This article discusses methods whereby reports of warranty claims can be used to estimate the expected number of warranty claims per unit in service as a function of the time in service. These methods provide estimates that are adjusted for delays or lags corresponding to the time from the claim until it is entered into the data base used for analysis. Forecasts of the number and cost of claims on the population of all units in service are also developed, along with standard errors for these forecasts. The methods are based on a log-linear Poisson model for numbers of warranty claims. Both the case of a known distribution of reporting lag and simultaneous estimation of that distribution are considered. The use of residuals for model checking, extensions to allow for extra-Poisson variation, and the estimation of warranty costs are also considered.