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• Development of a bi-level Bayesian control scheme for fault detection. • Multivariate hidden Markov model describes the deterioration process. • SMDP approach to formulate the control problem and to optimize the Bayesian policy. • Considerably better fault detection compared with published results. • Development of case studies and demonstration of the improved performance using multivariate data. Due to limitations of sensor techniques and system structures, the internal states of most complex devices are unobservable. Only partial observations can be monitored at discrete time epochs, which poses great challenges for fault detection and prediction. To facilitate the development of advanced approaches, this paper proposes a bi-level Bayesian control scheme for detecting faults of complex devices under partial observations. The deterioration of an operational system is modeled as a hidden three-state multivariate Markov process, in which the parameter estimates are obtained by an expectation maximization (EM) algorithm. Based on the multivariate Markov process, a bi-level Bayesian control scheme is presented to monitor the Bayesian posterior probability of the system in a warning state and uses two levels of sampling frequency to dynamically detect impending failures. The decision variables of the bi-level fault detection scheme are optimized and solved in a semi-Markov decision process (SMDP) framework. The particularity of this work is that two phases of system deterioration are considered into detection scheme design to avoid unnecessary false alarms. Using partially observed multivariate data from discrete monitoring, the proposed approach is validated to be capable of detecting the early fault occurrences. By comparing with other advanced methods, the superiority of the proposed model is demonstrated. [ABSTRACT FROM AUTHOR]