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We prove some stochastic comparisons between reliability structures' lifetimes using their signatures. In the present article, we provide a signature-based analysis of a 2-within-consecutive-k-out-of-n: F system consisting of exchangeable components. More specifically, we deduce recurrence relations for evaluation of its signature, while an exact formula for the computation of the same quantities is also presented. In addition, we establish several stochastic ordering results for the 2-within-consecutive-k-out-of-n: F systems, and some stochastic comparisons between reliability structures' lifetimes using their signatures are proved. Finally, we investigate the IFR property preservation under the formulation of 2-within-consecutive-k-out-of-n: F systems, and deduce simple conditions under which the IFR property is not preserved.