Abstarct: Operation performance of chemical, petrochemical and any industrial processes can be enhanced considerably by an integrated advisory system that is capable of performing simultaneous tasks of (1) instrument fault detection and identification and (2) process fault detection and diagnosis. Lack of such advisory system, at present, is due to the fact that one of the assumptions of normal process operation and functional sensors is always required in existing methods that perform tasks 1 and 2. This dissertation presents a data-driven method that is capable of performing task 1. In this thesis, first a geometrical approach to sensor fault detection is proposed. The sensor fault is isolated baxsed on the direction of residuals found from a residual generator. This residual generator can be constructed from an input-output model in model baxsed methods or from a Principal Component Analysis (PCA) baxsed model in data driven methods. Using this residual generator and the assumption of white Gaussian noise, the effect of noise on the isolability is studied, and the minimum magnitude of isolable fault in each sensor is found baxsed on the distribution of noise in the measurement system. Finally, the proposed linear method, is applied to sensor fault diagnosis in a smart structure. At the end, conclusions and some directions for future work are presented.