Information-Theoretic Reliability Analysis of Linear Consecutive r-out-of-n:F Systems and Uniformity Testing

This paper explores the reliability of linear consecutive r-out-of-n:F systems from an information-theoretic perspective, with a particular focus on testing for uniformity. At the heart of the study is extropy, a complementary measure to entropy that we use to gain deeper insights into the uncertainty associated with system lifetimes. We begin by deriving general expressions for extropy in these systems and examine how it behaves under different component lifetime distributions, particularly highlighting the role of heterogeneity. Theoretical bounds are developed, along with new characterization results, shedding light on the unique properties of the uniform distribution within this framework. To bridge theory and application, we propose a nonparametric estimator for extropy and build a new test statistic to assess uniformity. The effectiveness of this test is evaluated through comprehensive simulation studies, where we compare its power against several well-known alternatives across a range of scenarios. Overall, our findings offer both theoretical contributions to the understanding of information measures in reliability analysis and practical tools for statistical testing in applied settings.