Abstract
In this paper a fitting-adaptive approach to importance sampling is proposed, in which a fitting density function is introduced to calculate the failure probability instead of the importance sampling density function. The importance sampling density function is only used to generate sample points. The histogram is employed as the fitting adaptive density function for it is straightforward and fulfills the purpose. Moreover, if the fitting density function is not satisfactory, adaptive procedure is automatically performed. Several examples are presented to demonstrate the applicability of the proposed approach. It is shown that a significant reduction in variance of the failure probability can be achieved by use of this approach.
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