Test of covariance changes without a large sample and its application to fault detection and classification

► We propose test methods to detect the change of covariance matrix without a large sample requirement. ► The type-I error of our test methods can be correctly controlled. ► A novel fault classification rule for covariance matrix is also developed. ► The proposed test methods outperform conventional methods, especially in the case of small sample size. ► Simulation studies and a real dataset are used to demonstrate the usefulness of our method.