Tsallis Entropy in Consecutive r-out-of-n:G Systems: Bounds, Characterization, and Testing for Exponentiality

This paper investigates the role of Tsallis entropy as a generalized measure of uncertainty in the reliability analysis of consecutive r-out-of-n:G systems, a class of models widely used in engineering applications. 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. Although Tsallis entropy presents certain limitations, such as non-positivity and lack of additivity, our results support its value as a flexible tool in both reliability characterization and statistical inference.