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March 2010 P1 - An Analytically Tractable Approximation to the Renewal Function

An Analytically Tractable Approximation to the Renewal Function

Volume 6, Number 2, March 2010 - Paper 1  - pp. 109-121


Faculty of Automotive and Mechanical Engineering, Changsha University of Science and Technology, Changsha, Hunan 410114, China

(Received on February 02, 2009, revised October 18, 2009)


Many maintenance optimization models need to iteratively evaluate the integrals with a renewal function being a part of the integrated function. For those cases, a simple and analytically tractable approximation to the renewal function is desired in order to facilitate the applications of the models. This paper proposes such an approximation that is applicable for both the Weibull and non-Weibull distributions. The approximation is obtained by neglecting the probability of having more than two failures, and hence is suitable for the situation where the evaluated time interval is not too large. This is often the case for maintenance optimization problems. The usefulness and appropriateness of the approximation is illustrated using examples.


References: 23

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