresolved, have been investigated. Specifically, exponential bounds have been obtained for the survival function as well as the moments of a BFR distribution. Closure properties of the BFR family under the formation of coherent systems, convolutions and mixtures have been dealt with. Closure of the BFR class under the formation of limits in distribution and the equivalence of weak convergence and convergence of moment sequences have been established.