We introduce and study the Marshall-Olkin additive Weibull distribution in order
to allow a wide variation in the shape of the hazard rate, including increasing, decreasing, bathtub and unimodal shapes. The new distribution generalizes at least
eleven lifetime models extant in the literature. Various of its mathematical properties including explicit expressions for the ordinary and incomplete moments, generating function, moments of the residual and reversed residual life functions and
order statistics are derived. The parameters of the new distribution are estimated
by the maximum likelihood method. We illustrate empirically the superiority of
the new model over other distributions by means of a real life data set.