{
  "abstract": "A large family of regulated release decisions accepts a production lot if and only if the pair (sample mean, sample standard deviation) of $n$ units falls in a fixed plane region. Content uniformity (USP <905>), capability release, variables sampling and percent-within-limits highway acceptance all take this form. The acceptance probability under a hypothesized unit-level law is not, so far as we are aware, evaluated exactly in current practice: for a general parent the joint finite-$n$ law of $(\\bar X,s)$ is a constrained $n$-fold integral (Craig 1932 at $n=3,4$; Springer 1953 at general $n$) which admits no elementary reduction. Yet that probability is fixed by the law of the additive pair $(T_1,T_2)=(\\sum_{i=1}^{n} X_i,\\sum_{i=1}^{n} X_i^2)$, whose characteristic function is the $n$-th power of a one-observation transform. One two-dimensional Fourier inversion therefore delivers it for an arbitrary smooth parent - exactly, as an identity, and numerically on a grid whose dimension stays two whatever $n$ is - a deterministic alternative to both the simulation and the Normality assumption. The identity is exact; what we evaluate is a finite-grid inversion of it, whose error we report per example rather than bound. At $n=3$ the Uniform parent yields the joint law of $(\\bar X,s)$, the acceptance probability and the capability law in closed form; we derive these, use them as the anchor of a validation ladder, and then work three rules end to end under non-normal parents at their prescribed sample sizes ($n=10$-$30$). Against the exact answer the Normal-theory incumbent errs by enough to change the risk a plan is designed against, and errs in both directions along the operating curve, so no single constant corrects it. In general only the full distribution suffices.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.21577",
  "author_total": 1,
  "authors": [
    {
      "name": "Remus Osan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d249rpfs7292t.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.21577",
  "fulltext_url": null,
  "id": "d249rpfs7292t",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.21577",
  "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",
      "stat.ME"
    ],
    [
      "openalex",
      "1804|Advanced Statistical Process Monitoring"
    ]
  ],
  "openalex": "W7213915059",
  "pdf_url": "https://arxiv.org/pdf/2609.21577",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d249rpfs7292t.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:12Z",
      "native_id": "2609.21577",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.21577"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "Phasing out Monte Carlo: exact acceptance probabilities for mean-spread release rules",
  "title_text": "Phasing out Monte Carlo: exact acceptance probabilities for mean-spread release rules",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:12Z",
  "url": "https://research.draconitic.com/paper/d249rpfs7292t",
  "venue": "arXiv",
  "versions": []
}