# Reliability Estimation by Advanced Monte Carlo Simulation

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## Abstract

Monte Carlo simulation (MCS) offers a powerful means for evaluating the reliability of a system, due to the modeling flexibility that it offers indifferently of the type and dimension of the problem. The method is based on the repeated sampling of realizations of system configurations, which, however, are seldom of failure so that a large number of realizations must be simulated in order to achieve an acceptable accuracy in the estimated failure probability, with costly large computing times. For this reason, techniques of efficient sampling of system failure realizations are of interest, in order to reduce the computational effort.

In this chapter, the recently developed subset simulation (SS) and line sampling (LS) techniques are considered for improving the MCS efficiency in the estimation of system failure probability. The SS method is founded on the idea that a small failure probability can be expressed as a product of larger conditional probabilities of some intermediate events: with a proper choice of the intermediate events, the conditional probabilities can be made sufficiently large to allow accurate estimation with a small number of samples. The LS method employs lines instead of random points in order to probe the failure domain of interest. An “important direction” is determined, which points towards the failure domain of interest; the high-dimensional reliability problem is then reduced to a number of conditional one-dimensional problems which are solved along the “important direction.”

The two methods are applied on two structural reliability models of literature, i.e., the cracked-plate model and the Paris–Erdogan model for thermal-fatigue crack growth. The efficiency of the proposed techniques is evaluated in comparison to other stochastic simulation methods of literature, i.e., standard MCS, importance sampling, dimensionality reduction, and orthogonal axis.

## Keywords

Failure Probability Line Sampling Limit State Function Markov Chain Monte Carlo Simulation Failure Domain## References

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