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Stochastic model for maintenance in continuously deteriorating systems

Author

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  • Samuelson, Aviva
  • Haigh, Andrew
  • O'Reilly, Małgorzata M.
  • Bean, Nigel G.

Abstract

We construct a stochastic model for maintenance suitable for the analysis of real-life systems which deteriorate over time before they eventually fail and are replaced. The model uses a continuous deterioration level, where the rate of change depends on the current operating mode as well as the current level of deterioration. We demonstrate how to construct a model in which the uncertainty about the state of deterioration, when the system is not continuously observed, is accurately represented. This feature addresses some drawbacks of previous work that is known to cause modelling errors. The key performance measures for this model can be evaluated efficiently using existing algorithms. The theory is illustrated using numerical examples, in which we discuss how this model can be used in a practical evaluation of different maintenance strategies.

Suggested Citation

  • Samuelson, Aviva & Haigh, Andrew & O'Reilly, Małgorzata M. & Bean, Nigel G., 2017. "Stochastic model for maintenance in continuously deteriorating systems," European Journal of Operational Research, Elsevier, vol. 259(3), pages 1169-1179.
    • Handle: RePEc:eee:ejores:v:259:y:2017:i:3:p:1169-1179
    DOI: 10.1016/j.ejor.2016.11.032
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    References listed on IDEAS

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    1. Silva Soares, Ana da & Latouche, Guy, 2009. "Fluid queues with level dependent evolution," European Journal of Operational Research, Elsevier, vol. 196(3), pages 1041-1048, August.
    2. Horton, Graham & Kulkarni, Vidyadhar G. & Nicol, David M. & Trivedi, Kishor S., 1998. "Fluid stochastic Petri nets: Theory, applications, and solution techniques," European Journal of Operational Research, Elsevier, vol. 105(1), pages 184-201, February.
    3. Nigel Bean & Małgorzata O’Reilly, 2008. "Performance measures of a multi-layer Markovian fluid model," Annals of Operations Research, Springer, vol. 160(1), pages 99-120, April.
    4. Bean, Nigel G. & O’Reilly, Małgorzata M., 2014. "The stochastic fluid–fluid model: A stochastic fluid model driven by an uncountable-state process, which is a stochastic fluid model itself," Stochastic Processes and their Applications, Elsevier, vol. 124(5), pages 1741-1772.
    5. V. Ramaswami & Douglas Woolford & David Stanford, 2008. "The erlangization method for Markovian fluid flows," Annals of Operations Research, Springer, vol. 160(1), pages 215-225, April.
    6. Bean, Nigel G. & O'Reilly, Malgorzata M. & Taylor, Peter G., 2005. "Hitting probabilities and hitting times for stochastic fluid flows," Stochastic Processes and their Applications, Elsevier, vol. 115(9), pages 1530-1556, September.
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    Cited by:

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    2. Eleonora Deiana & Guy Latouche & Marie-Ange Remiche, 2021. "Fluid Flow Model for Energy-Aware Server Performance Evaluation," Methodology and Computing in Applied Probability, Springer, vol. 23(3), pages 801-821, September.
    3. Michiel A. J. uit het Broek & Ruud H. Teunter & Bram de Jonge & Jasper Veldman & Nicky D. Van Foreest, 2020. "Condition-Based Production Planning: Adjusting Production Rates to Balance Output and Failure Risk," Manufacturing & Service Operations Management, INFORMS, vol. 22(4), pages 792-811, July.
    4. Nikki Sonenberg & Peter G. Taylor, 2019. "Networks of interacting stochastic fluid models with infinite and finite buffers," Queueing Systems: Theory and Applications, Springer, vol. 92(3), pages 293-322, August.

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