# Six Sigma-Based Frequency Response Analysis for Power Transformer Winding Deformation
### Literature Survey  
A broad spectrum of electric faults and mechanical faults occur in transformers as shown in Table 1. Various techniques have been recommended to detect these faults. The FRA approach is commonly employed because it is highly sensitive, non-invasive,  
Figure 1: FRA test on a transformer: (**a**) tested unit, (**b**) FRA analyzer clamps attached to unit’s bushing, (**c**) FRA analyzer, (**d**) four-channel sound and vibration analyzer (SVAN 958), (**e**) accelerometer attached to unit’s tank [18]. and reliable. Nonetheless, there is a lack of reliable and common code to interpret the response signatures. In recent times, researchers have introduced some enhanced and innovative approaches to drawing out more detailed information from FRA signatures to embellish the FRA properties' interpretation. The impacts of impedance measurement, phase-sensitive detection, and parallelization schemes on the FRA signatures have been studied by [PERSON] et al. [32], who quantified sensitivities by employing a low-cost multicore microcontroller. In [33], [PERSON] et al. investigated the impact of window width on response signatures and the sensitivity analysis was explored using statistical indicators. In their further work [34], [PERSON] et al. extended this research to analyze how changes in capacitance and inductance impact the windings response signatures and highlighted that these can potentially lead to misinterpretations in results. Hence, using both computer modelling and experimental data, the study highlights how these parameter variations can cause misleading shifts in response signatures and emphasizes the need for careful assessment in transformer condition monitoring. In [35], [PERSON] et al. introduce the frequency response quality index (FRQI) as an improved method for interpreting response signatures and addressing the limitations of single-value numerical indices. The proposed FRQI analyzes three distinct features across the frequency spectrum, enhancing fault detection and enabling automated transformer condition assessment. The authors of [36] explore the application of deep learning for online transformer monitoring, addressing limitations in human-expert interpretation of narrow frequency bands. The results demonstrate that neural networks can detect faults in frequency ranges that are traditionally filtered out, offering advancements in automated fault diagnosis and signal processing for real-time monitoring. In recent years, various artificial intelligence (AI) approaches have been developed to diagnose transformer faults. Several relevant studies have successively employed AI algorithms in the context of FRA. For example, the authors of [37] proposed a transformer condition assessment algorithm using random forest (RF) classifiers for automatic interpretation of FRA results, reducing reliance on skilled personnel. Using data from 139 response signatures across 80+ transformers, the method classifies six common transformer states with up to 93% accuracy, enhancing fault detection and diagnostic automation. The authors of [38] proposed a support vector machine (SVM)-based method using vibration