Compound　faults　often　occur　simultaneously　or　successively　due　to　the　complexity　of　intelligent　mechatronic　systems.　The　generation　of　such　group　faults　will　bring　more　difficulties　to　fault　diagnosis.　To　separate　the　compound　fault　under　the　complex　condition　and　improve　the　accuracy　of　the　separated　signal,　a　step-by-step　compound　faults　diagnosis　method　for　equipment　based　on　majorization-minimization　(MM)　and　constraint　sparse　component　analysis　(SCA)　is　proposed　in　this　article.　The　method　can　perform　under　the　condition　that　the　measurements　are　not　enough　and　signal　sparsity　is　insufficient.　The　proposed　SCA　framework　is　the　main　technique　to　achieve　compound　faults　separation　and　it　is　divided　into　three　steps　in　this　case.　In　the　first　step,　MM　is　used　to　achieve　sparse　representation　of　vibration　signal　to　satisfy　the　prerequisites　for　SCA　and　obtained　content　clustering　for　matrix　estimation.　In　the　second　step,　expanded　potential　function　is　utilized　to　estimate　matrix,　which　can　take　advantage　of　sparse　information　from　mixtures.　In　the　final　step,　constraint　based　on　the　adaptive　Laplace　dictionary　is　introduced　to　obtain　the　precise　source　signal.　Results　of　bearing　vibration　analysis　by　simulation,　experiment,　and　comparison　are　presented　to　illustrate　the　proposed　technique.