The main goal of this paper is to introduce a continuous distributions based on the zero truncated Poisson which accommodates
increasing, bathtub, decreasing, J-shaped, constant and unimodal shapes of monotone failure rates. A comprehensive
account of some of its mathematical properties are provided. The new probability density function can be expressed as a linear
combination of exponentiated Weibull densities. The method of the maximum likelihood is used to estimate the model
parameters. Empirically, we proved the importance and flexibility of the new distribution in modeling two data sets.