In reliability theory, various [ ]-shock models are used to study the shock-exposed systems that are sensitive to the length of intershock times. In this paper, a new generalized [ ]-shock model is introduced and studied, under which a system fails when the intershock time is smaller than a threshold [ ] or larger than another threshold [ ] for the first time, where [ ]. Reliability characteristics of the corresponding lifetimes are investigated under the new model when the intershock times follow an arbitrary distribution. As an illustrative example to demonstrate the practical aspects of the new model in the real world, we discuss the reliability behavior of an adult heart. Furthermore, we present an application of the discrete-time version of the new model in agricultural engineering. Numerical examples illustrate our theoretical findings.