In this paper the two widely used methods, Tang and Melchers'* method and Gollwitzer and Rackwitz's method, for evaluating a multi-normal distribution function are firstly compared. It is observed that the accuracy of the two methods was at a similar level, there was no significant difference in the results. An extended use of Tang and Melchers' method are then suggested in the context of structural system reliability analysis. Combining with bounds techniques, the intermediate values in Tang and Melchers* method are used in a discarding process during searching for significant failure modes so that the failure paths with very low failure probability would not be included in the calculation of system reliability. This technique can improve the efficiency in structural system reliability analysis.
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