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

Jan van Noortwijk and J.A.M. van der Weide

Reliability Engineering and System Safety, 2008, vol. 93, issue 12, 1853-1860

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).

Keywords: Discrete renewal process; Renewal function; Second-moment properties; Gamma process; Geometric distribution (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:reensy:v:93:y:2008:i:12:p:1853-1860

DOI: 10.1016/j.ress.2008.03.023

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