Summary: In this paper, we prove that the lifetime distribution of a device subject to random shakes with different interarrival mean times belongs to the HNBUE class without and assumption about the class of survival probabilities to the consecutive shocks. Following the model considered by Esary et al. (1973), we obtain conditions under which the survival function belongs to the HNBUE class which differ from those given by Klefsjö (1981). From a practical point of new, these results simplify the study of failure times. We apply our results via a simulation study and obtain the life time distribution of a device when shocks arrive following a linear birth process.