Aiming at the problems that the eigenvalues of independent component analysis(ICA) are approximately equal and the representative variables cannot be extracted effectively after dimensionless standardization processing, a fault detection method based on relativetransformation ICA (RTICA) is proposed. The method introduces the relativetransformation based on Euclidean distance. Firstly, the RTICA approach transfers the original data space into relative space by computing the Euclidean distance. Secondly, ICA approach is used to reduce the dimensions of the data in the relative space, extract the independent PCs possess greater adaptability, build the fault detection model and implement online fault detection. The proposed method has been applied to Tennessee Eastman (TE) and the fault simulation experiment in electric spindle system. The results show that the method can effectively reduce the number of independent principal components, simplify the complexity of fault detection model, and enhance the performance of state detection.