Abstract
In a δ-shock model, a system subject to randomly occurring shocks, the system fails when the time between two successive shocks lies below a threshold δ. In this note, we study the generalization of this model where such δ-shocks are accumulated and the system fails on the occurrence of k^th such a δ-shock. The probability distribution of the system failure time and the statistical characteristics are explicitly obtained. Normal approximation to the failure time distribution is proposed.