# Six Sigma-Based Frequency Response Analysis for Power Transformer Winding Deformation
## 4 Discussion  
The results presented in Table 9 provide a comprehensive comparative analysis between the proposed FRA6\(\sigma\) approach and physical inspection findings across three different transformer cases. This discussion explores how the proposed methodology enhances fault detection, particularly in identifying incipient mechanical and insulation failures that are often missed by traditional FRA analysis and physical assessment. The analysis is structured according to different frequency ranges, linking each to the expected transformer faults and their physical interpretations as outlined in Table 9.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  
The low-frequency region predominantly reflects core deformation, movement, and magnetostriction effects. In Case 1, the FRA6\(\sigma\) approach detected minor core movement, indicated by a slight deviation in the FRA response, although physical inspection did not reveal any visible deformation. This suggests that mechanical stress is developing but has not yet led to observable displacement. Case 2, however, presented a more severe case where significant core deformation was detected by FRA6\(\sigma\), with \(C_{pk}\) values dropping below 1.0. In contrast, physical inspection only revealed minor displacement, demonstrating how FRA6\(\sigma\) can quantify structural deviations before they become critical. Case 3 showed a stable core response, confirmed by both the FRA6\(\sigma\) method and visual inspection. These findings highlight the ability of the FRA6\(\sigma\) framework to detect core-related faults at an early stage, allowing for proactive maintenance before substantial damage occurs. The statistical control limits set by Six Sigma ensure that even minor deviations from the transformer's baseline fingerprint are flagged, whereas traditional FRA relies heavily on human interpretation, which often overlooks such subtleties. The 1000-10,000 Hz range is highly sensitive to clamping pressure loss, bulk winding movement, and mechanical displacement. In Case 1, the proposed approach detected early clamping pressure relaxation, yet physical inspection found no immediate signs of loosening. This suggests that the mechanical integrity of the clamping system is weakening but has not yet reached a level where it becomes physically noticeable. In Case 2, a more pronounced bulk winding movement was identified by FRA6\(\sigma\), with the response shifting close to the \(UCL\), indicating a progressing mechanical shift. Physical inspection, however, only observed slight shifting, reinforcing the higher sensitivity of FRA6\(\sigma\) in quantifying winding movement. Interestingly, Case 3 exhibited no major issues in this frequency range, as both FRA6\(\sigma\) and inspection showed stability. This serves as a control case, reinforcing the method's reliability in distinguishing between stable and unstable transformer conditions. The results emphasize how FRA6\(\sigma\) can serve as an early-warning system for mechanical failures, allowing engineers to act before physical loosening or misalignment occurs. The 10,000-100,000 Hz range provides insights into axial and radial winding deformation, disc spacing variations, and insulation compression failures. Case 1 presented incipient radial winding deformation, with \(C_{pk}\) values nearing 1.0 but remaining above the threshold for immediate concern. No physical deformation was found during inspection, reaffirming the ability of FRA6\(\sigma\) to detect subtle changes in winding structure before they become physically measurable. Conversely, Case 2 exhibited significant disc spacing variation, with FRA6\(\sigma\) detecting deviations outside the LCL. However, during physical inspection, no clear signs of disc compression were visible, emphasizing that the FRA6\(\sigma\) approach can capture early-stage winding distortions that standard FRA alone cannot identify. Case 3, again, presented a