An attempt is made to assess the rate at which failures occur within a group of similar structures, or structural components, when each structure is subjected to the same set of applied loads. The structures are similar in every respect except for small inherent differences in strength from one structure to another. On infrequent occasions the applied loads may be so intense as to destroy the weaker members of the group. For the problem in which the structural strengths are distributed within the group in a “normal” fashion, and when the frequency of severe loads diminishes exponentially, it is found that the rate at which failures occur within the group of structures is governed by two simple non-dimensional parameters. Numerical values of these parameters are studied more fully.