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

Area of Science:

• Reliability Engineering
• Information Theory
• Statistical Inference

Background:

• Multicomponent systems are crucial in engineering.
• Assessing system reliability and uncertainty is complex.
• Existing methods may lack comprehensive information-theoretic approaches.

Purpose of the Study:

• To develop an information-theoretic framework for reliability inference in consecutive r-out-of-n:G systems.
• To utilize residual extropy as a key measure for system uncertainty.
• To provide practical tools for reliability analysis and estimation.

Main Methods:

• Employing residual extropy, a dual measure to entropy.
• Deriving explicit analytical representations and novel bounds for system lifetime models.
• Examining preservation properties under stochastic orders and aging notions.
• Investigating a conditional formulation for operational components.
• Proposing a maximum likelihood estimator for residual extropy.

Main Results:

• Established analytical representations and bounds for system reliability.
• Provided insights into system uncertainty through monotonicity and characterization results.
• Developed a conditional formulation yielding new theoretical findings.
• Demonstrated the effectiveness of the proposed estimator via simulations and real data.

Conclusions:

• Residual extropy is a powerful tool for modeling and estimation in reliability systems.
• The developed framework enhances decision-making in multicomponent systems.
• This work aligns statistical inference with information-theoretic measures for reliability.