Operators' mental models play a central role in safety-critical domains like the chemical process industries. Accurate mental models, i.e., a correct understanding of the process and its causal linkages, are prerequisites for safe operation. Mental models are often defined and explained in abstract terms that make their interpretation subjective and prone to bias. In this work, we propose a Hidden Markov Model (HMM) based formalism to characterize control room operators' mental models while handling abnormal situations. We show that a suitable HMM representing the operator's mental model – including the states, state transition probabilities, and emission probability distributions – can be identified experimentally using data of the operator's control actions, eye gaze, and process variable values. This HMM can be used for the quantitative assessment of operators' mental models as illustrated using various case studies. We discuss the potential applications of the model in identifying various cognitive errors and human reliability assessment. In Part 2 of this paper, we use the proposed approach to assess operators' learning during training. © 2022 Elsevier Ltd