A numerical approximation of the renewal function solution to the renewal equation - Raneses, Earl M. (2002)
The expected number of renewals as a function of time, called the renewal function, is important in determining performance measures in maintenance management equipment, in controlling inventories, and calculating warranty policies of manufactured items. One of the ways of obtaining such function given the probability distribution of the interoccurence of events is solving an integral equation called the renewal equation. In this study, the renewal function was approximated as a numerical solution to the renewal equation. Such solution was obtained by developing a quadrature method based on the concept of Riemann integration. The renewal functions having Rayleigh, Gamma (3, 0.25), and Chi-square (8) distributions were obtained. Using the exponential and Erlang-2 distributions with scale parameter , the algorithm was validated by comparing the approximation and the true renewal function. The algorithm produced a good approximation for exponential and Erlang-2 distributions for small values of t it is limited, however, to t = 13 and t = 24 for the exponential and Erlang-2 distributions, respectively
Thesis (BS Applied Mathematics) -- University of the Philippines Mindanao, 2002