In this chapter, the empirical approach to the problem of anomaly detection is presented, which is free from the pre-defined model and user-and problem-specific parameters and is data driven. The well-known Chebyshev inequality has been simplified by using the standardized eccentricity. An autonomous anomaly detection method is proposed, which is composed of two stages. In the first stage, all the potential global anomalies are selected out based on the data density and/or on the typicality, and in the second stage, the local anomalies are identified based on the data clouds formed from the potential global anomalies. In addition, a fully autonomous approach for the problem of fault detection has been outlined, which can also be extended to a fully autonomous fault detection and isolation approach. © 2019, Springer Nature Switzerland AG.