A novel method for selecting the number of principal components (PCs) is proposed in this paper. This method adopts a new fault detection performance index and a new fault identification performance index to complete the selection. The new fault detection performance index is developed to represent the fault detection ability using the concept of detectable fault coverage, and the new fault identification performance index is proposed for the purpose of judging whether the fault identification result is correct or not. Furthermore, detailed mathematical analysis is given to explain the influence of the number of PCs on the fault identification performance index. The Monte Carlo numerical model and the quadruple-tank process model are used to demonstrate the advantages of our proposed indices and to illustrate the implementation of our proposed method.