{
  "abstract": "This paper investigates the well-posedness (WP) and asymptotic stability of a standby repairable system with partial failure and priority, wherein components in a partial failure state remain unrepaired during system operation. The governing integro-differential equations are reformulated as an abstract Cauchy problem (ACP) on an appropriately chosen Banach space via the introduction of a linear operator. Using C0−semigroup theory together with spectral analysis, we prove that the system operator generates a positive contraction C0−semigroup, thereby guaranteeing the existence of unique time-dependent solution (TDS). Moreover, through a detailed examination of the spectral distribution of the generator on the imaginary axis, we establish the strong convergence of the TDS to its steady-state solution (SSS) as time tends to infinity. Complementing these analytical results, a Monte Carlo simulation (MCS) is performed to track the transient evolution of reliability indices, providing numerical validation of the theoretical predictions. These results offer a theoretical basis for evaluating system reliability and inform maintenance strategies in continuous-production environments.",
  "abstract_shown": true,
  "affiliations": [
    "College of Mathematics and Systems Science, Xinjiang University, Urumqi 830046, China"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Ehmet Kasim",
      "orcid": "0000-0001-6680-7999"
    },
    {
      "affs": [
        0
      ],
      "name": "Rena Eskar",
      "orcid": "0000-0001-7488-7896"
    },
    {
      "affs": [
        0
      ],
      "name": "Taiyong Wang",
      "orcid": "0009-0008-1551-8589"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2z1g17w7mxg87.bib",
  "cited_by": 0,
  "doi": "10.3390/math14203780",
  "fulltext_url": null,
  "id": "2z1g17w7mxg87",
  "issns": [
    "2227-7390"
  ],
  "landing_url": "https://www.mdpi.com/2227-7390/14/20/3780",
  "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": "W7222942097",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-18",
  "publisher": "MDPI AG",
  "ris": "https://research.draconitic.com/paper/2z1g17w7mxg87.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:29Z",
      "native_id": "10.3390/math14203780",
      "source": "crossref",
      "url": "https://www.mdpi.com/2227-7390/14/20/3780"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "issn:2227-7390",
      "subfield": "general"
    }
  ],
  "title": "Well-Posedness and Asymptotic Behavior of the Standby Repairable System with Partial Failure and Priority",
  "title_text": "Well-Posedness and Asymptotic Behavior of the Standby Repairable System with Partial Failure and Priority",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:29Z",
  "url": "https://research.draconitic.com/paper/2z1g17w7mxg87",
  "venue": "Mathematics",
  "versions": []
}