{
  "abstract": "This paper develops a 2-out-of-6:G repairable system with state-dependent preventive maintenance (PM) for functioning components. The 2-out-of-6:G configuration is adopted as a representative nontrivial case of the general k-out-of-n:G system, since it retains the essential features of component redundancy, multiple failure states, and a critical pre-failure state while remaining analytically tractable. When only two components remain functioning, PM is activated with probability β to reduce the risk of an immediate system breakdown caused by an additional failure. Using the supplementary variable method, the model is formulated as an abstract Cauchy problem. Within the C0-semigroup framework, the main operator is proved to generate a positive contraction C0-semigroup, ensuring the existence and uniqueness of a positive solution. By combining Greiner’s boundary perturbation method with spectral analysis, the strong convergence of the solution to the steady-state solution is established. Numerical simulations further illustrate the theoretical results and demonstrate the influence of preventive maintenance on system reliability performance.",
  "abstract_shown": true,
  "affiliations": [
    "College of Mathematics and Systems Science, Xinjiang University, Urumqi 830046, China"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Ruijuan Li"
    },
    {
      "affs": [
        0
      ],
      "name": "Ehmet Kasim",
      "orcid": "0000-0001-6680-7999"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e83c0eb9yf33v.bib",
  "cited_by": 0,
  "doi": "10.3390/axioms15100727",
  "fulltext_url": null,
  "id": "e83c0eb9yf33v",
  "issns": [
    "2075-1680"
  ],
  "landing_url": "https://www.mdpi.com/2075-1680/15/10/727",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2213|Reliability and Maintenance Optimization"
    ]
  ],
  "openalex": "W7214904331",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": "MDPI AG",
  "ris": "https://research.draconitic.com/paper/e83c0eb9yf33v.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:30Z",
      "native_id": "10.3390/axioms15100727",
      "source": "crossref",
      "url": "https://www.mdpi.com/2075-1680/15/10/727"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "journal-openalex:F26",
      "subfield": "general"
    }
  ],
  "title": "Dynamic Analysis of a 2-out-of-6:G Repairable System with Preventive Maintenance",
  "title_text": "Dynamic Analysis of a 2-out-of-6:G Repairable System with Preventive Maintenance",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:30Z",
  "url": "https://research.draconitic.com/paper/e83c0eb9yf33v",
  "venue": "Axioms",
  "versions": []
}