Extropy analysis in consecutive r-out-of-n:G systems with applications in reliability and exponentiality testing

This study explores the extropy of consecutive r-out-of-n:G systems, offering a detailed framework for theoretical analysis and practical applications. Exact expressions for system lifetime extropy are derived, with comparative evaluations across diverse lifetime distributions. Theoretical contributions include bounds, characterization results, and insights into the variability of extropy. Practically, a nonparametric extropy estimator is introduced and validated through simulations and image processing applications. A novel test statistic for exponentiality is also proposed, with the critical values computed numerically and the performance assessed against alternative distributions. The results highlight the test's superior efficacy in specific contexts while noting its limitations. This work combines theoretical and practical advances, providing valuable tools for reliability analysis and statistical inference.