{
  "abstract": "We prove that, for the pairwise-ordering model with at least three components, adding any run to an order-of-addition orthogonal array gives a $D$-optimal design among all exact designs of the enlarged size, allowing replication. We also establish the corresponding result for foldover designs: adding any reversal pair to a foldover order-of-addition orthogonal array gives a $D$-optimal design within the foldover class at the enlarged size. Both augmentations also minimise the average prediction variance and a covariance-scaled information discrepancy, and maximise the minimum relative efficiency. The key step represents the scaled discrepancy through signed comparisons of triples and derives a sharp integer lower bound; classical spectral inequalities then give the exact-size optima, and signed four-component relative-order counts characterise equality. Complete reversal pairs additionally protect the estimation of pairwise-ordering effects against arbitrary reversal-invariant nuisance means. At the smallest estimable five-component foldover size, exact enumeration identifies five determinant-optimal classes with different prediction and balance properties, and a seven-component example shows that deleting a reversal pair need not be optimal even when it minimises the discrepancy. Constructions through ten components illustrate the attained run sizes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.08793",
  "author_total": 3,
  "authors": [
    {
      "name": "Stelios D. Georgiou"
    },
    {
      "name": "Haralambos Evangelaras"
    },
    {
      "name": "Stella Stylianou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8epb6f2caw1b5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.08793",
  "fulltext_url": null,
  "id": "8epb6f2caw1b5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.08793",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.TH"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.08793",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8epb6f2caw1b5.ris",
  "sources": [
    {
      "first_seen": "2026-11-10T06:21:07Z",
      "native_id": "2611.08793",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.08793"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Exact optimality of augmented order-of-addition designs",
  "title_text": "Exact optimality of augmented order-of-addition designs",
  "type": "preprint",
  "updated_at": "2026-11-10T06:21:13Z",
  "url": "https://research.draconitic.com/paper/8epb6f2caw1b5",
  "venue": "arXiv",
  "versions": []
}