FAILURE PROBABILITY AND AVERAGE STRENGTH OF DISORDERED-SYSTEMS

Using a new recurrence-relation method, we have calculated the failure probability and average strength of random systems of up to linear dimension L = 5000. We find a deep minimum in the failure probability at an optimal sample size (L0). As the applied stress decreases the depth of this minimum grows exponentially and L0 increases algebraically. At large sample sizes the average strength exhibits a logarithmic size effect, in contrast to recent suggestions of algebraic scaling in related models.