A new multiway discrete hidden Markov model (MDHMM)-based approach is proposed in this article for fault detection and classification in complex batch or semibatch process with inherent dynamics and system uncertainty. The probabilistic inference along the state transitions in MDHMM can effectively extract the dynamic and stochastic patterns in the process operation. Furthermore, the used multiway analysis is able to transform the three-dimensional (3-D) data matrices into 2-D measurement-state data sets for hidden Markov model estimation and state path optimization. The proposed MDHMM approach is applied to fed-batch penicillin fermentation process and compared to the conventional multiway principal component analysis (MPCA) and multiway dynamic principal component analysis (MDPCA) methods in three faulty scenarios. The monitoring results demonstrate that the MDHMM approach is superior to both the MPCA and MDPCA methods in terms of fault detection and false alarm rates. In addition, the supervised MDHMM approach is able to classify different types of process faults with high fidelity. (c) 2011 American Institute of Chemical Engineers AIChE J, 2012