An efficient method for the estimation of structural reliability intervals with random sets, dependence modeling and uncertain inputs

By Diego A. Alvarez, J. Hurtado. 2014

46 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/f025413989f0c92907877519b66af272018919f1

How researchers see this paper

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In Civil and Structural Engineering

1. Diego A. Alvarez
2. J. Hurtado
3. Felipe Uribe
4. Marcos A. Valdebenito
5. Gerhart I. Schuëller

In Statistics and Probability

1. Diego A. Alvarez
2. J. Hurtado
3. Felipe Uribe
4. Marcos A. Valdebenito
5. Gerhart I. Schuëller

Citations in the corpus

• Estimation of the lower and upper bounds on the probability of failure using subset simulation and random set theory (2018, methodology): “…relations apply, I [Γ(α) ⊆ F] = IFLP [α] = I [ g(α) ≤ 0] (8a) I [Γ(α) ∩ F , ∅] = IFUP [α] = I [ g(α) ≤ 0 ] (8b) and therefore, the bounds on the probability of failure in equations (7) can be written as Alvarez and Hurtado (2014): Pf = ∫ Ω I [ g(α) ≤ 0] dC(α) (9a) Pf = ∫ Ω I [ g(α) ≤ 0 ] dC(α).”