The main aim of this thesis is to investigate available techniques and develop a methodology for the fault detection and diagnostics for two engineering systems, namely railway point systems (RPS) and three-phase separators (TPS). The fault detection of the RPS was performed on the measured current from the motor of point operating equipment (POE). The method of One Class Support Vector Machines has been chosen as the fault detection model. Elastic similarity measures, such as edit distance with real penalties and dynamic time warping, were chosen to compare the data of POE operations. A combination of Euclidean distance and elastic similarity measures has been proposed in order to take into account the absolute values and shape properties of the two compared time series. The proposed methodology has been tested on the in-field RPS data. The results indicated that the fault detection model was able to detect abnormal values and/or shape of the time series of measured current. However, not in all cases these changes could be related to a recorded failure of RPS in the database. The fault detection of TPS was performed given the sensor readings of flow and level transmitters of TPS. The method of Bayesian Belief Networks (BBN) has been proposed to overcome the late detection of faults with the threshold based alarm technique. An approach to observe sensor readings of TPS in several adjacent time intervals and to update the prior probabilities in the BBN after inserting the sensor readings as evidence was proposed. The proposed methodology has been tested on the data obtained from a TPS simulation model. The results indicated that the fault detection and diagnostics model was able to detect inconsistencies in sensor readings and link them to corresponding failure modes when single or multiple failures were present in the TPS.