{
  "abstract": "For a series system with heterogeneous proportional reversed-hazard-rate components coupled through an Archimedean survival copula, we determine the exact admissible range of power-mean indices for a universal homogeneous stochastic upper envelope. The characterization reduces to the convexity of a single transformed inverse-generator function; under complete monotonicity, this condition is necessary already from the two-component case. The resulting critical power index is sharp: every order at or above the threshold is universally valid, whereas every smaller order fails for a suitable two-component perturbation. Under independence, the threshold is zero, making the geometric mean optimal. Within the Clayton family, negative critical indices occur, with an exact threshold −a for 0 < a ≤ 1 and a threshold strictly below −1 for a > 1. Under additional generator concavity and monotonicity conditions, the same construction yields the stronger reversed hazard rate order, with exact thresholds for independence and for the Clayton model at a = 1. To address dependence uncertainty, we also derive a sharp classwise robust threshold and show that a negative Clayton-optimal order need not remain valid under an alternative Archimedean family. A deterministic sensitivity study confirms the computational scalability of the construction across system size, heterogeneity, dependence strength, and baseline choice.",
  "abstract_shown": true,
  "affiliations": [
    "Department of Quantitative Analysis, College of Business Administration, King Saud University, Riyadh 11362, Saudi Arabia",
    "Department of Statistics and Operations Research, College of Science, King Saud University, Riyadh 11451, Saudi Arabia"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Mashael A. Alshehri",
      "orcid": "0000-0003-3779-5209"
    },
    {
      "affs": [
        1
      ],
      "name": "Maha Al Mutairi",
      "orcid": "0009-0007-8351-8524"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/33szve8066xt1.bib",
  "cited_by": 0,
  "doi": "10.3390/math14193603",
  "fulltext_url": null,
  "id": "33szve8066xt1",
  "issns": [
    "2227-7390"
  ],
  "landing_url": "https://www.mdpi.com/2227-7390/14/19/3603",
  "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": "W7220461773",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-04",
  "publisher": "MDPI AG",
  "ris": "https://research.draconitic.com/paper/33szve8066xt1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:29Z",
      "native_id": "10.3390/math14193603",
      "source": "crossref",
      "url": "https://www.mdpi.com/2227-7390/14/19/3603"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "issn:2227-7390",
      "subfield": "general"
    }
  ],
  "title": "Exact Critical Power Indices for Heterogeneous PRHR Series Systems Under Archimedean Dependence",
  "title_text": "Exact Critical Power Indices for Heterogeneous PRHR Series Systems Under Archimedean Dependence",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:29Z",
  "url": "https://research.draconitic.com/paper/33szve8066xt1",
  "venue": "Mathematics",
  "versions": []
}