Tsallis Entropy in Consecutive k-out-of-n Good Systems: Bounds, Characterization, and Testing for Exponentiality.

This study explores the application of Tsallis entropy in evaluating uncertainty within the framework of consecutive k-out-of-n good systems, which are widely utilized in various reliability and engineering contexts. We derive new analytical expressions and meaningful bounds for the Tsallis entropy under various lifetime distributions, offering fresh insight into the structural behavior of system-level uncertainty. The approach establishes theoretical connections with classical entropy measures, such as Shannon and Rényi entropies, and provides a foundation for comparing systems under different stochastic orders. A nonparametric estimator is proposed to estimate the Tsallis entropy in this setting, and its performance is evaluated through Monte Carlo simulations. In addition, we develop a new entropy-based test for exponentiality, building on the distinctive properties of system lifetimes. So, Tsallis entropy serves as a flexible tool in both reliability characterization and statistical inference.