Fault diagnosis is important to the design and maintenance of large multiprocessor systems. PMC model is the most famous diagnosis model in the system level diagnosis of multiprocessor systems. Under the PMC model, only node faults are allowed. But in real circumstances, link faults may occur. So based on the PMC model, we propose in this paper a diagnosis model called the generalized PMC(GPMC) model to adapt to the real circumstances. The foundation of GPMC model has been established. And to measure the fault diagnosis capability of multiprocessor systems under the GPMC model, the fault diagnosis capability measuring parameters: $h$-edge restricted diagnosability and $h$-vertex restricted edge diagnosability have been introduced. As an application, the $h$-edge restricted diagnosability and $h$-vertex restricted edge diagnosability of hypercubes are explored.