The density is There are two important special cases: The family of distributions accommodates unimodal, bathtub shaped*[1] and monotone failure rates.
Crevecoeur introduced it in assessing the reliability of ageing mechanical devices and showed that it accommodates bathtub shaped failure rates (1993, 1994).
Mudholkar, Srivastava, and Kollia (1996) applied the generalized Weibull distribution to model survival data.
Mudholkar et al. (1995) applied the exponentiated Weibull distribution to model failure data.
They showed that the exponentiated Weibull distribution has increasing, decreasing, bathtub, and unimodal hazard rates.