A predictive maintenance model for [formula omitted]-out-of-[formula omitted]:F continuously deteriorating systems subject to stochastic and economic dependencies

Abstract

New concepts of Industry 4.0 make industrial systems more and more complex due to the strong dependencies among a large number of stochastically deteriorating units. Ignoring such dependencies in maintenance modeling usually leads to high maintenance costs. With this spirit, we develop in the present paper an innovative predictive maintenance model for k-out-of-n:F continuously deteriorating systems considering both the stochastic dependency due to the common impact of working environment and the economic dependency issued by the set-up cost sharing. Compared with related works, the originality of our model is fourfold. Firstly, we adopt a multivariate Gamma subordinator to describe the dependent degradation behavior among units in the context of maintenance modeling. Secondly, we use probabilistic measures of the remaining useful life at unit and system levels as maintenance decision indices. Thirdly, we elaborate a proactive maintenance policy allowing the consideration of both the stochastic and economic dependencies in maintenance decision-making. Finally, we evaluate analytically the long-run cost rate of the maintenance policy thanks to the semi-regenerative theory. Various comparative studies with benchmarks under different configurations of system characteristics and maintenance costs confirm the high performances of the developed maintenance model, and emphasize the value of introducing multiple kinds of dependencies in maintenance modeling.