Existence of MLE for Weibull Distribution with Grouped and Censored Data

In this paper we consider the estimation problem in the situation where the lifetime of some products follows a Weibull distribution, and the observed data are grouped and right-censored. All possible cases are discussed, and a necessary and sufficient condition for the existence of the maximum likelihood estimate of the unknown parameters is given. The paper is concluded with a short discussion about one failure situation and about the calculation of the maximum likelihood estimate with a true data set.