Abstract: The analytical renewal function(RF) is not tractable of the exponential Weibull(EW) distribution. In the proposed model, the n-fold convolution of the EW cumulative distribution function(CDF) is approximated by a n-fold convolutions of Gamma and normal CDFs. We obtain the EW RF by a series approximation model. The method is very simple in the computation. When the parameters are unknown, we present the asymptotic confidence interval of the RF. The validity of the asymptotic confidence interval is checked via some numerical experiments. 

Key words: Renewal function, EW distribution, Gamma distribution, Normal distribution, Series truncation approximation