MC_SubSam: Monte Carlo Simulation with Subset-Sampling

In TesiproV: Reliability Analysis Methods for Structural Engineering

Monte Carlo Simulation with Subset-Sampling

Description

MonteCarlo with Subset-Sampling (MC_SubSam) method for the estimation of small failure probabilities in structural reliability analysis.

Subset Simulation is an advanced Monte Carlo technique that expresses a rare failure event as a sequence of intermediate conditional events with higher probabilities.

Failure is defined as g(x) < 0. The intermediate events are g(x) \le q_j with the p0-quantile q_j of the limit-state values of level j. Only the last level uses the failure event g(x) < 0.

The method combines conditional sampling with Markov Chain Monte Carlo (MCMC) techniques to efficiently estimate very small probabilities of failure, which would be computationally expensive to obtain using crude Monte Carlo simulation.

Usage

MC_SubSam(
  lsf,
  lDistr,
  Nsubset = 1e+05,
  p0 = 0.1,
  MaxSubsets = 10,
  Alpha = 0.05,
  variance = "uniform",
  debug.level = 0,
  seed = NULL
)

Arguments

lsf	limit-state function
lDistr	list of basevariables in input space
Nsubset	number of samples in each simulation level
p0	level probability or conditional probability
MaxSubsets	maximum number of simulation levels that are used to terminate the simulation procedure to avoid infinite loop when the target domain cannot be reached
Alpha	Significance level of the confidence interval. The interval covers the probability 1 - Alpha (default 0.05, i.e. 95 percent).
variance	gaussian, uniform
debug.level	If 0 no additional info if 2 high output during calculation
seed	Optional integer value. If specified, sets a fixed seed for reproducible random numbers (useful for testing).

Value

MC_SubSam returns an object containing the following elements:

• beta: Estimated reliability index.

• pf: Estimated probability of failure.

• betaCI: Confidence interval of the reliability index.

• pfCI: Confidence interval of the probability of failure.

• CoV: Coefficient of variation of the estimator.

• NumOfSubsets: Number of simulation levels.

• NumOfEvalLSF_nom: Nominal number of limit-state function evaluations (Markov chains / iterations).

• NumOfEvalLSF_eff: Effective number of limit-state function evaluations.

• runtime: Total runtime of the function.

Author(s)

(C) 2021-2026 K. Nille-Hauf, T. Feiri, M. Ricker, T. Lux – Hochschule Biberach (until 2022), TU Dortmund University - Chair of Structural Concrete (since 2023)

References

Au, S. K., & Beck, J. L. (2001). Estimation of small failure probabilities in high dimensions by subset simulation. Probabilistic Engineering Mechanics, 16(4), 263-277.

Marelli, S., & Sudret, B. (2014). UQLab: A framework for uncertainty quantification in Matlab. In Proceedings of the 2nd International Conference on Vulnerability, Risk Analysis and Management (ICVRAM2014), Liverpool, United Kingdom, 2554-2563.

TesiproV documentation built on Oct. 28, 2026, 5:13 p.m.