Taking Advantage of Separable Limit States in Sampling Procedures

Abstract

Sampling procedures are commonly used to estimate probability of failure in reliabilitybased structural design. For estimating very low probabilities the number of required samples can be high, and the present paper suggests that this number can be reduced when the limit state (or failure criterion) is expressed as the difference of two functions of independent sets of random variables (e.g., capacity minus response). For this case of separable limit states, the sampling may be performed in two stages. First the cumulative distribution function (CDF) of one of the function created by sampling one set of random variables, and then the probability of failure is obtained by sampling the other set of variables using the CDF constructed in the first phase. The paper first considers simple Monte Carlo sampling, then incorporates tail-modeling for constructing the CDF. A simple example of two uniformly distributed variables is used for illustrating the method, and a beam problem is used to demonstrate its usefulness. Nomenclature