Optimal preventive maintenance for coherent systems whose failure occurs due to aging or external shocks

•A coherent system consisting of several types of independent components is considered.•The system is subject to internal failures and environmental shocks.•Optimal age-based and block preventive maintenance models are proposed.•Some formulas for the average long-run cost rate are provided.•The derivations rely on the concept of survival signature. In this paper, we study some preventive maintenance policies for coherent systems with n,n⩾1, components. We consider a coherent system consisting of K,K⩾1, different types of independent components. The system may fail due to the aging of its components, or it may fail due to fatal shocks arriving from external sources. Under this mechanism of system failure, we propose optimal age-based and block preventive maintenance models by considering the costs of preventive maintenance, corrective maintenance, and minimal repairs. We provide some formulas for the average long-run cost rate of the proposed strategies. The existence of optimal values under which the imposed cost functions are minimized has been discussed. In addition, Monte Carlo simulations are carried out to evaluate the cost functions of the proposed maintenance models. Our derivations rely on the concept of survival signature. Real examples of coherent systems are also presented to examine and illustrate the theoretical results.