In this paper, a new family of distribution is introduced to model the lifetime of a system consisting of series and parallel systems having a random number of components. As a submodel, the Weibull baseline is considered in detail and some basic mathematical properties are examined such as quantile function and moments. Several estimation methods are considered to estimate the parameters of the proposed distribution. A comprehensive Monte Carlo simulation study is designed to assess the performance of these estimators in terms of mean squared errors. Two numerical examples are also provided to illustrate the flexibility of the proposed distribution. The proposed model reveals to be better than other current models considered in the examples based on the Akaike information criterion and some goodness-of-fit statistics.