Extropy analysis in consecutive r-out-of-n:G systems with applications in reliability and exponentiality testing

Faten Alrewely; Mohamed Kayid; Faten Alrewely; Mohamed Kayid

doi:10.3934/math.2025276

AIMS Mathematics

2025, Volume 10, Issue 3: 6040-6068. doi: 10.3934/math.2025276

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Research article

Extropy analysis in consecutive r-out-of-n:G systems with applications in reliability and exponentiality testing

Faten Alrewely ,
Mohamed Kayid ^,

Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

Received: 05 January 2025 Revised: 28 February 2025 Accepted: 07 March 2025 Published: 18 March 2025
MSC : 62N05, 94A17

This study explores the extropy of consecutive r-out-of-n:G systems, offering a detailed framework for theoretical analysis and practical applications. Exact expressions for system lifetime extropy are derived, with comparative evaluations across diverse lifetime distributions. Theoretical contributions include bounds, characterization results, and insights into the variability of extropy. Practically, a nonparametric extropy estimator is introduced and validated through simulations and image processing applications. A novel test statistic for exponentiality is also proposed, with the critical values computed numerically and the performance assessed against alternative distributions. The results highlight the test's superior efficacy in specific contexts while noting its limitations. This work combines theoretical and practical advances, providing valuable tools for reliability analysis and statistical inference.
- consecutive $ r $-out-of-$ n $:G systems,
- extropy,
- goodness-of-fit test,
- stochastic orders,
- image processing
Citation: Faten Alrewely, Mohamed Kayid. Extropy analysis in consecutive r-out-of-n:G systems with applications in reliability and exponentiality testing[J]. AIMS Mathematics, 2025, 10(3): 6040-6068. doi: 10.3934/math.2025276

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Abstract

This study explores the extropy of consecutive r-out-of-n:G systems, offering a detailed framework for theoretical analysis and practical applications. Exact expressions for system lifetime extropy are derived, with comparative evaluations across diverse lifetime distributions. Theoretical contributions include bounds, characterization results, and insights into the variability of extropy. Practically, a nonparametric extropy estimator is introduced and validated through simulations and image processing applications. A novel test statistic for exponentiality is also proposed, with the critical values computed numerically and the performance assessed against alternative distributions. The results highlight the test's superior efficacy in specific contexts while noting its limitations. This work combines theoretical and practical advances, providing valuable tools for reliability analysis and statistical inference.

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