This paper defines a generalized probabilistic linear latent variable model (GPLLVM) that under specific restrictions reduces to various probabilistic linear models used for process monitoring. For the defined model, we rigorously derive the monitoring statistics and their respective null distributions. Monitoring statistics of the defined model also reduce to the monitoring statistics of various probabilistic models when restricted with the corresponding conditions. The paper presents insightful equivalence between the classical multivariate techniques for process monitoring and their probabilistic counterparts, which is obtained by restricting the generalized model. We also provide an estimation approach based on the expectation maximization algorithm (EM) for GPLLVM. The results presented in the paper are verified using numerical simulation examples. (C) 2018 Elsevier Ltd. All rights reserved.