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Modelling and Optimizing Imperfect Maintenance of Coatings on Steel Structures

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  • Nicolai, R.P.
  • Frenk, J.B.G.
  • Dekker, R.

Abstract

Steel structures such as bridges, tanks and pylons are exposed to outdoor weathering conditions. In order to prevent them from corrosion they are protected by an organic coating system. Unfortunately, the coating system itself is also subject to deterioration. Imperfect maintenance actions such as spot repair and repainting can be done to extend the lifetime of the coating. In this paper we consider the problem of finding the set of actions that minimizes the expected maintenance costs over a bounded horizon. To this end we model the size of the area affected by corrosion by a non-stationary gamma process. An imperfect maintenance action is to be done as soon as a fixed threshold is exceeded. The direct effect of such an action on the condition of the coating is assumed to be random. On the other hand, maintenance may also change the parameters of the gamma deterioration process. It is shown that the optimal maintenance decisions related to this problem are a solution of a continuous-time renewal-type dynamic programming equation. To solve this equation time is discretized and it is verified theoretically that this discretization induces only a small error. Finally, the model is illustrated with a numerical example.

Suggested Citation

  • Nicolai, R.P. & Frenk, J.B.G. & Dekker, R., 2007. "Modelling and Optimizing Imperfect Maintenance of Coatings on Steel Structures," ERIM Report Series Research in Management ERS-2007-043-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    • Handle: RePEc:ems:eureri:10455
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    References listed on IDEAS

    as
    1. Nicolai, Robin P. & Dekker, Rommert & van Noortwijk, Jan M., 2007. "A comparison of models for measurable deterioration: An application to coatings on steel structures," Reliability Engineering and System Safety, Elsevier, vol. 92(12), pages 1635-1650.
    2. Frenk, J.B.G. & Nicolai, R.P., 2007. "Approximating the Randomized Hitting Time Distribution of a Non-stationary Gamma Process," ERIM Report Series Research in Management ERS-2007-031-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    3. van Noortwijk, J.M., 2009. "A survey of the application of gamma processes in maintenance," Reliability Engineering and System Safety, Elsevier, vol. 94(1), pages 2-21.
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    Cited by:

    1. Zhang, Mimi & Gaudoin, Olivier & Xie, Min, 2015. "Degradation-based maintenance decision using stochastic filtering for systems under imperfect maintenance," European Journal of Operational Research, Elsevier, vol. 245(2), pages 531-541.
    2. Bretó, Carles, 2014. "Trajectory composition of Poisson time changes and Markov counting systems," Statistics & Probability Letters, Elsevier, vol. 88(C), pages 91-98.
    3. Nguyen, T.P.K. & Castanier, Bruno & Yeung, Thomas G., 2014. "Maintaining a system subject to uncertain technological evolution," Reliability Engineering and System Safety, Elsevier, vol. 128(C), pages 56-65.
    4. Mitra Fouladirad & Antoine Grall, 2015. "Monitoring and condition-based maintenance with abrupt change in a system’s deterioration rate," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(12), pages 2183-2194, September.
    5. W Zhu & M Fouladirad & C Bérenguer, 2015. "Bi-criteria maintenance policies for a system subject to competing wear and δ-shock failures," Journal of Risk and Reliability, , vol. 229(6), pages 485-500, December.
    6. Frenk, J.B.G. & Nicolai, R.P., 2007. "Approximating the randomized hitting time distribution of a non-stationary gamma process," Econometric Institute Research Papers EI 2007-18, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    7. Do, Phuc & Voisin, Alexandre & Levrat, Eric & Iung, Benoit, 2015. "A proactive condition-based maintenance strategy with both perfect and imperfect maintenance actions," Reliability Engineering and System Safety, Elsevier, vol. 133(C), pages 22-32.
    8. Tinga, Tiedo, 2010. "Application of physical failure models to enable usage and load based maintenance," Reliability Engineering and System Safety, Elsevier, vol. 95(10), pages 1061-1075.
    9. Nguyen, Dinh Tuan & Dijoux, Yann & Fouladirad, Mitra, 2017. "Analytical properties of an imperfect repair model and application in preventive maintenance scheduling," European Journal of Operational Research, Elsevier, vol. 256(2), pages 439-453.
    10. A Ponchet & M Fouladirad & A Grall, 2011. "Maintenance policy on a finite time span for a gradually deteriorating system with imperfect improvements," Journal of Risk and Reliability, , vol. 225(2), pages 105-116, June.
    11. P Baraldi & M Compare & A Despujols & E Zio, 2011. "Modelling the effects of maintenance on the degradation of a water-feeding turbo-pump of a nuclear power plant," Journal of Risk and Reliability, , vol. 225(2), pages 169-183, June.
    12. Si, Xiao-Sheng & Wang, Wenbin & Hu, Chang-Hua & Zhou, Dong-Hua, 2011. "Remaining useful life estimation - A review on the statistical data driven approaches," European Journal of Operational Research, Elsevier, vol. 213(1), pages 1-14, August.
    13. Ponchet, Amélie & Fouladirad, Mitra & Grall, Antoine, 2010. "Assessment of a maintenance model for a multi-deteriorating mode system," Reliability Engineering and System Safety, Elsevier, vol. 95(11), pages 1244-1254.

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    More about this item

    Keywords

    condition-based maintenance; degradation modelling; imperfect maintenance; life-cycle management; non-stationary gamma process; renewal-type dynamic programming equation;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • L61 - Industrial Organization - - Industry Studies: Manufacturing - - - Metals and Metal Products; Cement; Glass; Ceramics
    • L74 - Industrial Organization - - Industry Studies: Primary Products and Construction - - - Construction
    • M - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics
    • O31 - Economic Development, Innovation, Technological Change, and Growth - - Innovation; Research and Development; Technological Change; Intellectual Property Rights - - - Innovation and Invention: Processes and Incentives
    • O32 - Economic Development, Innovation, Technological Change, and Growth - - Innovation; Research and Development; Technological Change; Intellectual Property Rights - - - Management of Technological Innovation and R&D
    • O33 - Economic Development, Innovation, Technological Change, and Growth - - Innovation; Research and Development; Technological Change; Intellectual Property Rights - - - Technological Change: Choices and Consequences; Diffusion Processes

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