A new concurrent projection to latent structures for the monitoring of output-relevant faults that affect the quality and input-relevant process faults is proposed. The input and output data spaces are concurrently projected to five subspaces, a joint input-output subspace that captures covariations between input and output, an output-principal subspace, an output-residual subspace, an input-principal subspace, and an input-residual subspace. Fault detection indices are developed based on the concurrent projection to latent structures (CPLS) partition of subspaces for various fault detection alarms. The proposed CPLS monitoring method offers complete monitoring of faults that happen in the predictable output subspace and the unpredictable output-residual subspace, as well as faults that affect the input spaces and could be incipient for the output. Numerical simulation examples and the Tennessee Eastman challenge problem are used to illustrate the effectiveness of the proposed methods. (C) 2012 American Institute of Chemical Engineers AIChE J, 59: 496-504, 2013