This chapter presents a fault detection method through uni- and multivariate hypothesis testing for wind turbine (WT) faults. A data-driven approach is used based on supervisory control and data acquisition (SCADA) data. First, using a healthy WT data set, a model is constructed through multiway principal component analysis (MPCA). Afterward, given a WT to be diagnosed, its data are projected into the MPCA model space. Since the turbu- lent wind is a random process, the dynamic response of the WT can be considered as a stochastic process, and thus, the acquired SCADA measurements are treated as a random process. The objective is to determine whether the distribution of the multivariate random samples that are obtained from the WT to be diagnosed (healthy or not) is related to the distribution of the baseline. To this end, a test for the equality of population means is performed in both the univariate and the multivariate cases. Ultimately, the test results establish whether the WT is healthy or faulty. The performance of the proposed method is validated using an advanced benchmark that comprehends a 5-MW WT subject to various actuators and sensor faults of different types.