Gamma processes and peaks-over-threshold distributions for time-dependent reliability

In the evaluation of structural reliability, a failure is defined as the event in which stress exceeds a resistance that is liable to deterioration. This paper presents a method to combine the two stochastic processes of deteriorating resistance and fluctuating load for computing the time-dependent...

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Bibliographic Details
Published in:Reliability engineering & system safety 2007-12, Vol.92 (12), p.1651-1658
Main Authors: van Noortwijk, J.M., van der Weide, J.A.M., Kallen, M.J., Pandey, M.D.
Format: Article
Language:English
Subjects:
Applied sciences
Deterioration
Exact sciences and technology
Gamma process
Kac functional equation
Load
Operational research and scientific management
Operational research. Management science
Peaks-over-threshold distribution
Poisson process
Reliability theory. Replacement problems
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Summary:In the evaluation of structural reliability, a failure is defined as the event in which stress exceeds a resistance that is liable to deterioration. This paper presents a method to combine the two stochastic processes of deteriorating resistance and fluctuating load for computing the time-dependent reliability of a structural component. The deterioration process is modelled as a gamma process, which is a stochastic process with independent non-negative increments having a gamma distribution with identical scale parameter. The stochastic process of loads is generated by a Poisson process. The variability of the random loads is modelled by a peaks-over-threshold distribution (such as the generalised Pareto distribution). These stochastic processes of deterioration and load are combined to evaluate the time-dependent reliability.
ISSN:0951-8320
1879-0836
DOI:10.1016/j.ress.2006.11.003