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This paper presents a generalized surveillance model for predicting the performance of complex systems consisting of many subsystems (units). These subsystems are frequently inspected to keep the entire system operating satisfactorily. Systems of this type are encountered in many areas, including nuclear power plant, national defense system, transportation stations, medical monitoring control rooms, etc. The particular application that motivated a development of this model is an FAA project, where we were asked to develop a surveillance model to better understand both the inspection process and the repair station itself and to provide information that can be used to assist inspectors in scheduling and prioritizing their visits to the stations. A distinguishing feature of this surveillance model is that it combines two mutually dependent stochastic processes. One is a two-stage stochastic process for the occurrence of unfavorable condition in an individual subsystem and the other is a nonhomogeneous Poisson process for the frequency of surveillance.