IDEAS home Printed from https://ideas.repec.org/a/sae/risrel/v231y2017i4p429-445.html
   My bibliography  Save this article

Modelling and numerical assessment of a maintenance strategy with stock through piecewise deterministic Markov processes and quasi Monte Carlo methods

Author

Listed:
  • Jeanne Demgne
  • Sophie Mercier
  • William Lair
  • Jérôme Lonchampt

Abstract

To ensure a power generation level, the French national electricity supply (EDF) has to manage its producing assets by putting in place adapted preventive maintenance strategies. In this article, a fleet of identical components is considered, which are spread out all around France (one per power plant site). The components are assumed to have stochastically independent lifetimes, but they are made functionally dependent through the sharing of a common stock of spare parts. When available, these spare parts are used for both corrective and preventive replacements, with priority to corrective replacements. When the stock is empty, replacements are delayed until the arrival of new spare parts. These spare parts are expensive, and their manufacturing time is long, which makes it necessary to rigorously define their ordering process. The point of the article is to provide the decision maker with the tools to take the right decision (make or not the overhaul). To do that, two indicators are proposed, which are based on an economic variable called the net present value. The net present value stands for the difference between the cumulated discounted cash-flows of the purely corrective policy and the preventive one which including the overhaul. Piecewise deterministic Markov processes are first considered for the joint modelling of the stochastic evolution of the components, stock and ordering process with and without overhaul. The indicators are next expressed with respect to these piecewise deterministic Markov processes, which have to be numerically assessed. Instead of using the most classical Monte Carlo simulations, we here suggest alternate methods based on quasi Monte Carlo simulations, which replace the random uniform numbers of the Monte Carlo method by deterministic sequences called low-discrepancy sequences. The obtained results show a real gain of the quasi Monte Carlo methods in comparison with the Monte Carlo method. The developed tools can hence help the decision maker to take the right decision.

Suggested Citation

  • Jeanne Demgne & Sophie Mercier & William Lair & Jérôme Lonchampt, 2017. "Modelling and numerical assessment of a maintenance strategy with stock through piecewise deterministic Markov processes and quasi Monte Carlo methods," Journal of Risk and Reliability, , vol. 231(4), pages 429-445, August.
    • Handle: RePEc:sae:risrel:v:231:y:2017:i:4:p:429-445
    DOI: 10.1177/1748006X17712121
    as

    Download full text from publisher

    File URL: https://journals.sagepub.com/doi/10.1177/1748006X17712121
    Download Restriction: no
    File URL: https://libkey.io/10.1177/1748006X17712121?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. El Haddad, R. & Lécot, C. & L’Ecuyer, P. & Nassif, N., 2010. "Quasi-Monte Carlo methods for Markov chains with continuous multi-dimensional state space," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(3), pages 560-567.
    2. Hashimzade, Nigar & Myles, Gareth & Black, John, 2017. "A Dictionary of Economics," OUP Catalogue, Oxford University Press, edition 5, number 9780198759430.
    3. Saleh, J.H. & Marais, K., 2006. "Reliability: How much is it worth? Beyond its estimation or prediction, the (net) present value of reliability," Reliability Engineering and System Safety, Elsevier, vol. 91(6), pages 665-673.
    4. Marais, Karen B. & Saleh, Joseph H., 2009. "Beyond its cost, the value of maintenance: An analytical framework for capturing its net present value," Reliability Engineering and System Safety, Elsevier, vol. 94(2), pages 644-657.
    5. Pierre L'Ecuyer & Christian Lécot & Bruno Tuffin, 2008. "A Randomized Quasi-Monte Carlo Simulation Method for Markov Chains," Operations Research, INFORMS, vol. 56(4), pages 958-975, August.
    6. Peter W. Glynn & Ward Whitt, 1992. "The Asymptotic Efficiency of Simulation Estimators," Operations Research, INFORMS, vol. 40(3), pages 505-520, June.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Gómez Fernández, Juan F. & Márquez, Adolfo Crespo & López-Campos, Mónica A., 2016. "Customer-oriented risk assessment in network utilities," Reliability Engineering and System Safety, Elsevier, vol. 147(C), pages 72-83.
    2. Nabil Kahalé, 2020. "Randomized Dimension Reduction for Monte Carlo Simulations," Management Science, INFORMS, vol. 66(3), pages 1421-1439, March.
    3. L’Ecuyer, Pierre & Munger, David & Lécot, Christian & Tuffin, Bruno, 2018. "Sorting methods and convergence rates for Array-RQMC: Some empirical comparisons," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 143(C), pages 191-201.
    4. Marais, Karen B., 2013. "Value maximizing maintenance policies under general repair," Reliability Engineering and System Safety, Elsevier, vol. 119(C), pages 76-87.
    5. Giesecke, K. & Schwenkler, G., 2019. "Simulated likelihood estimators for discretely observed jump–diffusions," Journal of Econometrics, Elsevier, vol. 213(2), pages 297-320.
    6. Johannes Zahner, 2020. "Above, but close to two percent. Evidence on the ECB’s inflation target using text mining," MAGKS Papers on Economics 202046, Philipps-Universität Marburg, Faculty of Business Administration and Economics, Department of Economics (Volkswirtschaftliche Abteilung).
    7. Sevdalina Hristova, 2022. "The Impact of the Public Procurement System Reform on Bulgarian Small and Medium-Sized Enterprises," Economic Studies journal, Bulgarian Academy of Sciences - Economic Research Institute, issue 6, pages 172-184.
    8. Yosuke Shigetomi & Keisuke Nansai & Shigemi Kagawa & Susumu Tohno, 2016. "Influence of income difference on carbon and material footprints for critical metals: the case of Japanese households," Journal of Economic Structures, Springer;Pan-Pacific Association of Input-Output Studies (PAPAIOS), vol. 5(1), pages 1-19, December.
    9. Mai, Nhat Chi, 2022. "Rubber In French Indochina," OSF Preprints yzdp6, Center for Open Science.
    10. Weber, Florian & Schmid, Thomas & Pietz, Matthäus & Kaserer, Christoph, 2010. "Simulation-based valuation of project finance: does model complexity really matter?," CEFS Working Paper Series 2010-03, Technische Universität München (TUM), Center for Entrepreneurial and Financial Studies (CEFS).
    11. Ahammed, Faisal & Azeem, Abdullahil, 2013. "Selection of the most appropriate package of Solar Home System using Analytic Hierarchy Process model in rural areas of Bangladesh," Renewable Energy, Elsevier, vol. 55(C), pages 6-11.
    12. Nanjing Jian & Shane G. Henderson, 2020. "Estimating the Probability that a Function Observed with Noise Is Convex," INFORMS Journal on Computing, INFORMS, vol. 32(2), pages 376-389, April.
    13. Georg Ch. Pflug & Philipp Thoma, 2016. "Efficient calculation of the Greeks for exponential Lévy processes: an application of measure valued differentiation," Quantitative Finance, Taylor & Francis Journals, vol. 16(2), pages 247-257, February.
    14. Hamidi, Maryam & Liao, Haitao & Szidarovszky, Ferenc, 2016. "Non-cooperative and cooperative game-theoretic models for usage-based lease contracts," European Journal of Operational Research, Elsevier, vol. 255(1), pages 163-174.
    15. Martyna Tomala & Andrzej Rusin & Adam Wojaczek, 2020. "Risk-Based Planning of Diagnostic Testing of Turbines Operating with Increased Flexibility," Energies, MDPI, vol. 13(13), pages 1-16, July.
    16. Lécot, Christian & L’Ecuyer, Pierre & El Haddad, Rami & Tarhini, Ali, 2019. "Quasi-Monte Carlo simulation of coagulation–fragmentation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 161(C), pages 113-124.
    17. Andersson, Patrik & Kohatsu-Higa, Arturo & Yuasa, Tomooki, 2020. "Second order probabilistic parametrix method for unbiased simulation of stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 130(9), pages 5543-5574.
    18. Hoepfer, V.M. & Saleh, J.H. & Marais, K.B., 2009. "On the value of redundancy subject to common-cause failures: Toward the resolution of an on-going debate," Reliability Engineering and System Safety, Elsevier, vol. 94(12), pages 1904-1916.
    19. Castet, Jean-Francois & Saleh, Joseph H., 2012. "On the concept of survivability, with application to spacecraft and space-based networks," Reliability Engineering and System Safety, Elsevier, vol. 99(C), pages 123-138.
    20. Humburg, Anja, 2012. "Post-growth on the move: The environmental movement as agent of change for the transition to a post-growth economy - Evidence from Germany," Zukunftsimpulse 7, Wuppertal Institute for Climate, Environment and Energy.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:sae:risrel:v:231:y:2017:i:4:p:429-445. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: SAGE Publications (email available below). General contact details of provider: .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.