<p>This paper presents a comprehensive analysis of the properties of the consecutive system of generating-information function of entropy. New analytical formulations and informative bounds are derived for this system under various lifetime distributions, providing a deeper understanding of its structural characteristics and the nature of system-level uncertainty. In addition, stochastic ordering and characterization results are established. To strengthen the link between theory and application, two non-parametric estimation procedures are introduced for the consecutive system of generating-information functions, along with a novel test statistic designed to examine uniformity. The performance of the proposed test is assessed through extensive Monte Carlo simulations, where its statistical power is compared with several well-established competing methods in a variety of situations. The results highlight both theoretical advancements in the study of information-based reliability measures and practical methodologies for hypothesis testing in applied statistics. Finally, a case study based on real-world data concerning malignant tumors is performed to assess the applicability and robustness of the proposed estimators and the goodness-of-fit test. Simulation and real data analyses demonstrate that the second estimator provides more accurate and stable estimates than the first, particularly in terms of bias reduction and estimation precision.</p>