A novel statistical model based on a locally linear embedding projection to latent structure (LLEPLS) is proposed, which not only has a concise expression and similar analytical solutions to the projection to latent structure (PLS) model but also has the ability to maintain the local geometric structure of the locally linear embedding (LLE) model. Furthermore, to eliminate the adverse effects of oblique decomposition, a locally linear embedding orthogonal projection to latent structure (LLEOPLS) model is also proposed. The input and output data spaces are projected to three subspaces, namely, a joint input output subspace that captures the nonlinear relationship between the input and output, an output-residual subspace that monitors the unpredictable output faults, and an orthogonal input-residual subspace that detects the quality-irrelevant faults. Then, the corresponding monitoring strategies are established based on the LLEPLS and LLEOPLS models. The Tennessee Eastman process (TEP) benchmark is used to illustrate the nonlinear mapping ability and effectiveness of the monitoring on quality-relevant and process-relevant faults of the proposed methods.