The authors consider a cumulative damage shock model. Shocks occur according to a renewal process with intershock times .. At the time of the n-th epoch, , the magnitude of the damage is . It is assumed that the pairs , , are independent and identically distributed but and may be dependent. Failure of the underlying item occurs at where z is a fixed breaking threshold and N(t), is the counting process associated with the renewal process
The authors obtain the Laplace transform, the distribution function and the moments of . They also find conditions which imply that is NBU, NBUE and HNBUE. The limiting distributions of (normalized) as and a strong law of large numbers for are also given. The case in which and are dependent but not and , , is also studied and analogous results are obtained.