Let Xi, i ≥ 1, describe the lifetimes of items with finite mean μ = E (Xi) which are successively placed in service. In order to estimate the replacement rate 1/μ or related quantities, the random variables Xi are usually assumed to be independent and identically distributed. It is shown that a nonparametric estimation of the replacement rate and other reciprocal functions of renewal theory is possible while using a delta method with weakened requirements upon the global growth of f which also allows dependent observations and respects the unboundedness of the analyzed reciprocal functions. Moreover, results on the moments and, furthermore, on corresponding simulations are included.