# Six Sigma-Based Frequency Response Analysis for Power Transformer Winding Deformation
###### Abstract  
Winding deformities in distribution transformers pose significant risks to operational reliability and system safety. Frequency response analysis (FRA) is a well-established technique for identifying mechanical faults; however, its diagnostic reliability is hindered by subjectivity in interpreting response signatures. This study proposes a novel diagnostic technique, termed FRA6\(\sigma\), which integrates Six Sigma (6\(\sigma\)) statistical tools with FRA to enable objective fault detection. The methodology employs control charts (\(\overline{X}\) chart, \(\overline{R}\)-chart) to monitor deviations from baseline signatures and utilizes process capability indices (\(C_{p}\) and \(C_{pk}\)) to quantify the severity of deviations. Three transformer cases were evaluated across five defined frequency regions (10 Hz to 2 MHz), each associated with distinct physical fault types. The FRA6\(\sigma\) approach successfully identified early-stage faults across all cases. In one instance, axial and radial winding deformation was detected with a \(C_{p}\) of 1.0 and corresponding range chart violations, preceding any visible damage. Another case revealed inter-turn insulation degradation in the 100 kHz-1 MHz band with \(C_{pk}\) values below 0.9, prompting immediate intervention. Compared to traditional FRA interpretation, the proposed method improved diagnostic sensitivity by 31.25% and enabled fault detection earlier based on retrospective physical inspection benchmarks. The integration of Six Sigma with FRA provides a structured, quantifiable, and repeatable approach to transformer fault diagnostics. FRA6\(\sigma\) enhances early detection of winding deformities and dielectric issues, offering a robust alternative to subjective analysis and supporting predictive maintenance strategies in power systems.  
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Footnote †: journal: Applied sciences  
cores [8; 9; 10], defect prediction of bushings [11; 12; 13], and transformer fault diagnosis [14; 15; 16]. The most credible and commonly used technique for transformer fault diagnosis is frequency response analysis (FRA), a comparative technique which compares frequency response signatures under different conditions [17; 18]. When the comparison is performed either by baseline (fingerprint), phase-to-phase/transformer-to-transformer comparison, and pre-and post-event, a determination should be taken for the transformer; that is to say, whether it can continue in operation, or it should be taken out of service for maintenance. In practice, FRA is performed as demonstrated in Figure 1[18].  
Nevertheless, no reliable technique has been generally acknowledged hitherto for discriminating the winding condition of transformers using FRA. To appraise the winding condition, a robust interpretation technique is imperative. Consequently, numerous studies have zeroed in on FRA [19; 20; 21; 22]. Therefore, an accurate interpretation technique that can discriminate and categorize winding faults is fundamental.  
Six sigma (6\(\sigma\)) is a novel technique proposed to monitor the existing variations compared to the previous baseline, phase, transformer, or pre-event healthy status; a fault is detected, provided that, variations have eventuated in distribution characteristics, i.e., the way that winding and core impedance, inductance, capacitance, and resistance are distributed across different frequency ranges. These characteristics help diagnose mechanical and electrical faults by analyzing how the transformer's electrical network responds at various frequencies. Inherently, this study proposes 6\(\sigma\) control chart limits using the healthy/normal baseline data. The \(\overline{X}\)-chart, \(\overline{R}\)-chart, process capability index (Cp), process capability performance index (Cpk) of the proposed FRA6\(\sigma\) will help improve the consistency, repeatability, and reliability of FRA results by eliminating process inefficiencies.