Unpublished
Stefan Bedbur, Johann Köhne, Fabian Mies
2025
2025
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APA
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Bedbur, S., Köhne, J., & Mies, F. (2025). Simultaneous Nonparametric Confidence Bands for Load-Sharing Systems.
Chicago/Turabian
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Bedbur, Stefan, Johann Köhne, and Fabian Mies. “Simultaneous Nonparametric Confidence Bands for Load-Sharing Systems,” 2025.
MLA
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Bedbur, Stefan, et al. Simultaneous Nonparametric Confidence Bands for Load-Sharing Systems. 2025.
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@unpublished{stefan2025a,
title = {Simultaneous Nonparametric Confidence Bands for Load-Sharing Systems},
year = {2025},
author = {Bedbur, Stefan and Köhne, Johann and Mies, Fabian}
}
In reliability, sequential order statistics serve as a flexible model for ordered failure
times, for instance, of components of some load-sharing system, where the resid-
ual lifetime distribution of the components is allowed to change after each com-
ponent failure. In a proportional hazard rate setting, the model consists of some
baseline distribution function and several model parameters describing successive
adjustments of the hazard rates of the operating components. This work provides
nonparametric confidence bands for the baseline distribution function, where the
model parameters may be known or unknown. In case of known model parameters,
we show how to construct exact confidence bands based on Kolmogorov-Smirnov
type statistics, which are distribution-free with respect to the baseline distribu-
tion. If the model parameters are unknown, finite sample inference turns out to
be infeasible, and asymptotic confidence bands for the baseline distribution func-
tion are derived. As a technical tool, we extend the existing asymptotic theory of
semiparametric estimators based on the profile-likelihood approach.
Keywords: Generalized order statistics; sequential order statistics; proportional
hazard rate; k-out-of-n system; nonparametric inference; confidence band
times, for instance, of components of some load-sharing system, where the resid-
ual lifetime distribution of the components is allowed to change after each com-
ponent failure. In a proportional hazard rate setting, the model consists of some
baseline distribution function and several model parameters describing successive
adjustments of the hazard rates of the operating components. This work provides
nonparametric confidence bands for the baseline distribution function, where the
model parameters may be known or unknown. In case of known model parameters,
we show how to construct exact confidence bands based on Kolmogorov-Smirnov
type statistics, which are distribution-free with respect to the baseline distribu-
tion. If the model parameters are unknown, finite sample inference turns out to
be infeasible, and asymptotic confidence bands for the baseline distribution func-
tion are derived. As a technical tool, we extend the existing asymptotic theory of
semiparametric estimators based on the profile-likelihood approach.
Keywords: Generalized order statistics; sequential order statistics; proportional
hazard rate; k-out-of-n system; nonparametric inference; confidence band