A simple approximation for IFR weibull renewal functions

Abstract

The renewal function is useful in reliability theory and is often needed to compute optimal maintenance policies. Although the Weibull is frequently the distribution of choice for reliability estimation, it is seldom used in maintenance models. One reason for this is that the renewal function for the Weibull is intractable. Existing methods used to numerically compute or to approximate this function typically involve algorithms that are O( n 2) in complexity and have large storage requirements. Although the renewal function converges to a linear expression as t → ∞, these methods become increasingly expensive as t becomes large. In this paper, we present a simple and accurate approximation that has computational complexity that is O( n) with O(1) storage requirements. The approximation is based on the limiting expression of the renewal function and makes use of several well known relations for IFR renewal functions. We demonstrate the usefulness and the accuracy of the approximation with several examples.