This work proposes a diagnosis method based on mutual dimensionless indices (MDIs) and receiver operating characteristic (ROC) analysis for the detection of rolling bearing faults, which is of great importance to maintain the functionality of rotating machines. The proposed method consists of five steps. Firstly, the mutual dimensionless technique is used to extract five MDIs from the raw vibration signal. Secondly, the principal components analysis (PCA) is employed to reduce the five MDIs to a one-dimensional feature. Thirdly, we obtain the areas under the ROC curve (AUC) and associated variances using two sliding windows along the one-dimensional feature sequence. Fourthly, the potential fault occurring time is estimated via comparing the AUC and the associated variances with the corresponding detection thresholds. Finally, a parameter K is introduced to delete the false alarms, and then the predicting fault occurring time is chosen from the local extrema of the potential fault occurring times. Experimental results demonstrate that our proposed approach is capable to detect fault occurring time with high accuracy and a low false-positive rate.