In general, gearbox is prone to occur compound fault due to its harsh working environment and its fault vibration signal contains multi-components which correspond to each gearbox parts. As the multi-components are often coupled with each other and accompanied by strong noise which brings great difficulties to diagnose fault, however, the existing diagnosis methods are mainly applied on single fault rather than the entire gearbox health maintenance, therefore, this paper presents a gearbox compound fault diagnosis method and develops a diagnosis system which has potential value for gearbox health maintenance. In specific, on account of the morphological difference between multi-components, this paper uses resonance sparse signal decomposition (RSSD) to decompose the fault vibration signal into high and low resonance components respectively for achieving gearbox compound fault separation. Furthermore, as for low resonance component containing rolling bearing fault information, a weak fault feature extraction algorithm based on singular value decomposition (SVD) and cepstrum pre-whitening stochastic resonance is proposed, besides, aiming at the high resonance component containing gear fault information, an early gear fault warning algorithm based on local mean decomposition and two-dimensional approximate entropy of chaotic oscillator is also given. Finally, a gearbox fault diagnosis system, which has the ability such as the gearbox vibration signal acquisition, fault indicator warning, health status evaluation, fault signal storage is developed. Simulation validation and comparison prove the effectiveness of proposed method in this paper.