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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]

The study works on a multi-level maintenance policy combining system level and unit level under soft and hard failure modes. The system experiences system-level preventive maintenance (SLPM) when the conditional reliability of entire system exceeds SLPM threshold, and also undergoes a two-level maintenance for each single unit, which is initiated when a single unit exceeds its preventive maintenance (PM) threshold, and the other is performed simultaneously the moment when any unit is going for maintenance. The units experience both periodic inspections and aperiodic inspections provided by failures of hard-type units. To model the practical situations, two types of economic dependence have been taken into account, which are set-up cost dependence and maintenance expertise dependence due to the same technology and tool/equipment can be utilised. The optimisation problem is formulated and solved in a semi-Markov decision process framework. The objective is to find the optimal system-level threshold and unit-level thresholds by minimising the long-run expected average cost per unit time. A formula for the mean residual life is derived for the proposed multi-level maintenance policy. The method is illustrated by a real case study of feed subsystem from a boring machine, and a comparison with other policies demonstrates the effectiveness of our approach. [ABSTRACT FROM AUTHOR]