Predictive Maintenance Optimization Under Stochastic Production in Complex Systems

Abstract

This paper focuses on predictive maintenance optimization under stochastic production in complex systems using prognostic Remaining Useful Life (RUL) information. At each stage of such a system, we consider redundant assets and use their RUL to guarantee system availability. However, the production capacity of our system is stochastic due to environmental and human factors. We aim at meeting client demands in a given optimization planning horizon while reducing the generated cost. We propose a deterministic mathematical model before providing a chance-constrained programming formulation to minimize the total cost. Two solution approaches for dealing with chance constraints are proposed to approximate the stochastic model in this maintenance optimization. Experimental results show the efficiency of the proposed model and chance-constrained approximation approaches.

Appendix

The complete version of scenario-based expectation chance-constrained programming model EXP is presented as follows.

$$\begin{aligned} {Model EXP:} \ \ {} {} & {} \min \left( C^{maintenance} + C^{failure} + C^{inventory}\right) / |\varOmega | \nonumber \\ C^{maintenance} {} & {} = c^m \cdot \sum _{\omega \in \varOmega }\sum _{k \in \mathcal {K}} \sum _{j \in \mathcal {J}_k} \sum _{t \in \mathcal {T}} X_{k,j}^t(\omega ) \nonumber \\ C^{failure} {} & {} = c^f \cdot \sum _{\omega \in \varOmega } \sum _{t \in \mathcal {T}} (1 - S^t(\omega )) \nonumber \\ C^{inventory} {} & {} = c^i \cdot \sum _{\omega \in \varOmega } \sum _{t \in \mathcal {T}} I^t(\omega ) \nonumber \end{aligned}$$