We consider datasets for which lifetimes associated with the units in
a population are observed if they occur within certain time intervals
but for which lengths of the time intervals, or censoring times of unf
ailed units, are missing. We consider nonparametric estimation of the
lifetime distribution for the population from such data; a maximum lik
elihood estimator and a simple moment estimator are obtained. An examp
le involving automobile warranty data is discussed at some length.