In this paper, we propose a new method for generating families of continuous distributions based on the star-shaped property which grantees the existences of some well know properties for the generated classes and distributions for any non-negative random variables. We refer to the new class as the composed family or shortly ( ) family. We study some mathematical properties of the new family. Some special families and sub-models of it from the family are discussed. To examine the performance of our new family and the generated models in fitting several data we use two real sets of data; censored and uncensored then comparing the fitting of a new produced model called composed- Lomax Weibull with some well-known models, which provides the best fit to all of the data. A simulation has been performed to assess the behavior of the maximum likelihood estimates of the parameters under the finite samples.