This paper studies the behavior of Industrial Gas Turbines (IGTs) based on time-series measurements with low sampling rates. The aim is to find the most suitable set of statistical/time-domain features derived from the measurements, which can represent the characteristic behavior of the IGTs, or alternatively, which can discriminate between different engines or different states of an engine. For this end, a scheme of optimal feature selection process is proposed in the paper. For cross-fleet analysis, signals from a group of inter-duct thermocouples on IGT engines are studied. A feature matrix is formulated at each sliding time step, by calculating the statistical features of the sensor group, after the time-domain features of the individual sensor measurements are calculated. Feature matrix values from different engines are then clustered, and a modified Davies–Bouldin index is introduced to measure the quality of the clusters. Finally, grid search is run to find the optimal set of the features, which form the clusters with the most similarity, or otherwise, the most discrepancy across the IGT engines. The window size effect is also investigated. To demonstrate that the optimal feature selection process is also useful for fault diagnosis of IGTs, the proposed scheme is then applied on a group of different measurements on an IGT, i.e. from burner tip thermocouples, in a fault diagnostic scenario, which is subsequently validated using a k-nearest neighbor classification algorithm. The case studies have demonstrated that, ultimately, the developed techniques can be broadly applied to other groups of measurements for both cross-fleet analysis and fault diagnosis of IGTs.