2014
DOI: 10.1016/j.ress.2014.07.025
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Relevance of control theory to design and maintenance problems in time-variant reliability: The case of stochastic viability

Abstract: The goal of this paper is twofold: 1) to show that time-variant reliability and a branch of control theory called stochastic viability address similar problems with different points of view, and 2) to demonstrate the relevance of concepts and methods from stochastic viability in reliability problems. On the one hand, reliability aims at evaluating the probability of failure of a system subjected to uncertainty and stochasticity. On the other hand, viability aims at maintaining a controlled dynamical system wit… Show more

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Cited by 15 publications
(6 citation statements)
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“…Reliability theory was initially developed in the field of mechanical engineering and was broadly diffused in other domains, especially in environmental management. , In these applications, the system, subject to uncertainties, belongs either to a failure domain or to a safety domain. The purposes of the reliability methods are (1) to approximate the limit decision state surface ( G ( X ) = 0) that separates the failure domain ( G ( X ) < 0) and the reliability domain ( G ( X ) > 0); (2) to deduce (from the approximation of the limit decision state surface) the probability that the system belongs to the failure domain.…”
Section: Methodsmentioning
confidence: 99%
“…Reliability theory was initially developed in the field of mechanical engineering and was broadly diffused in other domains, especially in environmental management. , In these applications, the system, subject to uncertainties, belongs either to a failure domain or to a safety domain. The purposes of the reliability methods are (1) to approximate the limit decision state surface ( G ( X ) = 0) that separates the failure domain ( G ( X ) < 0) and the reliability domain ( G ( X ) > 0); (2) to deduce (from the approximation of the limit decision state surface) the probability that the system belongs to the failure domain.…”
Section: Methodsmentioning
confidence: 99%
“…They are generally suitable for emergency or real-time applications, but not necessarily for monitoring applications, as environment monitoring, pollution control or agricultural field, where the frequency of collection is specific at different moments and it depends on the evolution stage of a plant for example [9]. For this kind of application (monitoring), a new approach is defined and used in literature: the theory of viability [9], [15]- [18]. It has been applied for the first time in sensors network fields by Kone et al in [19].…”
Section: Related Workmentioning
confidence: 99%
“…However, they may come at very different costs and levels of complexity. For example, early warning 10.1029/2018EF000852 approaches (based on variance, for instance) involve efficient measures against uncertainties and avoiding tipping points (Dakos et al, 2008(Dakos et al, , 2012Lenton et al, 2008;Scheffer et al, 2009) while backward techniques enable managers to take into account the dynamics of the system (Brias et al, 2015;Rougé et al, 2013Rougé et al, , 2014Rougé et al, , 2015. Here we highlight the impact of various adaptive management strategies on system collapse.…”
Section: Stylized Adaptive Strategiesmentioning
confidence: 99%