# Entropy-Based Uncertainty Quantification in Linear Consecutive k-out-of-n:G Systems via Cumulative Residual Tsallis Entropy

## TL;DR

This paper introduces a new method using entropy to quantify uncertainty in reliability systems, offering practical tools for analysis and real-world applications.

## Contribution

The paper introduces a novel entropy-based framework using cumulative residual Tsallis entropy for uncertainty quantification in linear consecutive k-out-of-n:G systems.

## Key findings

- CRTE provides analytical expressions and bounds for uncertainty in systems with continuous lifetime distributions.
- A nonparametric test for dispersive ordering is proposed and validated through simulations.
- CRTE is shown to be effective and interpretable for real-world reliability modeling.

## Abstract

Quantifying uncertainty in complex systems is a central problem in reliability analysis and engineering applications. In this work, we develop an information-theoretic framework for analyzing linear consecutive k-out-of-n:G systems using the cumulative residual Tsallis entropy (CRTE). A general analytical expression for CRTE is derived, and its behavior is investigated under various stochastic ordering relations, providing insight into the reliability of systems governed by continuous lifetime distributions. To address challenges in large-scale settings or with nonstandard lifetimes, we establish analytical bounds that serve as practical tools for uncertainty quantification and reliability assessment. Beyond theoretical contributions, we propose a nonparametric CRTE-based test for dispersive ordering, establish its asymptotic distribution, and confirm its statistical properties through extensive Monte Carlo simulations. The methodology is further illustrated with real lifetime data, highlighting the interpretability and effectiveness of CRTE as a probabilistic entropy measure for reliability modeling. The results demonstrate that CRTE provides a versatile and computationally feasible approach for bounding analysis, characterization, and inference in systems where uncertainty plays a critical role, aligning with current advances in entropy-based uncertainty quantification.