This paper provides two new proposed data-based fault diagnosis approaches using the principal component analysis (PCA). Since faults are really complex and may be in multidimensional directions, the first proposal is a generalized RBC method. The theoretical diagnosability analysis using this one guarantees correct fault diagnosis in the case of complex faults that have large magnitudes. Nevertheless, the common assumption resulting from the use of the contribution methods in general is that variables with largest contributions to the fault detection indices are more likely to be the root causes of the fault occurrence. To handle the more complex faults and remedy the defective of the RBC method, the second proposal presents an alternative approach called RBC ratio (RBCR). A theoretical diagnosability analysis testifies to its strong performance in identifying the detectable faults. Indeed, the isolation of fault is guaranteed once its magnitude has satisfied a sufficient condition for isolability. These proposed approaches have been successfully applied to a numerical example as well as the CSTR process. (C) 2015 Elsevier Ltd. All rights reserved.