Please use this identifier to cite or link to this item: https://doi.org/10.1080/03610920600728443
Title: Some analytical and numerical bounds on the renewal function
Authors: Ran, L.
Cui, L.
Xie, M. 
Keywords: Numerical bounds
Recursive equation
Reliability analysis
Renewal process
Stochastic processes
Issue Date: 1-Oct-2006
Source: Ran, L., Cui, L., Xie, M. (2006-10-01). Some analytical and numerical bounds on the renewal function. Communications in Statistics - Theory and Methods 35 (10) : 1815-1827. ScholarBank@NUS Repository. https://doi.org/10.1080/03610920600728443
Abstract: Renewal-type equations are frequently encountered in the study of reliability, warranty analysis, replacement and maintenance policies, and inventory control. Renewal equations usually do not have analytical solutions, and hence, bounds or approximations are very useful. In this article, analytical bounds are studied based on a simple iterative procedure which provides some analytical results and nice convergence properties when the number of iteration increases. Bounds and approximations are also investigated for a recursive algorithm for numerical computation. In addition, some interesting monotonicity properties are introduced and discussed. The approximation error, which is important for determining the stopping rule of the iterative procedure and the numerical algorithm, is also studied.
Source Title: Communications in Statistics - Theory and Methods
URI: http://scholarbank.nus.edu.sg/handle/10635/72409
ISSN: 03610926
DOI: 10.1080/03610920600728443
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