Optimal Repair Rate for a Repairable Machine with Nonlinear State Equation
Keywords:Machine breakdown, minor breakdown, major breakdown, repair, model predictive control
This work deals with two models of a single machine subject to breakdowns. The first model is a binary-state model while the second one is a multi-state model. Breakdowns are followed by repairs. The systems under study are of the tracking type. We use nonlinear model predictive control to determine the optimal repair rates that keep the variables as close as possible to their target. Numerical illustrations with sensitivity analysis are used to assess the effect of the system parameters on the optimal solution.
Barlow, R. E., Proschan, F. Mathematical theory of reliability. John Wiley and Sons, 1965.
Dekker, R. (1996). Applications of maintenance optimisation models: a review and analysis, Reliability Engineering and Systems Safety, Vol. 51,229-240.
Hartl, R. (1983). Optimal maintenance and production rates for a machine, Journal of Economic Dynamics and Control, Vol. 6, 281-306.
Marquez, A. and Heguedas, A. (2002). Models for maintenance optimization: a study for repairable systems and finite time periods, Reliability Engineering and System Safety, Vol. 75, 367-377.
Popova, E. and Popova, I. (2008). Replacement strategies, Article ID #eqr106 in: Encyclopedia of Statistics in Quality and Reliability, Eds: Ruggeri F., Faltin F., Kenett R. John Wiley and Sons.
Rausand, M. and Høyland, A. System Reliability Theory: Models, Statistical Methods, and Applications, 2nd Edition. John Wiley and Sons, 2004.
Sethi, S.P. and Thompson, G.L. Optimal Control Theory: Applications to Management Science and Economics. 2nd ed. Kluwer Academic Publishers, 2000.
Soltani, R. (2014). Reliability optimization of binary state nonrepairable systems: A state of the art survey, International Journal of Industrial Engineering Computations, Vol. 5, Issue 3, 339-364.
Valdez-Florez, C. and Feldman, R. (1989). A survey of preventive maintenance models for stochastically deteriorating single-unit systems, Naval Research Logistics, Vol. 36, No. (4), 419-446.
Copyright (c) 2022 Najeeb Al-Matar, Lotfi Tadj
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.