A two-level Bayesian early fault detection for mechanical equipment subject to dependent failure modes.

• New, two-level Bayesian fault detection scheme is developed. • Realistic failure modeling considering two dependent failure modes. • Mean residual life formula is derived considering two failure modes in a new HMM framework. • The proposed two-level Bayesian control scheme outperforms previously published Bayesian control scheme. • Considerably lower average cost, reduced number of failures and more precise residual life estimates. A two-level Bayesian control approach is presented to detect early fault for mechanical equipment subject to dependent degradation and catastrophic failures. The system degradation process is modeled using a continuous time stochastic process with three states. To model the dependence of two failure modes, we assume that the joint distribution of the time to catastrophic failure and sojourn time in the healthy state follows Marshall-Olkin bivariate exponential distribution. To avoid unnecessary sampling cost and to effectively detect impending failure, a two-level control policy, where longer sampling interval is applied for healthier state and shorter sampling interval is used in severe degradation state is proposed in Bayesian control chart framework for a multivariate observation process considering dependent failure modes. 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 using the Bayesian approach. The validation of the proposed methodologies is carried out using real multivariate degradation data obtained from a milling machine. A comparison with the multivariate Bayesian control chart with a single sampling interval and a single control limit is given, which illustrates the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]