Abstract. In this work, a new extension of the exponentiated Weibull model
is introduced with its mathematical properties and applications to failure times
and medical data using the maximum likelihood method. We assess the per-
formance of the maximum likelihood estimators in terms of biases and mean
squared errors by means of a simulation study. We prove empirically the im-
portance and zexibility of the new model in modeling two types of lifetime data.
We conclude that, the new model is much better than the Weibull , expone-
tiated Weibull, beta Weibull, Kumaraswamy Weibull, Transmuted Weibull,
Weibull generalized Weibull and McDonald Weibul models in modeling failure
times and breast cancer data.