Fault detection and process monitoring using principal component analysis (PCA) have been studied intensively and applied to industrial processes. This paper addresses some fundamental issues in detecting and identifying faults. We give conditions for detectability, reconstructability, and identifiability of faults described by fault direction vectors. Such vectors can represent process as well as sensor faults using a unified geometric approach. Measurement reconstruction is used for fault identification, and consists of sliding the sample vector towards the PCA model along the fault direction. An unreconstructed variance is defined and used to determine the number of principal components for best fault identification and reconstruction. The proposed approach is demonstrated with data from a simulated process plant. Future directions on how to incorporate dynamics and multidimensional faults are discussed.