Reliability inference for semi-Markov models based on multiple trajectories
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.
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BibTeX
@misc{trevezas2026reliability,
title = {{Reliability inference for semi-Markov models based on multiple trajectories}},
author = {Samis Trevezas and Mohamed Hamdaoui and Irene Votsi},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.19058},
eprint = {2609.19058},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.19058},
}
RIS
TY - UNPB
TI - Reliability inference for semi-Markov models based on multiple trajectories
AU - Samis Trevezas
AU - Mohamed Hamdaoui
AU - Irene Votsi
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.19058
UR - https://arxiv.org/abs/2609.19058
AB - 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.
ER -