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Applications to continuous-time processes of computational techniques for discrete-time renewal processes

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  • van Noortwijk, J.M.
  • van der Weide, J.A.M.

Abstract

For optimising maintenance, the total costs should be computed over a bounded or unbounded time horizon. In order to determine the expected costs of maintenance, renewal theory can be applied when we can identify renewals that bring a component back into the as-good-as-new condition. This publication presents useful computational techniques to determine the probabilistic characteristics of a renewal process. Because continuous-time renewal processes can be approximated with discrete-time renewal processes, it focusses on the latter processes. It includes methods to compute the probability distribution, expected value and variance of the number of renewals over a bounded time horizon, the asymptotic expansion for the expected value of the number of renewals over an unbounded time horizon, the approximation of a continuous renewal-time distribution with a discrete renewal-time distribution, and the extension of the discrete-time renewal model with the possibility of zero renewal times (in order to cope with an upper-bound approximation of a continuous-time renewal process).

Suggested Citation

  • van Noortwijk, J.M. & van der Weide, J.A.M., 2008. "Applications to continuous-time processes of computational techniques for discrete-time renewal processes," Reliability Engineering and System Safety, Elsevier, vol. 93(12), pages 1853-1860.
    • Handle: RePEc:eee:reensy:v:93:y:2008:i:12:p:1853-1860
    DOI: 10.1016/j.ress.2008.03.023
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    References listed on IDEAS

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    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. De Pril, Nelson, 1985. "Recursions for Convolutions of Arithmetic Distributions," ASTIN Bulletin, Cambridge University Press, vol. 15(2), pages 135-139, November.
    3. Dickson,David C. M., 2005. "Insurance Risk and Ruin," Cambridge Books, Cambridge University Press, number 9780521846400.
    4. Michael Tortorella, 2005. "Numerical Solutions of Renewal-Type Integral Equations," INFORMS Journal on Computing, INFORMS, vol. 17(1), pages 66-74, February.
    5. Mercier, Sophie, 2007. "Discrete random bounds for general random variables and applications to reliability," European Journal of Operational Research, Elsevier, vol. 177(1), pages 378-405, February.
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    Cited by:

    1. Khac Tuan Huynh & Anne Barros & Christophe Bérenguer, 2012. "Adaptive condition-based maintenance decision framework for deteriorating systems operating under variable environment and uncertain condition monitoring," Journal of Risk and Reliability, , vol. 226(6), pages 602-623, December.
    2. 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.
    3. Brezavšček Alenka, 2013. "A Simple Discrete Approximation for the Renewal Function," Business Systems Research, Sciendo, vol. 4(1), pages 65-75, March.

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