The Estimation of Renewal Functions Using the Mean Value Theorem for Integrals (MeVTI) Method

Abstract

In the analysis of warranty, renewal functions are important in acquiring the expected number of failures of a nonrepairable component in a time interval. It is very difficult and complicated -if at all possible- to obtain a renewal function analytically. This paper proposes a numerical integration method for estimating renewal functions in the terms of renewal integral equations. The estimation is done through the Mean Value Theorem for Integrals (MeVTI) method after modifying the variable of the renewal integral equations. The accuracy of the estimation is measured by its comparison against the existing analytical approach of renewal functions, those are for Exponential, Erlang, Gamma, and Normal baseline failure distributions. The estimation of the renewal function for a Weibull baseline failure distribution as the results of the method is compared to that of the well-known numerical integration approaches, the Riemann-Stieljies and cubic spline methods.

Keywords :    Mean Value Theorem for Integrals, Renewal Functions, Renewal Integral Equations.