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The class 
of life distributions for which 
, where 
, and 
, is studied. We prove that this class is larger than the HNBUE (HNWUE) class (consisting of those life distributions for which 
for x ≧ 0) and present results concerning closure properties under some usual reliability operations. We also study some shock models and a certain cumulative damage model. The class 
of discrete life distributions for which 
for 0 ≦ p ≦ 1, where 
, is also studied.
Suppose that a device is subjected to shocks and that 
denotes the probability of surviving k shocks. Then 
is the probability that the device will survive beyond t, where 
is the counting process which governs the arrival of shocks. A-Hameed and Proschan (1975) considered the survival function H(t) under what they called the pure birth shock model. In this paper we shall prove that 
is IFRA and DMRL under conditions which differ from those used by A-Hameed and Proschan (1975).
