Concepedia

Non-intrusive stochastic analysis with parameterized imprecise probability models: II. Reliability and rare events analysis

Pengfei Wei, Jingwen Song, Sifeng Bi, Matteo Broggi, Michael Beer, Zhenzhou Lü, Zhufeng Yue

Mechanical Systems and Signal Processing · 2019 · 76 citations · 40 references

Concepts

EngineeringMathematicsProbability TheoryStochastic ProcessesUncertainty QuantificationInferential StatisticsMarkov ProcessesProbabilistic ModelingReliability ModelingStatistical InferenceStochastic Systems ModelingImprecise ProbabilitiesProbabilistic Reliability ModelingRare Event InferenceRare Event ModelingRare-event SimulationStochastic Process AnalysisStochastic Process Reliability Models

References

40

Monte Carlo sampling methods using Markov chains and their applications

W. Keith Hastings · Biometrika · 1970 · 15.2K citations

Natural Sciences, Mathematics, Probability Theory +16

Exact and Invariant Second-Moment Code Format

A. M. Hasofer, Niels C. Lind · Journal of the Engineering Mechanics Division · 1974 · 3.1K citations

Computing, Computational Engineering, Measurement Invariance +10

Remarks on a Multivariate Transformation

Murray Rosenblatt · The Annals of Mathematical Statistics · 1952 · 2.9K citations · Full text

Natural Sciences, Biostatistics, Measurement Invariance +4

Estimation of small failure probabilities in high dimensions by subset simulation

Siu‐Kui Au, James L. Beck · Probabilistic Engineering Mechanics · 2001 · 2.4K citations

Business, Biostatistics, Probability Theory +15

AK-MCS: An active learning reliability method combining Kriging and Monte Carlo Simulation

Benjamin Echard, Nicolas Gayton, Maurice Lemaire · Structural Safety · 2011 · 1.9K citations

Computing, Computational Engineering, Machine Learning +13