Coherent systems subject to multiple shocks with applications to preventative maintenance

•It is assumed that the components of a coherent system are categorized to L different batches.•The reliability of the system is explored under the assumption that the components fail according to multiple external shocks.•The optimal time of preventive maintenance of the system is investigated by imposing some cost functions and some stationary availability criteria of the system.•To illustrate the results, some examples are given. This article is a study on the reliability and preventive maintenance of the coherent systems whose components are subject to failure according to multiple external shocks. We consider an n-component coherent system in which the components are categorized to L different batches, 2 ≤ L ≤ n. It will assume that the components of the batches are subject to failure according to independent external shocks arriving based on independent counting processes. Under this model of components failure, we obtain the survival signature based reliability function of the system lifetime. Then, we investigate the optimal time of preventive maintenance of the system by imposing some cost functions and some criteria on the stationary availability of the system. In order to illustrate the results, some examples have presented in which the failure of components in different batches occur due to the external shocks which arrive according to independent nonhomogeneous Poisson processes with different mean value functions.