In order to extract weak fault features from vibration signals efficiently, an equivalent power spectrum analysis approach is proposed which applies the Redundant Wavelet Transform (RWT) decomposition by using an orthogonal wavelet as a basis function. The new approach makes full use of multi-resolution information obtained by the RWT decomposition. Firstly, noise component in high-frequency-band is omitted, and the other decomposition components are treated as useful components to calculate their power spectrum respectively. Then a normalized operation is made for these power spectrums. Because the analytic frequency of the RWT decomposition components is the same, the equivalent power spectrum is gained by adding the normalized power spectrums. As a result, some weak frequency components that submerged in the signal before are revealed on the equivalent power spectrum. The proposed approach has been used to diagnose friction fault between gas-seal and rotor of a gas turbine in an oil refinery and detected the fault features effectively.