{
  "abstract": "We develop nonparametric inference for reliability indicators of discrete-time semi-Markov systems from independent trajectories observed over a common fixed horizon. Augmenting the physical state by the backward recurrence time yields a finite coupled Markov representation on the observed age range. We distinguish the resulting age-restricted failure-or-exit time from calendar truncation, since these two finite-horizon quantities coincide only in special cases. The framework covers restricted factorial moments and moment characteristics, calendar-truncated failure-time summaries, and the discrete-time intensity of the hitting time. Under explicit row-exposure conditions, strong consistency and joint asymptotic normality are established for the empirical initial law, the required transition rows and the corresponding plug-in functionals. The Gaussian random-matrix representation gives pointwise and joint covariance formulas, simultaneous confidence envelopes, Wald procedures for linear summaries, and curvature-adjusted Gaussian approximations. Restriction diagnostics and a target-specific horizon-selection rule based on exposure, boundary interaction and nested-horizon stability are developed separately. Numerical experiments assess the inferential formulas and the diagnostics, while a complete-case illustration from the European Group for Blood and Marrow Transplantation reports calendar-truncated failure-time summaries and finite-dimensional hitting intensities.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.19058",
  "author_total": 3,
  "authors": [
    {
      "name": "Samis Trevezas"
    },
    {
      "name": "Mohamed Hamdaoui"
    },
    {
      "name": "Irene Votsi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8pkcbq6yz0kp2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.19058",
  "fulltext_url": null,
  "id": "8pkcbq6yz0kp2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.19058",
  "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/2609.19058",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8pkcbq6yz0kp2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:04Z",
      "native_id": "2609.19058",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.19058"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Reliability inference for semi-Markov models based on multiple trajectories",
  "title_text": "Reliability inference for semi-Markov models based on multiple trajectories",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:10Z",
  "url": "https://research.draconitic.com/paper/8pkcbq6yz0kp2",
  "venue": "arXiv",
  "versions": []
}