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Highlights • Novel approach to the cost-optimal early fault detection of CNC equipment. • VAR modeling of multivariate positioning data and residual testing for control purposes. • Estimation of the remaining useful life of CNC equipment using Bayesian approach. • Presented method outperforms previously published method based on HMM. Abstract The goal of a computer numerically controlled (CNC) equipment is to guarantee high specified performance and to maintain it effectively over its life cycle time. Thus, the assessment of health condition is crucial for industrial systems. However, very few papers have dealt with the cost-optimal early fault detection and remaining useful life prediction of CNC equipment using multivariate positioning data. The novel approach presented here is based on vector autoregressive (VAR) degradation modeling and hidden semi-Markov modeling using the optimal Bayesian control technique. System condition is modeled using a continuous time semi-Markov chain with three states, i.e. unobservable healthy state 1, unobservable warning state 2 and observable failure state 3. Model parameter estimates are calculated using the expectation-maximization (EM) algorithm. The optimal control policy for the three-state model is represented by a Bayesian control chart for a multivariate observation process. The optimization problem is formulated and solved in the semi-Markov decision process (SMDP) framework. A formula for the mean residual life (MRL) is also derived based on Bayesian approach, which enables the estimation of the remaining useful life and early maintenance planning based on the observed data. The validation of the proposed methodologies is carried out using actual multivariate degradation data obtained from a CNC equipment. A comparison with the multivariate Bayesian control chart based on a hidden Markov model (HMM) is given, which illustrates the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

• Dynamic Bayesian control scheme for adaptive monitoring and detection. • Multivariate hidden semi-Markov model to describe the deterioration process. • SMDP approach to formulate and optimize the dynamic Bayesian scheme. • Considerably better fault detection compared with published results. • Development of case studies using multivariate data. Due to restrictions of mechanical structure and sensor installation, the actual status of modern engineered machine is unobservable and only partial observations can be indirectly collected. For this type of machine, existing research works used several measurable variables with fixed thresholds to monitor and detect the failures of the system, which leads to suboptimal results. This paper proposes a dynamic monitoring and detection approach for partially observed machines under discrete multivariate observations. The actual status of the partially observed machine system is modeled as a multivariate hidden semi-Markov process with unobservable operational states and an observable failure state under a general sojourn time structure. The process parameters are estimated using expectation maximization (EM) algorithm. Based on the dynamics of the hidden state of machine deterioration, a dynamic Bayesian control chart is formulated to monitor the posterior probability of system in warning state and adaptively switches the monitoring frequency according to risks of potential failures. As the posterior probability statistic exceeds a certain level, full inspection is initiated to detect the impending failures. The objective of the dynamic Bayesian control scheme is to achieve the maximum long-run system average availability, and the optimal control problem of monitoring and detection is formulated and solved by a computational algorithm in a semi-Markov decision process (SMDP) framework. The entire procedure is illustrated using multivariate data from case studies of mechanical generators and feed systems. Comparison with other advanced methods is also given, which demonstrates a considerably better performance of the proposed dynamic Bayesian approach. [ABSTRACT FROM AUTHOR]