Many process performance evaluation techniques are based on multivariate statistical methods. Various statistical methods that provide the foundations for model development, process monitoring and diagnosis are presented in this chapter. Section 3.1 introduces principal components analysis and partial least squares. Canonical variates analysis and independent components analysis are discussed in Sections 3.2 and 3.3. Contribution plots that indicate process variables that have made large contributions to signiﬁcant changes in monitoring statistics are presented in Section 3.4. Statistical methods used for diagnosis of source causes of process abnormalities detected are introduced in Section 3.5. Nonlinear methods for monitoring and diagnosis are introduced in Section 3.6.