Suppose that a device is subjected to shocks and that P sub(k), k = 0, 1, 2,..., denotes the probability of surviving k shocks. Then H(t) = Sigma super( infinity )@)dk sub(=) sub(0) P(N(t)=k)P sub(k) is the probability that the device will survive beyond t, where N = (N(t):t greater than or equal to 0) 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 H(t) is IFRA and DMRL under conditions which differ from those used by A-Hameed and Proschan (1975).