Abstract: Based on the impact vector method, the concept of weights is extended which separates single and double events of a specific multiplicity in a single observation. Moments and variances of multi-failure rates are obtained in terms of the weights by using probability generating functions. The examples show that the same results can be obtained when calculating the moments by the present method and traditional approximate method, while the variances calculated by the traditional approximate method are lower 15% than those calculated by the present method.