Extropy Properties of Consecutive k-Out-of-n:G Systems Under the Condition 2k ≥ n

Consecutive k-out-of-n:G systems are widely used reliability models in engineering and communications, and their survival functions possess an inherent structural symmetry under the condition 2k≥n. This paper investigates the extropy characteristics of such systems under the condition 2k≥n, which admits a tractable closed-form representation of the survival function. A closed-form expression for the extropy of the system lifetime is derived using a probability integral transform and a density-quantile representation, which separates the symmetric structural contribution from the baseline distributional component. Bounds, stochastic ordering results based on a density-quantile order, and a characterization theorem are established. A nonparametric spacing-based estimator is proposed, its consistency is proved under explicit regularity conditions, and bootstrap confidence intervals are provided. Monte Carlo simulations under three component lifetime distributions (Weibull, Gamma, and Pareto II) demonstrate that the estimator is consistent, with bias and root mean squared error decreasing monotonically as sample size increases. A sensitivity analysis confirms the adequacy of the default window size rule. The proposed framework extends extropy to structured reliability systems and provides a practical nonparametric estimation tool with implementation guidelines, illustrated via a real data example on glass fiber breaking strengths.