# Information-Theoretic Reliability Analysis of Consecutive r-out-of-n:G Systems via Residual Extropy

## TL;DR

This paper introduces a new method for analyzing system reliability using residual extropy, an information-theoretic measure, to better understand uncertainty in multicomponent systems.

## Contribution

The paper introduces novel bounds and preservation properties for residual extropy in consecutive r-out-of-n:G systems, along with a maximum likelihood estimator for exponential lifetimes.

## Key findings

- Residual extropy provides effective reliability analysis for systems where closed-form solutions are unavailable.
- Preservation properties under stochastic orders and aging notions are established for system uncertainty modeling.
- A maximum likelihood estimator for residual extropy is proposed and validated with simulations and real data.

## Abstract

This paper develops an information-theoretic reliability inference framework for consecutive r-out-of-n:G systems by employing the concept of residual extropy, a dual measure to entropy. Explicit analytical representations are established in tractable cases, while novel bounds are derived for more complex lifetime models, providing effective tools when closed-form expressions are unavailable. Preservation properties under classical stochastic orders and aging notions are examined, together with monotonicity and characterization results that offer deeper insights into system uncertainty. A conditional formulation, in which all components are assumed operational at a given time, is also investigated, yielding new theoretical findings. From an inferential perspective, we propose a maximum likelihood estimator of residual extropy under exponential lifetimes, supported by simulation studies and real-world reliability data. These contributions highlight residual extropy as a powerful information-theoretic tool for modeling, estimation, and decision-making in multicomponent reliability systems, thereby aligning with the objectives of statistical inference through entropy-like measures.