Some Analytical and Numerical Bounds on the Renewal Function |
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Authors: | Lun Ran Lirong Cui M Xie |
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Institution: | 1. School of Management &2. Economics , Beijing Institute of Technology , Beijing , China ranlunzhengyy@bit.edu.cn;4. Economics , Beijing Institute of Technology , Beijing , China;5. Department of Industrial and Systems Engineering , National University of Singapore , Kent Ridge Crescent , Singapore |
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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. |
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Keywords: | Numerical bounds Recursive equation Reliability analysis Renewal process Stochastic processes |
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