Abstract
Probability theory methods for calculating approximations of first excursion and fatigue failure probabilities in the case of arbitrary differentiable stochastic process models are discussed. The discrete random variable of uperossings of a level by a differentiable stochastic process is used to consider the functionals of stochastic processes which are of practical interest in reliability analysis.
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Beljajev, Y.K. Distribution of the maximum of a random field and its application to problems of reliability theory (in Russ.), Isv. Akad. Nauk SSSR, Techn. Kib. 2 (1970) 44–56
Bolotin, V.V. Wahrscheinlichkeitsmethoden zur Berechnung von Konstruktionen, Verlag für Bauwesen, Berlin 1981
Cramer, H., Leadbetter, M.R. Stationary and related processes, Wiley, New York 1969
Engelund, S., Rackwitz, R., Lange, C. Approximations of first-passage times for differentiable processes, publication in Prob. Eng. Mech. 1994
Friedrich, H., Lange, C. Niveauüberschreitungswahrscheinlichkeiten bei stochastisch belasteten mechanischen Systemen, Report R-Mech-04/81, Berlin 1981, 230 pp.
Hasofer, A.M. The mean number of maxima above high levels in Gaussian random fields, Journ. of Appl. Prob. 13 (1976) 377–379
Heinrich, W., Hennig, K. Zufallsschwingungen mechanischer Systeme, Akademieverlag, Berlin 1977
Hennig, K., Friedrich, H., Heinrich, W., Mauersberger, G. Studie zur Arbeit auf ausgewählten Gebieten der Sicherheit und Zuverlässigkeit im Maschinenbau und Bauwesen, AdW, ZIMM, Berlin 1979
Lange, C. First excursion probabilities for low threshold levels by differentiable processes, Proc. of the 4th WG 7.5 IFIP conference on reliability and optimization of structural systems 1991, Munich, Springer 1992, pp 261–275
Lange, C., Friedrich, H. Zuverlässigkeitsuntersuchungen für mechanische Systeme auf der Grundlage zufälliger Felder, FMC-Series No.43, Chemnitz 1989, 90 pp
Miles, J.W. On structural fatigue under random loading, Journal Aero. Sci. 21 (1954) 753–762
Renger, A., Mohr, H. Eine Studie über experimentielle Forschungen auf dem Gebiet der Zufallsschwingungen mechanischer Systeme, Forschungsbericht der HfR Festkörpermechanik, Berlin 1979
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1995 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Lange, C. (1995). Functionals of Stochastic Processes and Random Fields in Reliability Analysis. In: Rackwitz, R., Augusti, G., Borri, A. (eds) Reliability and Optimization of Structural Systems. IFIP — The International Federation for Information Processing. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-34866-7_17
Download citation
DOI: https://doi.org/10.1007/978-0-387-34866-7_17
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4757-6397-3
Online ISBN: 978-0-387-34866-7
eBook Packages: Springer Book Archive