{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T15:56:14Z","timestamp":1759334174794,"version":"build-2065373602"},"reference-count":40,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T00:00:00Z","timestamp":1759017600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deanship of Scientific Research at King Saud University for funding this work through the Waed Program","award":["W25-63"],"award-info":[{"award-number":["W25-63"]}]}],"content-domain":{"domain":["www.mdpi.com"],"crossmark-restriction":true},"short-container-title":["Entropy"],"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.3390\/e27101020","type":"journal-article","created":{"date-parts":[[2025,9,29]],"date-time":"2025-09-29T08:00:32Z","timestamp":1759132832000},"page":"1020","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Entropy-Based Uncertainty Quantification in Linear Consecutive k-out-of-n:G Systems via Cumulative Residual Tsallis Entropy"],"prefix":"10.3390","volume":"27","author":[{"given":"Boshra","family":"Alarfaj","sequence":"first","affiliation":[{"name":"Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6363-1246","authenticated-orcid":false,"given":"Mohamed","family":"Kayid","sequence":"additional","affiliation":[{"name":"Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3779-5209","authenticated-orcid":false,"given":"Mashael A.","family":"Alshehri","sequence":"additional","affiliation":[{"name":"Department of Quantitative Analysis, College of Business Administration, King Saud University, Riyadh 11362, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,9,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1016\/0951-8320(93)90017-S","article-title":"Linear consecutive-k-out-of-n: F system reliability with common-mode forced outages","volume":"41","author":"Jung","year":"1993","journal-title":"Reliab. Eng. Syst. 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