One of the most complex and costly systems in the industry is the Gas turbine (GT). Because of the complexity of these assets, various indicators have been used to monitor the health condition of different parts of the gas turbine. Turbine exit temperature (TET) spread is one of the significant indicators that help monitor and detect faults such as overall engine deterioration and burner fault. The goal of this article is to use data-driven approaches to monitor TET data to detect faults early, as fault detection can have a significant impact on gas turbine reliability and availability. In this study, the TET data of v94.2 GT is measured by six temperature transmitters to show a detailed profile. According to the statistical tests, TET data are high dimensional and time-dependent in the real world industry. Hence, three distinctive methods in the field of the gas turbine are proposed in this study for early fault detection. Conventional principal component analysis (PCA), moving window PCA (MWPCA), and incremental PCA (IPCA) were implemented on TET data. According to the results, the conventional PCA model is a non-adaptive method, and the false alarm rate is high due to the incompatibility of this approach and the process. The MWPCA based on V-step-ahead and IPCA approaches overcame the non-stationary problem and reduced the false alarm rate. In fact, these approaches can distinguish between the normal time-varying and slow ramp fault processes. The results showed that IPCA could detect fault situations faster than MWPCA based on V-step-ahead in this study.