VARIANCE REDUCTION BY TRUNCATED MULTIMODAL IMPORTANCE SAMPLING

This paper presents an importance sampling method for system reliability analyses of structures with failure domains defined by linear or appropriately linearized surfaces. Truncated multimodal simulation as a new technique is suggested. It provides an advantage of locating all samples in the failure domain and thus increasing computation efficiency. The variance of the estimator is evaluated by an analytically derived upper bound. It is compared with that of the conventional Monte Carlo method by a variance change factor for conservative estimation of the increase in accuracy and efficiency. The upper bound of variance can be used for a priori determination of the required sample size, given an acceptable maximum error associated with a confidence level. Various application examples of both series and parallel systems are included for illustration.