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• Development of a multi-attribute Bayesian control scheme for fault prediction. • Multivariate hidden Markov model describes the deterioration process. • Computational algorithm to optimize the multi-attribute Bayesian policy. • Development of a real case study and verification using multivariate data. Although Bayesian approaches have been utilized in engineering systems for health prognostics, very little work has been done using Bayesian methods for fault prediction of systems under multiple attributes. To address this issue, in this paper a novel multi-attribute Bayesian control chart is presented for predicting failures of hidden-state systems by jointly considering two performance measures of system operation. The system actual status is represented by a three-state multivariate hidden stochastic process with a normal state, an abnormal state, and a failure state. The working states are unobservable and failure state is observable. Based on the built hidden-state model, a fault prediction scheme integrating both system availability and cost objectives is constructed via a multi-attribute Bayesian control chart to monitor and predict impending risks of the operational systems. The Bayesian control chart alarms when the probability of impending risks reaches a certain control limit, which is optimized and determined by a computational algorithm developed in a semi-Markov decision process framework. The proposed fault prediction scheme provides an appearing feature to jointly consider multiple attributes for hidden-state systems. A real case study of mechanical generators is presented and a comparison with other Bayesian and non-Bayesian methods is also given, which demonstrates the effectiveness and superiority of the proposed approach. [ABSTRACT FROM AUTHOR]