FauM diagnosis is crucial to maintain safe and efficient operations of industrial processes. In this paper, a minimax probability machine (MPM) approach based on the framework of probabilistic representations is put forward for diagnosing process faults, without imposing any assumptions on data distributions. Moreover, a technique of pairwise discriminate analysis is incorporated to handle the classification of multiple faulty datasets. In addition to the enhanced handling of imbalanced distribution of datasets, the proposed MPM-based approach can also bring the benefits for fault diagnosis, owning to the utilization of an objective function in the form of summation of the pairwise separation probabilities between each pair of faulty datasets. The effectiveness of the proposed approach is demonstrated on the benchmark of Tennessee Eastman process.