Abstract Monte Carlo with Importance Sampling (MCIS) has been used to both evaluate the failure probability and search for the dominant failure modes of the system. Information generated from other schemes such as the First- and Second-Order Reliability Methods, and knowledge of the dominant modes, has been used to construct effective sampling densities to estimate failure probabilities. The implications of this information are discussed. In a system problem, a stratified density was used. Such a density tends to bound the weights and hence not cause the variance of the estimator to diverge. Also, the informationsused implies the knowledge of the unimportant random variables. The lack of this knowledge can lead to bad estimates. The use of the estimated coefficient of variation (COV) of the estimator is discussed. The estimated COV arising from densities contructed with the previously mentioned information tends to be small, i.e., the estimator is accurate. However, the COV can be misleading. In the second application, it is shown easily that MCIS can give erroneous answers.
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