In this paper, a new dependent model is introduced. The model is motivated using the structure of seriesparallel systems consisting of two series-parallel systems with a random number of parallel sub-systems that have fixed components connected in series. The dependence properties of the proposed model are studied. Two estimation methods, namely the moment method, and the maximum likelihood methods are applied to estimate the parameters of the distributions of the components based on observing the system’s lifetime data. A Monte Carlo simulation study is used to evaluate the performance of the estimators. Two real data sets are used to illustrate the proposed method. The results are useful for researchers and practitioners interested in analysing bivariate data related to extreme events.

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