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In the present paper, we deliver a reliability study of the weighted-<i>r</i>-consecutive-<i>k</i>-out-of-<i>n</i>: <i>F</i> reliability systems consisting of independent and identically distributed components. The signature vector of the structures is arithmetically determined by the aid of an appropriate Monte-Carlo simulation scheme. Several conclusions for the corresponding reliability polynomials are also drawn. An extensive numerical investigation is carried out to evaluate the performance of the weighted-<i>r</i>-consecutive-<i>k</i>-out-of-<i>n</i>: <i>F</i> reliability systems. Some stochastic signature-based comparisons among several members of the underlying family of reliability structures are also discussed.