Introduction.- Basic Statistical Fault Detection Problems.- Principal Component Analysis.- Canonical Variate Analysis.- Partial Least Squares Regression.- Fisher Discriminant Analysis.- Canonical Variate Analysis.- Fault Classification based on Local Linear Embedding.- Fault Classification based on Fisher Discriminant Analysis.- Quality-Related Global-Local Partial Least Square Projection Monitoring.- Locality-Preserving Partial Least-Squares Statistical Quality Monitoring.- Locally Linear Embedding Orthogonal Projection to Latent Structure (LLEPLS).- Bayesian Causal Network for Discrete Systems.- Probability Causal Network for Continuous Systems.- Dual Robustness Projection to Latent Structure Method based on the L_1 Norm.