Efficiency and accuracy of Monte Carlo (importance) sampling

Monte Carlo Analysis is often regarded as the most simple and accurate reliability method. Besides it is the most transparent method. The only problem is the accuracy in correlation with the efficiency. Monte Carlo gets less efficient or less accurate when very low probabilities are to be computed in combination with limit state functions that use a lot of computational time. The efficiency of Monte Carlo simulations can be improved by means of importance sampling. This however requires pre-information on the state function that may affect the accuracy. Several Monte Carlo simulation methods are compared with respect to efficiency and accuracy: Crude Monte Carlo, Importance Sampling, Increased Variance Sampling, and Directional Sampling. Furthermore a comparison is made with a special kind of response surface method.