This work presents a technique for fault detection and identification in centrifugal pumps (CPs) using a novel fault-specific Mann–Whitney test (FSU Test) and K-nearest neighbor (KNN) classification algorithm. Traditional fault indicators, such as the mean, peak, root mean square, and impulse factor, lack sensitivity in detecting incipient faults. Furthermore, for defect identification, supervised models rely on pre-existing knowledge about pump defects for training purposes. To address these concerns, a new centrifugal pump fault indicator (CPFI) that does not rely on previous knowledge is developed based on a novel fault-specific Mann–Whitney test. The new fault indicator is obtained by decomposing the vibration signature (VS) of the centrifugal pump hierarchically into its respective time-frequency representation using the wavelet packet transform (WPT) in the first step. The node containing the fault-specific frequency band is selected, and the Mann–Whitney test statistic is calculated from it. The combination of hierarchical decomposition of the vibration signal for fault-specific frequency band selection and the Mann–Whitney test form the new fault-specific Mann–Whitney test. The test output statistic yields the centrifugal pump fault indicator, which shows sensitivity toward the health condition of the centrifugal pump. This indicator changes according to the working conditions of the centrifugal pump. To further enhance fault detection, a new effect ratio (ER) is introduced. The KNN algorithm is employed to classify the fault type, resulting in promising improvements in fault classification accuracy, particularly under variable operating conditions.