Fault detection and location are critically significant applications of a supervisory control system in a smart grid. The methods, based on random matrix theory (RMT), have been practiced using measurements to detect short circuit faults occurring on transmission lines. However, the diagnostic accuracy is influenced by the noise signal in the measurements. The relationship between mean eigenvalue of a random matrix and noise is detected in this paper, and the defects of the Mean Spectral Radius (MSR), as an indicator to detect faults, are theoretically determined, along with a novel indicator of the shifting degree of maximum eigenvalue and its threshold. By comparing the indicator and the threshold, the occurrence of a fault can be assessed. Finally, an augmented matrix is constructed to locate the fault area. The proposed method can effectively achieve fault detection via the RMT without any influence of noise, and also does not depend on system models. The experiment results are based on the IEEE 39-bus system. Also, actual provincial grid data is applied to validate the effectiveness of the proposed method.