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Context: Verification techniques are being applied to ensure that software systems achieve desired quality levels and fulfill functional and non-functional requirements. However, applying these techniques to software product lines is challenging, given the exponential blowup of the number of products. Current product-line verification techniques leverage symbolic model checking and variability information to optimize the analysis, but still face limitations that make them costly or infeasible. In particular, state-of-the-art verification techniques for product-line reliability analysis are enumerative which hinders their applicability, given the latent exponential blowup of the configuration space. Objective: The objectives of this paper are the following: (a) we present a method to efficiently compute the reliability of all configurations of a compositional or annotation-based software product line from its UML behavioral models, (b) we provide a tool that implements the proposed method, and (c) we report on an empirical study comparing the performance of different reliability analysis strategies for software product lines. Method: We present a novel feature-family-based analysis strategy to compute the reliability of all products of a (compositional or annotation-based) software product line. The feature-based step of our strategy divides the behavioral models into smaller units that can be analyzed more efficiently. The family-based step performs the reliability computation for all configurations at once by evaluating reliability expressions in terms of a suitable variational data structure. Results: Our empirical results show that our feature-family-based strategy for reliability analysis outperforms, in terms of time and space, four state-of-the-art strategies (product-based, family-based, feature-product-based, and family-product-based) for the same property. It is the only one that could be scaled to a 220-fold increase in the size of the configuration space. Conclusion: Our feature-family-based strategy leverages both feature- and family-based strategies by taming the size of the models to be analyzed and by avoiding the products enumeration inherent to some state-of-the-art analysis methods.