This paper proposes reliability and maintenance mo-dels for systems suffering random shocks arriving according to a non-homogeneous Poisson process.The system degradation process include two stages:from the installation of a new sys-tem to an initial point of a defect(normal stage),and then from that point to failure(defective stage),following the delay time concept.By employing the virtual age method,the impact of ex-ternal shocks on the system degradation process is character-ized by random virtual age increment in the two stages,result-ing in the corresponding two-stage virtual age process.When operating in the defective state,the system becomes more sus-ceptible to fatigue and suffers from a greater aging rate.Re-placement is carried out either on failure or on the detection of a defective state at periodic or opportunistic inspections.This pa-per evaluates system reliability performance and investigates the optimal opportunistic maintenance policy.A case study on a cooling system is given to verify the obtained results.