Risk Measures in Reliability Engineering: Comparison, Duality and Decision-Making
Abstract
In order to guarantee the reliability of industrial systems, statistical studies can be carried out on a variable of interest, Y , or, more precisely, on a risk measure computed based on this variable. This article studies and compares different risk measures, on the one hand, according to their theoretical properties, and, on the other hand, according to their numerical estimation. In particular, a distinction is proposed between risk measures homogeneous to the variable of interest Y (margin, quantile, and superquantile) and risk measures homogeneous to a probability (failure and buffered failure probability). More specifically, a duality between these two categories is developed, showing the equivalence of using a Y -homogeneous risk measure with a dual, homogeneous, [0, 1]-homogeneous risk measure. Finally, a non-asymptotic statistical framework is proposed for decision-making using these risk measures. The latter can be used in practice in the case where the considered risk measures are the probability of failure and the quantile, and is equivalent, under one assumption, to a quantile estimation using the Wilks' method.
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BibTeX
@misc{templeboyer2026risk,
title = {{Risk Measures in Reliability Engineering: Comparison, Duality and Decision-Making}},
author = {Marie Temple-Boyer and Emma Cussenot and Guillaume Perrin and Vincent Chabridon and Julien Pelamatti and Emmanuel Remy and Bertrand Iooss},
howpublished = {HAL},
year = {2026},
month = sep,
url = {https://hal.science/hal-05295409v2},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Risk Measures in Reliability Engineering: Comparison, Duality and Decision-Making
AU - Marie Temple-Boyer
AU - Emma Cussenot
AU - Guillaume Perrin
AU - Vincent Chabridon
AU - Julien Pelamatti
AU - Emmanuel Remy
AU - Bertrand Iooss
PY - 2026
DA - 2026/09/04
PB - HAL
UR - https://hal.science/hal-05295409v2
AB - In order to guarantee the reliability of industrial systems, statistical studies can be carried out on a variable of interest, Y , or, more precisely, on a risk measure computed based on this variable. This article studies and compares different risk measures, on the one hand, according to their theoretical properties, and, on the other hand, according to their numerical estimation. In particular, a distinction is proposed between risk measures homogeneous to the variable of interest Y (margin, quantile, and superquantile) and risk measures homogeneous to a probability (failure and buffered failure probability). More specifically, a duality between these two categories is developed, showing the equivalence of using a Y -homogeneous risk measure with a dual, homogeneous, [0, 1]-homogeneous risk measure. Finally, a non-asymptotic statistical framework is proposed for decision-making using these risk measures. The latter can be used in practice in the case where the considered risk measures are the probability of failure and the quantile, and is equivalent, under one assumption, to a quantile estimation using the Wilks' method.
ER -