## 4 Statistical Indicators Results  
In this section, several statistical indicators are employed to help interpret the measured FRA signatures in the previous two case studies. To enhance the calculation accuracy, the FRA signature is divided into three frequency sub-bands; low-frequency (LF) range, mid-frequency (MF) range, and the high-frequency (HF) range, as shown in Figure 7. Each frequency range is dominated by a specific electric circuit component, e.g., LF range is affected by the winding resistance while the MF range is influenced by the winding inductance and the winding capacitance dominates the signature in the HF range. Figure 6: U–V terminals FRA measured responses for the 1 HP induction motor at (**a**) turn–to–turn SC (**b**) coil–to–coil SC (**c**) turn–to–ground SC (**d**) coil-to-ground SC (**e**) neutral–to–ground SC (**f**) phase–to–phase SC. According to Tables 4 and 5, the CC values indicate that there is an overlap between the normal case and SC turns, coil-to-coil, turn-to-ground, coil-to-ground, and neutral-to-ground at the LF and MF ranges. Within this range, all SC faults revealed a CC value greater than 0.999. However, the CC detects a huge variation between the responses at the HF range, especially for the turn-to-turn, phase-to-phase, coil-to-coil, and coil-to-ground SC. CC indicates substantial variation for phase-to-phase SC at the LF and HF regions. The CC value at the LF range was within 0.967 to 0.985 for the two case studies. The lowest value for the CC (0.731) was obtained in the HF range for phase-to-phase SC fault. On the other hand, the minimum value for the ASLE (0.001) was observed in the MF range of the neutral-to-ground SC fault, while the highest value (10.616) was obtained in the same frequency range but for phase-to-phase SC fault. According to these findings, ASLE was a highly sensitive statistical measure of the variance between two FRA signatures. ASLE values indicate variation within the entire frequency range for the coil-to-coil and phase-to-phase SC faults. The range of ASLE for the two case studies was between 0.803 and 10.616 for phase-to-phase SC fault. For other SC faults, the ASLE clearly indicates a variation in the MF range for the turn-to-turn SC and coil-to-ground fault and at the HF range for the neutral-to-ground fault. Similarly, the minimum value of the SD for the turn-to-ground fault was 0.003 at the LF range, while the highest value (10.637) was obtained at the MF range for the phase-to-phase SC fault. The MSE provides significant variations for phase-to-phase and coil-to-coil faults in the entire frequency range. The RMSE also reveals a substantial variation for the phase-to-phase SC fault. The highest value for the RMSE was 10.637 and was observed for phase-to-phase SC fault at MF phase-to-phase (Table 4). The DABS trend was almost similar to the trend of the RMSE. Results of the covariance show a small percentage in variation and all in the MF region. MM results show almost identical values for all fault types and are in the range of 1.001 to 1.423. The MM shows an obvious difference between the normal and SC faults at the HF region. Figure 8 shows the proposed statistical indicators threshold limits for each fault type based on the obtained values for the two case studies. Figure 7: The common used FRA ranges.